The effects of deregulation of opening hours on competition in the retail market

  1

The Effects of Deregulation of Opening Hours on

Competition in the Retail Market

Faculty of Economics and Business

MSc thesis, Economics, Industrial Organisation, Regulation & Competition Policy track Amsterdam, August 2014

Author: T. Douma, BSc Student number: 5619149

2 Table of contents

1. Introduction 3

2. Theoretical Model 5

3. Results 8

3.1 The case of a Small and a Large retailer: regulated 8 3.2 The case of a Small and a Large retailer: deregulated 9

3.2.1 Both open all days of the week 10

3.2.2 Asymmetric opening hours 10

3.2.3 Monopoly 11 3.3 Equilibrium 12 3.4 Welfare comparison 16 4. Conclusions 18 References 21 Appendix 22 A Proof of propositions 22 B Underlying calculations B1 Welfare 32 B2 Utility 36 B3 Prices 36

3

1.

Introduction

The deregulation of shopping hours has been part of a heated debate in the Netherlands since the 1990s. For instance, last year shops in Tilburg were in the news because they were threatened to be fined by the local government as they broke the local regulations by opening their shops every Sunday. Apparently shops prefer longer opening hours, though there are also valid arguments for regulation.

The current policy in the Netherlands for regulation of shopping hours is the

following. In general shops are allowed to be opened from 6 am to 10 pm during weekdays and Saturdays, and may open 12 Sundays a year excluding banking holidays. There are exceptions, for instance when a local government appoints the local area as a “touristic area” the shops are always allowed to be opened during Sundays. The decision on regulation of shopping hours is made by local governments, and mostly based on the level of tourism in the area or local political reasons.

Lately there has been a market trend towards deregulation of opening hours due to consumer demand (EC 2000). Originally regulation on shopping hours is based on religious motivation, or as a protection for employees to prevent them from working on Sundays or evening hours against their will (OECD 2001). Liberalization of opening hours can lead to higher welfare and employment, due to better use of economies of scale, which would benefit larger shops and consumers (OECD 2001).

Previous research on the effects of liberalization of regulation on shopping hours in the Netherlands is done by CPB (1995), EIM (1995), and B&A group (2006). They base their findings on surveys and simulations of previous cases in comparable European countries. From previous research on other European countries it is shown that it is likely that the opening hours of shops will increase when there is liberalization of shopping hours (Gradus 1996, CPB 1995). Though firms will not increase shopping hours to its maximum capacity and it is also shown that large firms will increase shopping hours more than smaller firms (CPB 1995).

The choice of shopping hours has various effects on the profitability of shops. Longer opening hours will lead to higher costs of labor. Longer opening hours can also lead to better cost allocation, which can lead to higher capital productivity due to fixed capital. It could also lead to a better dispersion of sales because there will be less peaks in sales throughout the week (CPB 1995). Small shops have higher cost for fixed labor and lower cost for fixed capital than larger shops. Therefore it is less profitable for small shops to extend their opening

4 hours (CPB 1995).

In this thesis, I will research the effects of deregulation of opening hours on competition in the retail market. My research questions are: Does deregulation lead to a change in shopping hours and entry or exit from the market? Does deregulation lead to a change in prices? And what are the effects on total and consumer welfare? In the research I am going to focus on the competition between two retail shops, one large and one small shop, under the assumption that the costs of additional opening hours on Sundays for a small shop are higher than for large shops. My model is based on the Hotelling (1929) model and

analyses two different time periods (weekdays and Sunday). In the case of deregulation shops can be opened on Sunday. To study the effect of deregulation of opening hours, I will

compare equilibrium outcomes in a regulated and in a deregulated market. In particular, I will analyse the welfare effects of deregulation considering three scenarios: both shops will open on Sunday, asymmetric competition where only one shops opens on Sunday, and the

monopoly case where one of the firms leaves the market.

My research is related to several other theoretical papers. Rouwendal and Rietveld (1999) developed an economic model to provide insight into the determinants of opening hours and prices within the retail industry. They focus on two extreme cases of competition, a monopoly case and a case of many shops where there are no differences in the cost function. They find that the number of firms is essential in the analysis of the effect of regulation on shopping hours in the retail sector. They also find that a monopolist chooses opening hours that are too short, in the sense that welfare could be higher when shopping hours would be extended. In the market with many firms they find that opening hours are shorter than optimal for total welfare. Inderst and Irmen (2005) study the effect of deregulation on shopping hours when there are asymmetric opening times and asymmetric cost structures between firms. They focus their research on competition in imperfectly competitive markets, and focus on the analysis of prices and profits. While Inderst and Irmen (2005) decided not to study the effects on welfare, Rouwendal and Rietveld (1999) find that with identical firms, restrictions on opening hours will never improve welfare. However, with heterogeneous firms there are situations in which restrictions on opening hours increase welfare. If firms are heterogeneous, restrictions on opening hours may result in an increase in welfare if the shop with the largest market share is induced to extend its opening hours as a result of the

increased demand originating from the tightened opening hours of the other shops

(Rouwendal & Rietveld, 1999). They find that retailers with a cost advantage are more likely to open around the clock. When associating cost advantage with shops size this would mean

5 large shops are more likely to extend their opening hours than small shops. Compared to the existing literature on this topic, Rouwendal and Rietveld (1999) and Inderst and Irmen (2005), I added two new aspects to the analysis: deregulation taking into account the extra costs for opening on Sunday and entry or exit from the market.

The setup of this thesis is as follows. The second chapter introduces my model. In chapter 3, I will analyse the welfare effects of deregulation. Chapter 4 concludes the thesis.

2.

Theoretical Model

In this chapter, I will outline my model. Consider a setting with two shops, one large and one small. The model consists of two dimensions. The first dimension is time in which shops open and close and consumers choose to shop. Time is modelled by differentiating between

weekdays and Sundays. The other dimension is space, where the location of the two retail shops is taken into account according to the Hotelling (1929) model.

In particular, I use a variant of the Hotelling (1929) spatial model that is visualized in figure 1. There is a continuum of representative consumers who live along a line segment of length 1. Without loss of generality I normalize total population to 2. Where one consumer prefers to shop on weekdays and the other consumer prefers to shop on Sundays. The two representative consumers live along a line segment of length 1. Each consumer is identified by her address ∈[0,1], which indicates the distance between the consumer’s location and the left end of the segment. From the viewpoint of the retailers, x is uniformly distributed on [0,1]. The linear model is represented as showed in Figure 1.

  6 Weekdays A B 0 x 11 Sundays A B 0 x 1

Figure 1. Representation of the structure of the Model.  

    Two retail shops (A and B) are located at the extremes of the line. Retailer A is at the left side of the line, and Retailer B is located at the right side. The retailers’ choice of opening time consists of two options, given the choice of the other retailer. The game runs as follows. The game consists of three stages. In the first stage of the game both firms independently choose to enter or exit the market. Without loss of generality, I assume that retailer A enters if only one retailer is active in the market in equilibrium. In the second stage both retailers independently decide on their opening times (if active in the market). The choices of opening times are to open the shop only during weekdays and to open the shop during weekdays and Sunday. In the third stage they independently set their price given the consumer demand and the opening times of the other retailer.

In the case of regulation on shopping hours I make the assumption that travel costs are higher than the fixed costs for the retailers ( and )1. Profit for the retailer is denoted by where and are the retailer’s price and demand

respectively and denotes retailer i's fixed costs.    Additionally I make the assumption that minimum profit is zero for the shops to open their store.  

1 For underlying derivations the reader is referred to Appendix A1.

t1≥ FB t1≥ FA i

πi= piDi− Fi s− F

i pi Di

7     Extending shopping hours on Sunday will lead to higher operating costs (CPB, 1995). These cost are denoted for retailer , where i∈{A, B} . These costs can be used to identify the difference in the effect of Sunday opening hours on a smaller versus a larger retailer. Retailer A is larger than retailer B. Therefore retailer A has lower operating costs on Sundays than retailer B, i.e. FB

S _{≥ F} A

S_{. Furthermore for simplicity, retailers are considered to have} identical marginal costs per unit sold, and these cost are normalized to zero.  

    Each consumer demands the same basket of shopping goods, which therefore can be considered as one unit of a composite good, and is willing to pay at most per unit, where

is assumed to be ‘large’ in the sense that all consumers buy the good. If the consumer buys on a weekday, the Utility on weekdays is UW

(d, p)= V − p − t1d and on Sundays UW

(d, p)= V − p − t1d− t2. If the consumer buys on a Sunday, the utility on Sundays is US(d, p)= V − p − t1d− t2 and on weekdays U

S

(d, p)= V − p − t1d . Where are travel costs which consumers incur for each unit of distance d they have to travel to the shop. Costs are waiting costs that consumers incur when they buy the product  in  the  period  they  least  

prefer.  Variable    is  the  price  of  the  product  and    is  distance  to  the  shop.  For simplicity I assume that travel costs and waiting costs are strictly positive, i.e. .

In my equilibrium analysis, I will examine the following four scenarios: • Regulation

• Deregulation

- Both retailers are open all days

- Retailer A is open all days, retailer B only opens on weekdays - Retailer B leaves the market

In the situation of government regulation on Sunday openings, retailers must keep their shops closed on Sundays. In the case of a deregulated market there are three options for the market situation. The first option is that both shops are open on Sundays. The second option is the asymmetric case, where one shop is open on Sunday and the other shop is closed. The

asymmetric case has two scenarios, the first scenario is that only one shop is open on Sunday and the other shop is only open during weekdays. The second scenario is that one shop is open on Sunday’s and the other shop is closed entirely. The latter is the monopoly case.

F_is i V V t1 t2 p d t1,t2 > 0

  8 In the next section, I will solve for the subgame perfect Nash equilibrium using backward induction:

• First, consumer demand is determined as a function of the retailers’ prices and opening hours.

• Second, given the demand and opening hours, the retailers will set their optimal prices.

• Third, the retailers’ decisions on their opening hours are determined.

3.

Results

In this chapter the results of the paper are presented. The objective of the chapter is to

research the effect of deregulation on opening hours. In this chapter I study market equilibria under the assumption that each firm maximises its own profits.

In section 3.1 the Subgame Perfect Nash Equilibrium (SPNE) will be found for the case of regulation. In this section the consumer’s choice between retailers is determined by shop location and opening times. In particular, I will derive the SPNE for the four different cases; the case of Regulation, where both retailers open all days of the week, asymmetric competition and the Monopoly case. When there is asymmetry in opening times, if one shop is closed and the other is not, this will lead to other consumer choices than if both shops are open at the same time. This consumer demand determines the prices of the firms.

In section 3.2 the SPNEs of the scenarios of deregulation are presented. To understand the behaviour of the firms under the set conditions the best responses of the firms are being studied in section 3.3. In section 3.3 there will be an analysis of the best responses for the retailers given the different scenarios. Entry and exit will be determined first. In the section 3.4 is a study of the effects on consumer and total welfare.

3.1 Regulation

In the situation of government regulation, retailers are restricted to close their shops on Sunday. When both retailer A and B are closed on Sunday the marginal consumer incurs waiting costs for the time the consumer has to wait for shopping until the shops open on weekdays.

9 conditions. For the marginal consumer location on Sunday the restrictions is

pA+ xt1+ t2 = pB+ (1− x)t1+ t2and for the marginal consumer location during weekdays the restriction is . The marginal consumer is indifferent between buying their products from retailer A and retailer B. Therefore by symmetry; the price for both shops, including waiting and travel cost is the same. Since the waiting costs for retailer A are as high as for retailer B these costs offset each other in the model. Demand for retailer A and B is given by the following demand equations:

,

Proposition 1. Suppose that in the SPNE both retailers cater to consumers on weekdays. Both

charge a price p= t1 and profits are π_i = t1− Fi where i∈{A, B} .

2

In the equilibrium both retailers are open during weekdays if opening hours are regulated in the sense that retailers are not allowed to open their shop on Sunday. Therefore there will be no exit from the market under Regulation.

Proposition 2. In equilibrium, both shops are open under Regulation.

This proposition relies on the assumption that travel costs are at least as high as the fixed costs of the shop. The price is equal to the travel costs, therefore the price has to be equal to or higher than the fixed costs of the shop. Therefore, in Equilibrium both retailers will enter the market.

3.2 Deregulated market

In a deregulated market there is no government regulation on the opening times of the retail shops. This increases the possible opening times with respect to the case of regulation. In the case of a deregulated market there are three options for the market situation. The first option is that both shops are open on Sundays. The second option is the asymmetric case, where one shop is open all days and the other shop is closed on Sunday. The asymmetric case has two scenarios, first that only one shop is open all days of the week and the other shop is only open                                                                                                                

2 _{For underlying calculations the reader is referred to Appendix A1.} pA+ xt1= pB+ (1− x)t1

DA( pA, pB)=

pB− pA

10 during weekdays. Second scenario is that one shop is open on all days and the other shop is closed entirely, this is the Monopoly case.

Without loss of generality, in the asymmetric case, I assume that retailer A will always be open, and retailer B will be closed on Sunday or all days of the week, in the monopoly case.

3.2.1 Both retailers are open all days of the week

If both shops are opened all days of the week the retailers occur extra costs for opening on a Sunday . When both shops are open all days, consumers do not incur waiting costs on Sunday because they could shop at both retailers at any time. The marginal consumer location therefore must satisfy the following conditions: on Sunday and

on weekdays. The marginal consumer is indifferent between buying their products from retailer A and retailer B. This gives for retailer A and retailer B the same demand function as in the case of Regulation:

;

Proposition 3. Suppose that in the SPNE both retailers cater to consumers all days of the

week. Both charge a price p= t1 and profit is π_i= t1− Fi− Fi

S _{where i∈{A, B} .}3

As can been seen from the equations above, the firm with the lowest fixed costs will make the highest profit.

3.2.2 Asymmetric Competition

In the case of asymmetric opening hours either retailer A or retailer B is open on all days while the other retailer is closed on Sunday. If for instance customers want to shop on Sunday but retailer B is closed on Sunday and retailer A is open, they are forced to choose whether to shop at the retailer A or to wait for retailer B to open and incur waiting cost . This decision depends on their distance to the shop and the price of the product at the different retailers. If retailer A is open on Sunday and retailer B is closed the location for the marginal consumer is given by on Sunday. On the left hand side there are no                                                                                                                

3 _{For underlying calculations the reader is referred to Appendix A2.} FS pA+ yt1= pB+ (1− y)t1 pA+ xt1= pB+ (1− x)t1 DA( pA, pB)= pB− pA t1 +1 DB( pA, pB)= 2 − DA( pA, pB) t2 pA+ yt1= pB+ (1− y)t1+ t2

11 waiting cost for shopping at retailer A. On the right-hand side there are waiting costs for shopping at retailer B because the shop is closed on Sunday. Consumers have the choice to either shop at retailer A without waiting costs or wait until Monday for retailer B to open and incur costs of waiting. For weekdays there are no waiting cost to incur because both shops are open: . Demand for retailer A and retailer B is given by respectively:

and .

Proposition 4. In the SPNE retailer A caters to consumers all days and retailer B only on

weekdays. Retailer A charges price pA = t1+ 1

6t2 and retailer B charges price pB = t1− 1 6t2. Profits are πA = t1+ 1 3t2+ 1 36 t2 2 t1 − FA− FA

S _{for retailer A and π}

B = t1− 1 3t2+ 1 36 t2 2 t1 − FB for retailer B. 4

In case of asymmetric opening hours, prices for retailer A increase with 1/6 times the waiting costs while prices for retailer B decrease with 1/6 times the waiting costs. Consumers can therefore choose to pay a higher price and shop on Sunday at retailer A, or pay a lower price by shopping at retailer B during the week and incur waiting costs on Sunday. When analysing these prices in the utility function on Sundays (equation 2), it can be shown that utility on Sunday when shopping on Sunday is higher than shopping during the week. Therefore utility for shopping at retailer A is higher than utility for shopping at retailer B on Sundays.5 Vice versa, utility during the week is higher for retailer B since the price for retailer B is lower.

3.2.3 Monopoly Case

In case of a monopoly only one retailer will be in the market. Without loss of generality, I assume that only retailer A enters the market. Because I made the assumption that V is large enough for all customers to buy a product I can determine that in the monopoly case retailer A serves the whole market. That is the situation where all consumers are willing to buy from retailer A. If retailer A serves the whole market the monopolist charges , which is the price that the consumer living farthest away is willing to pay minus the costs he has to                                                                                                                

4 _{For underlying calculations the reader is referred to Appendix A3.} 5 _{For underlying derivations the reader is referred to Appendix C.}

t2 p_A+ xt₁= p_B+ (1− x)t₁ DA( pA, pB)= 2 pB− 2 pA+ t2 2t₁ +1 DB( pA,pB)= 2 − DA( pA,pB) pA m= V − t 1

12 incur to travel denoted by . In the model used in this research these travel costs are therefore equal to . Since retailer A serves the whole market demand is equal to the whole market: . Under monopoly the profit for retailer A is: _.

Proposition 5. In the SPNE, if retailer B is closed, retailer A caters to consumers all days and

charges price p= V − t1. Profit for retailer A is . Retailer A caters to consumers only during weekdays if t2 < FA

S_{. Profit for retailer A in this situation is} πA = (V − t1− t2)− FA.

3.3 Equilibrium  

In the previous sections there was an overview of all possible outcomes in different scenarios of competition. To establish the equilibrium outcome of the game I use backward induction. For simplicity four possible scenarios are being reviewed:

• Both retailer are always open

• Retailer B is only open on weekdays and retailer A is always open

• Retailer B leaves the market and retailer A is only open during weekdays • Retailer B leaves the market and retailer  A is always open

t1 t1= t1*1 DA = 1 πA = pADA− FA S− F A πA = V − t

(

)

  13 Table 1. Overview of SPNE outcomes per scenario

Case Regulation Both open

Sunday Asymmetric: A always, B week Monopoly Firm A Firm A Price p_A = t1 p_A = t1 pA= t1+ 1 6t2 p_A = V − t1 Profit πA = t1− FA πA = t1− FA− FA S π A= t1+ 1 3t2+ 1 36 t2 2 t1 − FA− FA S π_A= V − t₁− F_B− F_BS Firm B Price p_B = t1 p_B = t1 pB= t1− 1 6t2 p_B= 0 Profit πB = t1− FB πB= t1− FB− FB S _π B= t1− 1 3t2+ 1 36 t₂2 t1 − FB πB= 0

Analysing the prices under the different scenarios I find that prices under regulation are equal to prices under deregulation when both shops are always open. When there is asymmetric competition in the case of deregulation prices for retailer A are higher than under regulation and prices for retailer B are lower. In the case of a Monopoly it can be shown that the price of retailer A is higher than the case of regulation and when both shops are always open when

V> 2t1.6

By constructing the profits given the four scenarios, the best responses of the retailers can be analysed as shown in Table 2. Whether the retailers choose to open their shop only during weekdays or also on Sundays depends on their fixed costs for opening on Sundays Fi

S

with respect to waiting and travel-costs. I will now study the optimal choice of retailer B, given that the prices will be adapted in a profit maximising way taking into account all possible scenarios of opening hours.

                                                                                                                6 _{For calculations see Appendix E.}

  14 Table 2. Profits for firm A and firm B conditional on opening hours

Retailer A Re ta il er B Opening

times Weekdays All Days

Closed 0 , V− t1− FA 0 , V− t₁− F_A− F_AS Weekdays _t 1− FB , t1− FA t1− 1 3t2+ 1 36 t2 2 t1 − FB , t1+ 1 3t2+ 1 36 t2 2 t1 − FA− FA S All days t1+ 1 3t2+ 1 36 t2 2 t₁ − FB− FB S_{, t} 1− 1 3t2+ 1 36 t2 2 t₁ − FA t1− FB− FB S _{, t} 1− FA− FA S

The best response for retailer B can be determined by analysing the profits in different scenarios. Retailer B chooses to open only during weekdays when retailer A chooses to open on weekdays if FB S _{is relatively large:}1 3t2+ 1 36 t2 2 t1 < FB S_{. If F} B

S _{is relatively small so that} 1 3t2+ 1 36 t2 2 t1 > FB

S_{, then retailer  B chooses to open its shop all days of the week. If retailer A} chooses to open all days of the week then retailer B chooses to open on weekdays if

1 3t2− 1 36 t2 2 t1 < FB

S_{. Retailers B chooses to open all days when} 1 3t2− 1 36 t2 2 t1 > FB S_.

Determining the choice of Entry or Exit for retailer B, the following situations are analysed. First is the situation that if retailer A is opened only during weekdays, both the profit for opening all days of the week and only during weekdays are below zero. This is the case when fixed costs is higher than the travel costs, FB > t1,  and FB + FB

S _{> t} 1+ 1 3t2+ 1 36 t2 2 t1 .     Second is the situation where retailer A is opened all days of the week and both the case of

15 opening on weekdays and opening all days of the week gives a lower profit than when the shop is closed. This is the case when fixed costs are higher than the travel costs,   FB+ FB

S _{> t} 1 and   FB+ FB S _{> t} 1− 1 3t2+ 1 36 t2 2 t1

.    As can been seen from the equations above, when the fixed costs of opening on Sundays is relatively high with respect to travel and waiting costs, retailer B is more likely to close its shop entirely.

Retailer A chooses to open only during weekdays, under the condition that retailer B chooses to open on weekdays if FA

S _{is relatively large, so that}1 3t2+ 1 36 t2 2 t1 < FA S_{. If F} B S _is

relatively small, so that 1 3t2+ 1 36 t2 2 t1 > FA

S _{then retailer A chooses to open its shop all days of} the week. When retailer B chooses to open all days of the week, retailer A will choose to also open all days of the week if 1

3t2− 1 36 t2 2 t1 < FA

S_{and to open only during weekdays if} 1 3t2− 1 36 t2 2 t1 > FA S_.    

Proposition 6. In the SPNE, both retailers are open all days of the week when

1 3t2− 1 36 t2 2 t1 > Fi S_{. If}1 3t2− 1 36 t2 2 t1 < Fi S and 1 3t2+ 1 36 t2 2 t1 > Fi S

one retailer is open all days of the week and the other is open only during weekdays. In this case retailer B closes its shop when

F_B+ F_BS _{> t} 1 and FB+ FB S _{> t} 1− 1 3t2+ 1 36 t2 2 t1

. Both retailers are open only during weekdays when 1 3t2+ 1 36 t₂2 t1 < Fi

S_{and retailer B closes its shop when}

FB > t1, andFB+ FB S > t 1+ 1 3t2+ 1 36 t₂2 t1 . When retailer B is closed, retailer A chooses to open on weekdays when FA

S _{> 0 .} 7

This shows that parameters exists for which in equilibrium one retailer will enter the market and the other one will exit.

  16 3.4 Welfare comparison

In this section the impact of the four scenarios on total welfare and consumer surplus is determined. To calculate the welfare, first I determine the location of the indifferent consumer, given prices for retailer A and B under the different scenarios. Consumer surplus during the week is calculated by taking the sum of the Utility of the consumers shopping at retailer A and retailer B. For Example: in the case of Regulation the consumer surplus during weekdays is determined by the following equation:

CSweekdays = (V − pA− t1x)dx 0 !x

∫

∫

Which shows that consumer surplus on weekdays is the sum of the consumer surplus when shopping at retailer A and the consumer surplus when shopping at retailer B on weekdays. The consumer surplus when the shops are open all days is equal to the sum of the Utility of the consumers shopping at retailer A when opened all days and the Utility of the consumers shopping at retailer B when opened all days of the week. For example in the case of

Regulation the consumer surplus on Sunday is determined by the following equation:

CSsunday = (V − pA− t1x− t2)dx+ 0 !x

∫

∫

The total welfare is equal to the sum of the consumer surplus during the week, the consumer surplus on Sunday and the profit of the retailers: TW = CSweek+ CSsunday+πA+πB

In Table 3. the welfare in the four scenarios will be presented according to the previous set up.

The loss or gain in welfare in the case of Regulation compared to the case when both retailers are always open is equal to the difference between the fixed costs of opening on Sundays and the waiting costs. As can been seen in the Table 3, if waiting costs on Sunday are larger than the fixed costs for both retailers to keep the shop open on Sunday then total welfare in the case of deregulation is higher than total welfare in the case that both retailers are open all days. That is when . When the fixed costs of opening on Sundays is higher than the waiting costs, the welfare under regulation is higher than the welfare when both retailers are open all days. An interesting finding is that consumer welfare in the case when both retailers are always open is higher than in the case of regulation.

!x

t2 = FA S_{+ F}

B S

  17 Table 3. Consumer Surplus and Total Welfare in Equilibrium.8

Case Consumer Surplus Total Welfare

Both only open during weekdays CS= 2V −5 2t1− t2 TW = 2V − 1 2t1− t2− FA− FB Both Open on Sunday CS= 2V −5 2t1 TW = 2V − 1 2t1− FA− FB− FA S_{− F} B S Firm A open, Firm B closed on Sunday CS= 2V −1 2t2− 1 12 t2 2 t1 TW = 2V + 2t1− 1 2t2− 1 36 t2 2 t1 − FB− FA− FA S Monopoly Firm A CS= 3 4t1 TW = V − 1 4t1− FA− FA S

For all other scenarios, the results are less unambiguous. In order to make firm conclusions, some of the parameters should be estimated empirically. Given these estimates the degrees of freedom in the equations are reduced, which would make it possible to deduct more concrete conclusions. I suggest an empirical study on these parameters for further research.

Proposition 7. Suppose 1 3t2− 1 36 t2 2 t1 > Fi

S_{,  thus  retailers  are  open  all  days  of  the  week,  then}

deregulation increases consumer welfare. Deregulation reduces total welfare if and only if t₂< FA

S _{+ F} B

S_.9

As shown by Proposition 7, consumer welfare under regulation is strictly lower than

consumer welfare under deregulation when both shops are always open. When fixed costs for opening on Sunday are higher than the waiting costs, deregulation reduces total welfare. Therefore if both shops are always open this will increase total welfare as long as total fixed costs for opening on Sunday is lower than the waiting costs.

                                                                                                                8 _{For calculations see Appendix B.}

18 Proposition 8. Suppose 1 3t2− 1 36 t2 2 t1 < Fi S_and  1 3t2+ 1 36 t2 2 t1 > Fi

S _{, in that case one  retailer  is}  

open  all  days  of  the  week  and  the  other  is  open  only  during  weekdays..    Then deregulation decreases consumer welfare if and only if 2t1+ t2−

1 36 t2 2 t1 <   0 . If and only if 5 2t1+ 1 2t2− 1 36 t2 2 t₁ < FA S

, deregulation reduces total welfare.  

Proposition 8 implies if waiting costs are high such that 2t1+ t2< 1 36

t2 2

t₁ , deregulation could decrease consumer welfare. Vice versa if the inequality holds the other way, deregulation strictly increases consumer welfare. Deregulation reduces total welfare if FA

S _{is relatively} high. Proposition 9. Suppose 1 3t2+ 1 36 t2 2 t₁ < Fi S_{and   F}

B > t1,  in that case only one shop chooses to open its store. Then 13

4 t1+ t2− 2V < 0 deregulation decreases consumer welfare. Vice versa if the inequality holds the other way, deregulation increases consumer welfare. If,

1

4t1+ t2−V  <   FA S _{− F}

B, deregulation reduces total welfare. Vice versa if the inequality holds the other way, deregulation increases welfare.

When deregulation causes exit from the market, this decreases consumer welfare if V is relatively high. Additionally, total welfare decreases if fixed costs are relatively high.

4.

Conclusions

In this thesis I researched the influence of deregulation of opening hours on two retail shops, for which one retailer is relatively larger than the other retailer. Under the assumption that fixed costs for opening on Sunday are relatively lower for a large retailer, the larger retailer is more likely to open the shop all days of the week than the small retailer. This coincides with findings of previous research such as CPB (1995), Inderst and Irmen (2005) and Gradus (1996) that large retailers are more likely to open for more hours in the case of deregulation. This is because the choice of opening hours depends on the fixed costs of opening on Sunday

19 relative to the travel and waiting costs. If fixed costs for opening on Sunday are relatively low, the retailer chooses to stay open all days. On the other hand if fixed costs for opening on Sunday are relatively high the retailer chooses to open only on weekdays.

Moreover, if the fixed cost of opening on Sundays is relatively high with respect to travel and waiting costs a retailer is more likely to close its shop entirely. Again taken into account that these costs are higher for a small retailer than for a large retailer, the small retailer is more likely to close its shop.

Analysing prices and profit it is shown that a small retailer will make less profit in the case of deregulation and will sooner make the decision to close its shop. In the case of

asymmetric competition prices for the larger retailer will be higher than under regulation, while prices for the smaller shops are lower. When both retailers are open all days the large retailer will make a higher profit than the small retailer. Because the firm with the lowest fixed costs will make the highest profit, under the assumptions made on the fixed costs. When both retailers are always open, prices under regulation are equal to prices under deregulation. In the case of a monopoly it can be shown that the price of the monopolist is higher than in the case of regulation when both retailers are always open if the maximum costs the consumer is willing to pay is two times higher than the travel costs. On Sundays consumers prefer to pay a higher price and shop on Sundays at the large retailer rather than incur waiting costs and shop only during weekdays, though the price for the small retailer is lower.

The loss or gain in welfare in the case of regulation compared to the case when both shops are always open is equal to the difference between the fixed costs of opening on Sundays and the waiting costs. Consumer welfare in the case when both shops are always open is higher than in the case of regulation. For all other scenarios, the results are

ambiguous. On the demand side the parameters for waiting costs and travel costs and the value that consumers are willing to pay (V ) have to be estimated to make more concrete conclusions on the subject. On the supply side information on parameters for the prices of both retailers and the fixed costs and fixed costs for opening on Sundays is needed. It would also be interesting to empirically research whether small shops exit the market after

deregulation and if consumer welfare decreases after deregulation.

In my research, I made various assumptions to simplify the analysis. I considered only the case of one small and one large retailer on one line segment, for four different types of competition given a set number of competitors and where all retailers sell the same product. I suggest further research on the topic in a different setting, such as the scenario with many retailers or retailers who have a differentiated product portfolio. Also I did not incorporate the

20 influence of consumer preferences for different companies and shopping on Sunday with respect to shopping during weekdays, for further research this would be a useful addition to the model. Furthermore I used the Hotelling model. It has to be taken in to account that the results of this paper depend on the model that is used (Rouwendal & Rietveld 1999). This issue deserves further investigation of different models used on this research subject.

  21 References

B&A Groep. 2006. Evaluatie Winkeltijdenwet. (Evaluation Law on Shoppinghours). Ministry of Economic Affairs. The Hague

CPB 1995. Economische effecten van liberalisering van winkeltijden in Nederland. (The economic effects of liberalised shop opening hours in the Netherlands). Working Paper, No. 74, The Hague.

EIM/Centrum voor Retail Research (1995), Verruiming Winkelsluitingswet, plussen en minnen, zakelijk bekeken, uitgevoerd in opdracht MKB-Nederland

Gradus, R., 1996. The economic effects of extending opening hours. Journal of Economics, Vol. 64, pp. 247–263

Hotelling, H., 1929. Stability in competition. Economic Journal. Vol. 39, pp 41–57.

Inderst R. and A. Irmen. 2005. Shopping hours and price competition. European Economic Review. Vol 49. pp 1105-1124.

OECD. 2000. Assessing barriers to trade in services: retail trade services. TD/TC/WP(99)41/FINAL, OECD, Paris.

Rouwendal J. and P. Rietveld. 1999. Prices and opening hours in the retail sector: welfare effects of restrictions on opening hours. Environment and Planning A. Vol 31. pp. 2003-2016.

22 Appendix:

Appendix A: Proofs of propositions

A1 Regulation

Proposition 1. Suppose that in the SPNE both retailers cater to consumers on weekdays. Both

charge a price and profits are where i∈{A, B} .

Proof of Proposition 1.

By assumption, all consumers always buy. So, a retailer’s demand depends on the fraction of consumers that travel to its shop. Let us first consider the marginal consumer, i.e., the

consumer who is indifferent between travelling to retailer A and retailer B. Regardless of the preferred shopping time, the location x of the marginal consumer follows from

As a consequence, demand for A and B is given by

respectively. Retailer A chooses pA to maximize profit: p= t1 πi = t1− Fi pA+ xt1= pB+ (1− x)t1 2xt1= pB− pA+ t1 x= pB− pA+ t1 2t1 DA( pA,pB)= x + y DA( pA,pB)= p_B− p_A+ t₁ 2t1 + pB− pA+ t1 2t1 = 2( pB− pA+ t1) 2t1 = pB− pA+ t1 t1 D_B( p_A,p_B)= 2 − D_A( p_A,p_B) DB( pA,pB)= 2 − pB− pA+ t1 t₁ πA = pADA− FA πA = pA pB− pA+ t1 t1 ⎛ ⎝⎜ ⎞ ⎠⎟− FA

23 Maximizing gives:

By symmetry we may assume pA = pB. Therefore,

and

As a consequence, the profit for retailer A equals:

so that retailer A enters if Similarly, retailer B enters if

Because by assumption, , both retailers A and B will enter the market.

A2 Both open on all days.

Proposition 3. Suppose that in the SPNE both retailers cater to consumers all days of the

week. Both charge a price and profit is where i∈{A, B} .

Proof of Proposition 3.

By assumption, all consumers always buy. So, a retailer’s demand depends on the fraction of consumers that travel to its shop. Let us first consider the marginal consumer, i.e., the consumer who is indifferent between travelling to retailer A and retailer B. Regardless of the preferred shopping time, the location x of the marginal consumer follows from

As a consequence, demand for A and B is given by dπA dpA = pB t1 −2 pA t1 +t1 t1 = 0 pA = 1 2

(

)

24

respectively retailer A chooses pA to maximize profit:

;

Maximizing gives:

By symmetry we may assume pA = pB. Therefore, and As a consequence, the profit for retailer A equals:

so that retailer A enters if t1≥ FA + FA S

Similarly, retailer B enters if t1≥ FB + FB S So if t1≥ FA + FB + FA

S_{+ F} B

S _{then both retailers A and B will enter the market.} DA( pA,pB)= x + y DA( pA,pB)= pB− pA t1 +1 DB( pA,pB)= 2 − DA( pA,pB) D_B( p_A,p_B)= 1− pB− pA t1 πA = pADA− FA S_{− F} A W π A = pA pB− pA t₁ +1 ⎛ ⎝⎜ ⎞ ⎠⎟− FA S_{− F} A W dπA dp_A = pB t₁ − 2 pA t₁ +1 = 0 pA = 1 2

(

)

(

)

  25 A3 Asymmetric Case (A open on Sunday, B closed on Sunday)

Proposition  4.  In  the  SPNE  retailer  A  caters  to  consumers  all  days  and  retailer  B  only  on   weekdays.  Retailer  A  charges  price    and  retailer  B  charges  price  

.  Profits  are    for  retailer  A  and  

 for  retailer  B.  

Proof of proposition 4.

By assumption, all consumers always buy. So, a retailer’s demand depends on the fraction of consumers that travel to its shop. Let us first consider the marginal consumer, i.e., the consumer who is indifferent between travelling to retailer A and retailer B. Because of the asymmetry in opening times the location x of the marginal consumer on weekdays could be different than on Sundays. The marginal consumer location on Sunday follows from:

and on weekdays

pA+ xt1= pB+ (1− x)t1

As a consequence, demand for A and B is given by

pA = t1+ 1 6t2 pB = t1− 1 6t2 πA = t1+ 1 3t2+ 1 36 t2 2 t1 − FA− FA S πB = t1− 1 3t2+ 1 36 t2 2 t1 − FB pA+ yt1= pB+ (1− y)t1+ t2 2t1y= pB− pA+ t1+ t2 y= pB− pA+ t2 2t1 +1 2 x= pB− pA 2t1 +1 2 DA( pA,pB)= x + y DA( pA, pB)= 2 pB− 2 pA+ t2 2t1 +1 DB( pA,pB)= 2 − DA( pA,pB)

26 respectively retailer A chooses pA to maximize profit:

; Maximizing gives:

Similarly retailer B chooses pB to maximize profit: ;

Maximizing gives:

Therefore, and

As a consequence, the profit for retailer A and retailer B equals:

so that retailer A enters if

DB( pA, pB)= 1− 2 pB− 2 pA+ t2 2t1 πA = pADA− FA S_{− F} A πA= pA 2 pB− 2 pA + t2 2t₁ +1 ⎛ ⎝⎜ ⎞ ⎠⎟− FA S _{− F} A dπA dpA = pB t1 −2 pA t1 + t2 2t1 +1 = 0 pA = 1 2

(

)

(

)

27 Similarly, retailer B enters if

Appendix A4 Best Response.

Proposition 6. In the SPNE, both retailers are open all days of the week when

1 3t2− 1 36 t2 2 t1 > Fi S_{. If}1 3t2− 1 36 t2 2 t1 < Fi S_and 1 3t2+ 1 36 t2 2 t1 > Fi

S_{one retailer is open all days of the}

week and the other is open only during weekdays. In this case retailer B closes its shop when FB+ FB S > t 1 and FB+ FB S > t 1− 1 3t2+ 1 36 t₂2 t1

. Both retailers are open only during weekdays

when 1 3t2+ 1 36 t2 2 t1 < Fi

S_{and retailer B closes its shop when}

F_B > t1, andF_B+ F_BS _{> t} 1+ 1 3t2+ 1 36 t2 2 t1 . When retailer B is closed, retailer A chooses to open on weekdays when FA

S > 0

Proof of proposition 6.

Appendix A4.1 Best response of retailer B when is retailer A is open all days

The best response for retailer B is opening during the week when the profit when opened during the weekdays is higher than when opened on Sunday.

πWEEK >πSUN ≥ 0

Profit when opened on Sunday and during the week is: πSUN = t1− FB− FB S πWEEK = t1− 1 3t2+ 1 36 t2 2 t1 − FB− FB S

The assumptions for opening on Sunday and on weekdays are: t1− 1 3t2+ 1 36 t2 2 t1 > FB

28 t1− 1 3t2+ 1 36 t2 2 t₁ − FB− FB S _{> t} 1− FB− FB S_{if −}1 3t2+ 1 36 t2 2 t₁ > 0 and t1− 1 3t2+ 1 36 t2 2 t1 − FB− FB S _{> t1− F} B− FB S _{≥ 0 if t1}≥ F B+ FB S

Therefore the assumptions are: −1 3t2+ 1 36 t2 2 t₁ > 0 andt1≥ FB+ FB S_.

The best response for retailer B is opening its shop on all days of the week if the profit of retailer B when opened on Sundays is higher than the profit when opened during the week. Where both profits should be higher than zero.

πSUN >πWEEK ≥ 0

Where profit when opened on Sunday and on weekdays is πSUN = t1− FB− FB S _; π WEEK = t1− 1 3t2+ 1 36 t2 2 t1 − FB− FB S

Stating the assumptions to the best response: t1− FB− FB S _{> t} 1− 1 3t2+ 1 36 t2 2 t1 − FB− FB S _if −1 3t2+ 1 36 t2 2 t1 < 0 and t1− FB− FB S _{> t} 1− 1 3t2+ 1 36 t2 2 t1 − FB− FB S _{> 0 if t} 1− 1 3t2+ 1 36 t2 2 t1 ≥ FB+ FB S_.

Therefore the assumptions are: −1 3t2+ 1 36 t2 2 t1 < 0 and t1− 1 3t2+ 1 36 t2 2 t1 ≥ FB+ FB S

Best Response for retailer B is closing its shop during the week and on Sundays if profit for retailer B when opened during the week and on Sundays is smaller than zero.

and

Where profit when opened on Sunday and on weekdays is:

;

Stating the assumptions to the best response: πSUN < 0 πWEEK < 0 πSUN = t1− FB− FB S π WEEK = t1− 1 3t2+ 1 36 t₂2 t1 − FB− FB S

29

if and if

Therefore the assumptions are: and .

Appendix A4.2 Best Response for retailer B If retailer A is only open during weekdays. Best Response is opening during the week if the profit for retailer B when opened during the week is higher than the profit when opened on Sunday. Where both profits should be higher or equal to zero.

Where profit when opened on Sunday and on weekdays is: ;

Stating the assumptions to the best response:

if and

if

Therefore the assumptions are: and .

The best response for retailer B is opening on all days of the week if the profit for retailer B when opened on Sundays is higher than the profit when opened during the week. Where both profits should be higher than zero.

Where profit when opened on Sunday and on weekdays is: ;

Stating the assumptions to the best response:

if and if t1− 1 3t2+ 1 36 t2 2 t1 − FB− FB S _{< 0 t1−}1 3t2+ 1 36 t2 2 t1 < FB+ FB S t1− FB− FB S _{< 0} t1< FB+ FB S t1− 1 3t2+ 1 36 t2 2 t1 < FB+ FB S t1< FB+ FB S πWEEK >πSUN ≥ 0 πSUN = t1+ 1 3t2+ 1 36 t2 2 t₁ − FB− FB S _π WEEK = t1− FB t1− FB > t1+ 1 3t2+ 1 36 t2 2 t1 − FB− FB S 1 3t2+ 1 36 t2 2 t1 − FB S < 0 t₁− F_B > t₁+1 3t2+ 1 36 t2 2 t1 − FB− FB S _{≥ 0} t₁+1 3t2+ 1 36 t2 2 t1 ≥ FB+ FB S 1 3t2+ 1 36 t2 2 t₁ − FB S _{< 0} t1+ 1 3t2+ 1 36 t2 2 t₁ ≥ FB+ FB S πSUN >πWEEK ≥ 0 πSUN = t1+ 1 3t2+ 1 36 t2 2 t1 − FB− FB S π WEEK = t1− FB t1+ 1 3t2+ 1 36 t2 2 t1 − FB− FB S _{> t} 1− FB 1 3t2+ 1 36 t2 2 t1 − FB S _{> 0} t1+ 1 3t2+ 1 36 t₂2 t1 − FB− FB S > t 1− FB ≥ 0 t1≥ FB

30

Therefore the assumptions is: and

The best response for retailer B is closing its shop during the week and on Sundays if profit for retailer B when opened during the week and on Sundays is smaller than zero.

πSUN < 0 and πWEEK < 0

Where profit when opened on Sunday and on weekdays is: πSUN = t1+ 1 3t2+ 1 36 t2 2 t1 − FB− FB S; π WEEK = t1− FB Stating the assumptions to the best response:

t1+ 1 3t2+ 1 36 t₂2 t1 − FB− FB S < 0 if t 1+ 1 3t2+ 1 36 t₂2 t1 < FB+ FB S _{and t} 1− FB < 0 if t1< FB Therefore the assumptions are: t1+

1 3t2+ 1 36 t2 2 t1 < FB+ FB S_{and t1}< F B.

Appendix A4.3 Best Response of retailer A

The best response conditions are symmetric for both retailer A and B except for the case of exit out of the market. This situation is only applicable for retailer B. One additional condition holds for retailer A, which is when retailer B is closed retailer A chooses to open on

weekdays:

The best response for retailer A when retailer B has exit the market: Profit when opened on Sunday and on weekdays is:

πSUN = V − t1− FA− FA S_; π

WEEK = V − t1− FA Stating the assumptions to the best response:

V− t1− FA > V − t1− FA− FA S_{if F}

A S _{> 0}

Therefore if fixed costs for opening on Sunday is more than zero, retailer A chooses to open only on weekdays. 1 3t2+ 1 36 t2 2 t1 − FB S _{> 0} t1≥ FB

31 Appendix A5

Proposition  7.  In  the  SPNE,  if   t2< 0 ,   2t1+ t2− 1 36 t2 2 t1 < 0  and  13 4 t1+ t2− 2V <   0 then  

deregulation  decreases  consumer  welfare.  Vice  versa  if  the  inequaltiy  holds  the  other  way,   deregulation  increases  consumer  welfare.    If   t2< FA

S_{+ F} B S_,  5 2t1+ 1 2t2− 1 36 t2 2 t1 < FA S_and   1 4t1+ t2−V  <   FA S_{− F}

B  deregulation  reduces  total  welfare.  Vice  versa  if  the  inequality  holds   the  other  way,  deregulation  increases  welfare.    

Proof of proposition 7.  

Deregulation  increases  consumer  welfare  if  welfare  under  deregulation  in  the  different   scenarios  is  higher  than  under  regulation.    

If  in  the  SPNE  both  retailers  are  open  all  days  of  the  week,  deregulation  decreases   consumer  welfare  if    CS= 2V −5

2t1− t2>CS= 2V − 5

2t1.  Thus  when t2< 0 .      

If  in  the  SPNE  there  are  assymetric  opening  hours,  deregulation  decreases  consumer   welfare  if    CS= 2V −5 2t1− t2> CS= 2V − 1 2t2− 1 36 t2 2 t1  thus  when   2t1+ t2− 1 36 t2 2 t1 <   0 .        

If  in  the  SPNE  only  one  shop  chooses  to  open  it’  s  shop,  deregulation  decreases   consumer  welfare  ifCS= 2V −5

2t1− t2<  CS= 3

4t1.  Thus  when   13

4 t1+ t2− 2V >   0 .   Deregulation  increases  total  welfare  if  welfare  under  deregulation  in  the  different   scenarios  is  higher  than  under  regulation.    

If  in  the  SPNE  both  retailers  are  open  all  days  of  the  week,  deregulation  total  decreases   welfare  if    2V−1 2t1− t2− FA− FB>2V− 1 2t1− FA− FB− FA S_{− F} B S_{.  Thus  when  t} 2< FA S _{+ F} B S_.    

If  in  the  SPNE  there  are  assymetric  opening  hours,  deregulation  decreases  total  welfare   if    TW = 2V −1 2t1− t2− FA− FB>  TW = 2V + 2t1− 1 2t2− 1 36 t2 2 t1 − FA− FB− FA S_{.  Thus  when} 5 2t1+ 1 2t2− 1 36 t2 2 t1 < FA S_.      

32 If  in  the  SPNE  only  one  shop  chooses  to  open  it’  s  shop,  deregulation  decreases  total   welfare  ifTW = 2V −1 2t1− t2− FA− FB  >  TW = V − 1 4t1− FA− FA S_{.  Thus  when}  1 4t1+ t2−V  <   FA S− F B.  

Appendix B: Additional calculations

B1 Welfare

B1.1 Welfare under Regulation:

The utility of the indifferent consumer located at point _!x per retailer is given by:

U_A(d, p)= V− pA− t1!x,weekdays V− pA− t1!x− t2, sunday ⎧ ⎨ ⎩ ⎫ ⎬ ⎭ UB(d, p)= V− p_A− t₁!x,weekdays V− p_A− t₁!x− t₂, sunday ⎧ ⎨ ⎩ ⎫ ⎬ ⎭

By symmetry we may assume pA = pB. Therefore the location of the indifferent consumer is !x= pB− pA+ t1

2t1

= 1 2.

As a consequence the consumer surplus during weekdays is:

CS_weekdays = (V − p_A− t₁x)dx+ 0 !x

∫

∫

And on Sunday it is:

CSsunday = (V − p₀ A− t1x− t2)dx+ !x

∫

∫

33 = V −5

4t1− t2

So that total consumer surplus is CS= V −5

4t1+V − 5

4t1− t2= 2V − 5 2t1− t2 And total producers surplus is: PS= t1− FA+ t1− FB = 2t1− FA− FB

Therefore total welfare is given by: TW = CS + PS

= 2V −1

2t1− t2− FA− FB

B1.2 Welfare both open on Sunday

The utility of the indifferent consumer located at point _!x per firm is given by:

UA(d, p)= V− pA− t1!x,weekdays V− pA− t1!x,sunday ⎧ ⎨ ⎩ ⎫ ⎬ ⎭ U_B(d, p)= V− pA− t1!x,weekdays V− pA− t1!x,sunday ⎧ ⎨ ⎩ ⎫ ⎬ ⎭

By symmetry we may assume pA = pB. Therefore the location of the indifferent consumer is !x= pB− pA+ t1

2t1

= 1 2.

As a consequence the consumer surplus during weekdays is:

CSweekdays = (V − pA− t1x)dx+ 0 !x

∫

∫

There are no waiting costs on Sunday therefore .

34 So that total consumer surplus is CS= 2 * V −5

4t1 ⎛

⎝⎜ ⎞⎠⎟ =2V−52t1 And total producers surplus is: PS= t1− FA+ t1− FB = 2t1− FA− FB

Total welfare is given by: TW _{= CS + PS}

TW = 2(V − t1− 1 4t1 2 )+πA+πBwhere and . = 2V −1 2t1− FA− FB− FA S _{− F} B S

B1.3 Welfare under Asymmetric Case

The utility of the indifferent consumer located at point _!x per firm is given by:

UA(d, p)= V− p_A− t₁!x,weekdays V− pA− t1!x,sunday ⎧ ⎨ ⎩ ⎫ ⎬ ⎭ UB(d, p)= V− pA− t1!x,weekdays V− pA− t1!x− t2, sunday ⎧ ⎨ ⎩ ⎫ ⎬ ⎭

The prices for firm A and B are respectively: pA = t1+ 1

6t2 and pB = t1− 1

6t2. Therefore the location of the indifferent consumer during weekdays is

!x= pB− pA+ t1 2t1 = − 2 6t2+ t1 2t1 = 1 2− 1 6 t2 t1 . And on Sundays .

Consumer Surplus during weekdays is:

CSweekdays = (V − pA− t1x)dx+ 0 !x

∫

∫

35 And on consumer surplus on Sunday is

CS_sunday = (V − p_A− t₁x)dx+ 0 !x

∫

∫

As a concequence total consumer surplus is CS= V +5 4t1− 1 36 t2 2 t1 +V −5 4t1− 1 2t2+ 1 9 t2 2 t1 = 2V −1 2t2− 1 12 t2 2 t1

Total welfare is given by: TW = CS_week+ CS_sunday+π_A+π_B . TW = 2V + 2t₁−1 2t2− 1 36 t2 2 t1 − FB− FA− FA S

B1.4 Welfare under Monopoly

The utility of the indifferent consumer located at point _{!x& !y per firm is given by}

UA(d, p)= V− pA− t1∈week V− pA− t1∈sunday ⎧ ⎨ ⎩ ⎫ ⎬

⎭ When A is open on Sundays.

Consumer surplus is given by:

CSweekdays = (V − pA− t1x)dx 0 1

∫

36

By symmetry we may assume

Therefore total consumer surplus is CS= 2 * 3 8t1 ⎛

⎝⎜ ⎞⎠⎟ = 43t1

And total welfare is: TW = CS +π_A TW = 3 4t1+V − t1− FA− FA S = V −1 4t1− FA− FA S Appendix B2 Utility

The utility of a consumer on Sundays when shopping on Sundays is USUNDAY S _:V− p − t1 d− t2 V− (t1− 1 6t2)− t1d− t2 = V − t1− 5 6t2− t1d.

The utility of a consumer on Sundays when shopping during weekdays is UWEEK S _:V− p − t1 d− t2 with UWEEK S _:V − p − t1 d V− (t₁−1 6t2)− t1d= V − t1− 1 6t2− t1d As a consequence V− t1− 1 6t2− t1d> V − t1− 5 6t2− t1d if t2 > 0 .

Therefore we may assume .

Appendix B3 Prices  

If   pA > 0  then   pA = V − t1> 0 .  Therefore  V > t1.  The  price  under  regulation  and  when   both  retailers  are  open  is   pA = t1.  The  price  under  Monopoly,   pA = V − t1,  is  higher  than   the  price  under  regulation  if  V− t1> t1  so  that  V > 2t1.

CS_week = CS_sunday

USUNDAY S _{> U}

WEEK S