Question

A perfectly competitive market has a demand curve given by the equation 𝑄 = 2000 − 2𝑃 where Q is the market quantity demanded and P the price per unit. Each firm in the market has the total cost given by 𝑇𝐶 = 1000 + 100𝑞 + 10𝑞' and the marginal cost

𝑀𝐶 = 100 + 20𝑞.

A. If the current market price is $400,

A.1 Calculate the market quantity. Q= 1200

A.2 Find the quantity maximizing profit for each firm. q= 15

A.3 How much profit does each firm earn? Profit = $1250

A.4 Assess whether the situation in A.3 is a long run or a short run. Justify your answer. SR b/c Profit > 0

A.5 Graph your results. OK

B. Suppose that the market is in the long run.

B.1, How much profit will each firm earn and what will be the market price?

II=0, P=$300

B.2 What is the market quantity? Q=1400

B.3 How many firms operate in this market? N =140

B.4 Why is the number of firms in A different from the number of firms in B?

Answer 1

A1.

$Q = 2000 -2p\\ Q = 2000 - 2\times 400\\ Q = 1200$

A2.

Max. profit condition will be 

Price = Marginal cost 

$400 = 100 +20q\\ 300= 20q\\ 30 = 2q\\ 15 = q$

A3.

So, 

Profit = revenue - Total cost 

When P = 400 , Q = 1200 and q = 30

$Profit = 1200\times 400 - (1000 +100\times (30) + 10\times 30)\\ Profit = 480000 - 1000 - 30000 - 300 \\ Profit = 448,700$

A4.

Profit = 448,700

profit >0

A.5

B.

B1.

MR = Avg. Cost =MC 

$Avg . cost = 1000q + 100 + 10q\\ 1000 +100q + 10q^2 = q\times (100 +20q)\\ 1000 + 100q +10q^2 = 100q + 20q^2\\ 1000 = 10q^2\\ q = 10= MR$

B2.

At profit max. condition

$ATC = \frac{1000}{10} + 100 + (10) = P\\ ATC = 210 = P\\ Profit = Revenue - Total \space cost \\ Profit = 210\times 10 - (1000 + 1000 + 10\times 100)\\ Profit = 2100 - 3000\\ Profit = -900$

B3.

Market quantity = 1200

B4.

each firm is making 15 unit each so, 1200/15 = 80

Which means there are "80" firms