Please Write Your Name and ID # as these appear in ROSI Last Name: First Name: 9-Digit ID #:

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1 UNIVERSITY OF TORONTO Faculty of Arts and Sciences August Examinations 2013 ECO 204 Y1Y Duration: 3 hours Total Points: 100 points Examination Aid Allowed: Calculator. Instructions: - This exam consists of 3 questions in 19 pages, single-sided. Please Write Your Name and ID # as these appear in ROSI Last Name: First Name: 9-Digit ID #: YOU CANNOT LEAVE THE ROOM DURING THE LAST 15 MINUTES OF THE EXAM PLEASE REMAIN SEATED UNTIL THE PROCTOR ANNOUNCES THAT YOU CAN LEAVE THE ROOM. KEEP ANSWERS AS BRIEF AS POSSIBLE Question Maximum Possible Points Score Total Score out of 100 = Page 1 of 19

2 QUESTION 1 [50 POINTS] 204 Cupcakes owns and operates shops across the city of Two-ronto ( TwO ) and it is the only company that sells cupcakes in TwO. All stores are identical and each store has ample capacity. (1.1) [3 POINTS] The quantity of cupcakes that can be produced at shop per day is given by the production function: ( ) Here Technological Level of shop ; Number of workers per day at shop ; Number of cash registers per day at shop, and are store-specific parameters. Calculate: the optimal number of workers and cash registers required to process an (exogenously given) target output per day and derive store cost function Show all necessary calculations. Page 2 of 19

3 (1.2) [3 POINTS] [THIS PART IS INDEPENDENT OF ALL PARTS BELOW] True or false: an individual store has constant returns to scale but diseconomies of scale. Show all necessary calculations. Page 3 of 19

4 (1.3) [3 POINTS] [THIS PART IS INDEPENDENT OF ALL PARTS BELOW] Calculate store s marginal cost due to a small increase in the wage rate (i.e. the change in due to a change in ). Show all necessary calculations. Page 4 of 19

5 (1.4) [3 POINTS] Use these parameter values in all parts below: and at each store, a cash register is staffed by two workers. Show that each store s 20 and use this figure in all parts below. Show all necessary calculations and state all assumptions. Page 5 of 19

6 (1.5) [10 POINTS] Let price of a cupcake sold at any store and number of cupcakes sold at store (where ). Suppose that the demand curve facing the 204 Cupcakes chain is: Here are exogenously given parameters. Suppose that all stores act independently and compete with each other as Cournot rivals in a one-shot game. Calculate the profit maximizing output and price at each store; the total quantity of cupcakes sold across all stores; the gross profit at each store; and the gross profit across all stores. Show all necessary calculations and state all assumptions and don t forget to use Page 6 of 19

7 (1.6) [3 POINTS] [EXCEPT FOR PART 1.7 THIS PART IS INDEPENDENT OF ALL OTHER PARTS BELOW] Calculate the for the case when all stores are competing as Cournot rivals. How many stores must there be for the cupcakes market (at store-level) to be characterized as competitive? Do not use this value of in later parts. Show all necessary calculations and don t forget to use Page 7 of 19

8 (1.7) [5 POINTS] Now suppose that each store produces cupcakes as if it s a monopoly. Assuming this is a one-shot game, calculate the profit maximizing output and price at each store; the total quantity sold across all stores; and the gross profit at each store as well as across all stores. Show all necessary calculations and state all assumptions and don t forget to use Page 8 of 19

9 (1.8) [3 POINTS] Consider a hypothetical scenario when there atomistic competition in TwO s cupcake market (i.e. as ). Calculate the profit maximizing output and price at each store as well as the total quantity sold across all stores. Is atomistic competition the same thing as perfect competition? Show all necessary calculations and state all assumptions and don t forget to use Page 9 of 19

10 (1.9) [3 POINTS] Now suppose that the 204 Cupcakes Head Quarters chooses the output of each store to maximize total profits across all stores. Assuming there are stores and that this is a one-shot game, calculate the profit maximizing output and price at each store, the total quantity sold across all stores, and the gross profit at each store as well as across all stores. Show all necessary calculations and state all assumptions and don t forget to use Page 10 of 19

11 (1.10) [10 POINTS] Suppose that the 204 Cupcakes chain has 2 stores and that the price of cupcakes at store is: Recall that Solve for the pure strategies Nash Equilibrium in a simultaneous move one shot game where each store can produce either the Cournot output or the Cartel output. Please enter your answers in the matrices below. Show all necessary calculations and state all assumptions Page 11 of 19

12 (1.11) [4 POINTS] Suppose that the simultaneous move game in part (1.10) is played repeatedly forever. Solve this dynamic game. Show all necessary calculations and state all assumptions. Page 12 of 19

13 QUESTION 2 [30 POINTS] In Project 3 you used the Supermarket Scanner Data Set containing various data on reg and lit varieties of two brands of soda ( X and Y ) sold in seven stores over 52 weeks. The following table contains a portion of the regression output for the supermarket s demand function for Brand Y: the quantity of brand Y was regressed on a constant, the price of brand X, the price of brand Y and a dummy variable which takes the value 1 if there was an in-store promo (i.e. not a price promo) on brand Y (and 0 otherwise): Dependent Variable = Coefficient Constant The following table contains a portion of the regression output for the supermarket s of brand Y was regressed on the quantity of brand Y: function for Brand Y: the Dependent Variable = Coefficient Constant Throughout this question assume that the supermarket has ample capacity and answer all parts up to 4 decimal places. Page 13 of 19

14 (2.1) [5 POINTS] Suppose that currently: and there are no in-store promos on Brand Y. Without deriving the utility function calculate the change in the representative Brand Y customer s utility due to a 1% decrease in across all stores. Show all necessary calculations. Page 14 of 19

15 (2.2) [10 POINTS] Suppose that currently: and there are no in-store promos on Brand Y. Derive the utility function of the representative Brand Y consumer and calculate the change in the representative Brand Y customer s utility due to a 1% decrease in without computing and using the new output. Show all necessary calculations. Note: Due to rounding errors your answer in part (2.2) may be slightly different from the answer in part (2.1) this is OK. Page 15 of 19

16 (2.3) [10 POINTS] Suppose that currently: and there are no in-store promos on Brand Y. Calculate the price, income and substitution effects from a 1% decrease in. Show all necessary calculations. Page 16 of 19

17 (2.4) [5 POINTS] Suppose that currently: and there are no in-store promos on Brand Y. Does the current price of brand Y maximize profits? If not, calculate the optimal uniform price of brand Y. Show all necessary calculations. Page 17 of 19

18 Question 3 [20 POINTS] (3.1) [10 POINTS] Under what conditions will a company with market power charging a uniform price produce at full capacity? Then derive the optimal price rule for the case when the company is producing at full capacity. this question in general form (i.e. without using numerical values). Hint: Solve the PMP: ( ) ( ) And only examine the case when the company produces at full capacity. Show all necessary calculations. Page 18 of 19

19 (3.2) [10 POINTS] Suppose that the solution to this PMP is: ( ) ( ) ( ) You are told that at the optimal solution: What s the most this company should pay per unit of extra capacity? Show all necessary calculations and calculate all numbers to 4 decimal places. Page 19 of 19