Question

Please show work.

There are 40 companies with a weekly TC = 232 + 4q + q2where q is bags of candy. Inverse market demand for candy is P = 76 - 25 QD. (aka 76 minus two-fifths of Q) .

1. what's the equilibrium price of candy market

2. what's the total quantity produced by each of the 40 companies and in total?

3. what's the profit and/or Loss of each company?

4. How many companies can be in the long term equilibrium?

5. How many bags of candy can each company make per week?

6. What's the total output?

7. what is the profit or loss for each company?

Answer 1

Number of firms = 40

TC = 232 + 4q + q2

MC = 4 + 2q

AC = 232/q + 4 + q

Demand is P = 76 - 2QD/5 or P = 76 - 0.4Q

Now each firm has a supply function P = MC

4 + 2q = P or q = (P - 4)/2. For 40 firms market supply is Qs = 40(P - 4)/2 or Qs = 20P - 80. Inverse supply function is P = 4 + 0.05Q

1. At the equilibrium Qs = Qd

4 + 0.05Q = 76 - 0.4Q

Q = 160 and P = 12

Thus, at equilibrium, the price of candy is $12.

2. Total quantity produced by each of the 40 companies is 160/40 = 4 units and in total = 160 units

3.Profit = (P - ATC)*Q or (12 - 232/4 - 4 - 4)*4 = -216

4. In the long run we have AC = MC

4 + 2q = 232/q + 4 + q

q = 232/q

q = 15.23

Price = 4 + 2*15.23 = 34.46

Qd = (76 - 34.46)/0.4 = 104 approx

Then number of firms = 104/15.23 = 6 firms

5. Each firm produces 15.23 candies

6. It is 104 units

7. There is no profit or loss.