Question

Problems and Applications Q11

Suppose that each firm in a competitive industry has the following costs:


Total Cost: TC=50+12q2TC=50+12q2

Marginal Cost: MC=qMC=q

where qq is an individual firm's quantity produced.


The market demand curve for this product is:


Demand QD=140?2PQD=140?2P

where PP is the price and QQ is the total quantity of the good.


Each firm's fixed cost is.


What is each firm's variable cost?


12q212q2


qq


50+12q50+12q


12q12q


Which of the following represents the equation for each firm's average total cost?


50q50q


50+12q50+12q


50q+12q50q+12q


12q12q


Complete the following table by computing the marginal cost and average total cost for qq from 5 to 15.


q Marginal Cost Average Total Cost

(Units) (Dollars) (Dollars)

5 12.50

6 11.33

7 10.64

8 10.25

9 10.06

10 10.00

11 10.05

12 10.17

13 10.35

14 10.57

15 10.83

The average total cost is at its minimum when the quantity each firm produces (qq) equals .


Which of the following represents the equation for each firm's supply curve in the short run?


50?q50?q


12q212q2


qq


120?12q2120?12q2


In the long run, the firm will remain in the market and produce if .


Currently, there are 8 firms in the market.


In the short run, in which the number of firms is fixed, the equilibrium price isand the total quantity produced in the market isunits. Each firm producesunits. (Hint: Total supply in the market equals the number of firms times the quantity supplied by each firm.)


In this equilibrium, each firm makes a profit of. (Note: Enter a negative number if the firm is incurring a loss.)


Firms have an incentive to the market.


In the long run, with free entry and exit, the equilibrium price isand the total quantity produced in the market isunits. There arefirms in the market, with each firm producingunits.

Answer 1

Each firm's variable cost is 12q². The equation for each firm's average total cost is (50 + 12q²) / q. The average total cost is at its minimum when the quantity each firm produces equals 10.

Each firm's variable cost can be calculated by subtracting the fixed cost from the total cost. In this case, the fixed cost is the constant term in the total cost equation, which is 50. So, each firm's variable cost is 12q2.

The equation for each firm's average total cost can be obtained by dividing the total cost by the quantity produced. Therefore, the equation for average total cost is (50 + 12q2) / q.

The average total cost is at its minimum when the marginal cost is equal to the average total cost. From the table provided, we can see that the marginal cost is 10 at quantity 10. Therefore, the average total cost is also 10 at that quantity.