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The market for pies is competitive and has the following demand schedule: Price: $1, 2, 3, 4, 5, 6, 7, 8, 10, 11, 12, 13 Quantity demanded: 1200, 1100, 1000, 900, 800, 700, 600, 500, 400, 300, 200, 100, 0 Each producer in the market has fixed costs of $9 and the following marginal cost: Quantity: 1 pie, 2, 3, 4, 5, 6 Marginal cost: $2, 4, 6, 8, 10, 12 a) Compute each producer's total cost and average total cost for 1 to 6 pies. b) The price of a pie is now $11.How many pies are sold? How many pies does each producer make? How many producers are there? How much profit does each producer earn? c) Is the situation described in part (b) a long-run equilibrium? Why or why not? d) Suppose that in the long run there is free entry and exit. How much profit does each P producers earn in the long-run equilibrium? What is the market price? How many pies does each producer make? How many pies are sold in the market? How many pie producers are operating?

Question

The market for pies is competitive and has the following demand schedule: Price: 1,2,3,4,5,6,7,8,10,11,12,13Quantitydemanded:1200,1100,1000,900,800,700,600,500,400,300,200,100,0Eachproducerinthemarkethasfixedcostsof1, 2, 3, 4, 5, 6, 7, 8, 10, 11, 12, 13 Quantity demanded: 1200, 1100, 1000, 900, 800, 700, 600, 500, 400, 300, 200, 100, 0 Each producer in the market has fixed costs of 9 and the following marginal cost: Quantity: 1 pie, 2, 3, 4, 5, 6 Marginal cost: $2, 4, 6, 8, 10, 12

a) Compute each producer's total cost and average total cost for 1 to 6 pies.

b) The price of a pie is now $11.How many pies are sold? How many pies does each producer make? How many producers are there? How much profit does each producer earn?

c) Is the situation described in part (b) a long-run equilibrium? Why or why not?

d) Suppose that in the long run there is free entry and exit. How much profit does each P producers earn in the long-run equilibrium? What is the market price? How many pies does each producer make? How many pies are sold in the market? How many pie producers are operating?

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Solution 1

a) To compute each producer's total cost and average total cost for 1 to 6 pies, we need to add the fixed costs to the marginal cost for each quantity of pies, and then divide the total cost by the quantity to get the average total cost.

Total Cost (TC) = Fixed Cost (FC) + Marginal Cost (MC) Average Total Cost (ATC) = Total Cost (TC) / Quantity (Q)

For 1 pie: TC = 9+9 + 2 = 11ATC=11 ATC = 11 / 1 = $11

For 2 pies: TC = 9+9 + 4 = 13ATC=13 ATC = 13 / 2 = $6.50

For 3 pies: TC = 9+9 + 6 = 15ATC=15 ATC = 15 / 3 = $5

For 4 pies: TC = 9+9 + 8 = 17ATC=17 ATC = 17 / 4 = $4.25

For 5 pies: TC = 9+9 + 10 = 19ATC=19 ATC = 19 / 5 = $3.80

For 6 pies: TC = 9+9 + 12 = 21ATC=21 ATC = 21 / 6 = $3.50

b) At a price of 11,thequantitydemandedis300pies(fromthedemandschedule).Eachproducerwillproducewherepriceequalsmarginalcost,soatapriceof11, the quantity demanded is 300 pies (from the demand schedule). Each producer will produce where price equals marginal cost, so at a price of 11, each producer will produce 5 pies (since the marginal cost of the 5th pie is 10andthemarginalcostofthe6thpieis10 and the marginal cost of the 6th pie is 12). To find out how many producers there are, we divide the total quantity demanded by the quantity each producer makes, so there are 300/5 = 60 producers. Each producer's profit is total revenue minus total cost, so profit = (115)11 * 5) - 19 = 5555 - 19 = $36.

c) This situation is not a long-run equilibrium because in the long run, firms will enter or exit the market until economic profit is zero. Here, each firm is making a positive profit of $36, so more firms will enter the market.

d) In the long-run equilibrium, each producer earns zero economic profit. The market price will be equal to the minimum average total cost, which is 3.50(when6piesareproduced).Eachproducerwillproduce6pies,sothetotalquantityofpiessoldinthemarketwillbethequantitydemandedatapriceof3.50 (when 6 pies are produced). Each producer will produce 6 pies, so the total quantity of pies sold in the market will be the quantity demanded at a price of 3.50, which is 700 pies (from the demand schedule). The number of pie producers operating will be the total quantity demanded divided by the quantity each producer makes, so there are 700/6 = approximately 117 producers.

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Solution 2

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