Question

Question 3: (22 points)

Suppose you are given the following information about a particular industry:

Q^d= 1600 – 150P                   Market demand

Q^s= 250P                               Short run market Supply

The Firm total cost function consists of a Fixed Cost of 45 and a Variable Cost of (q^2)/5

Assume that all firms are identical in a market that is perfectly competitive.

1. (1 point) Correctly write the Firm total cost function
2. (4 point) Using the demand and supply curves for this industry, find the short run equilibrium price and quantity in the industry.
3. (1 point) Using the total cost function from part (a), derive the marginal cost function for firms in the industry.
4. (4 points) Using your answers to parts (b) and (c), find the quantity produced by each firm in a short run competitive equilibrium. Find the profit or loss of each firm in the short run equilibrium.
5. (2 points) Using your answers to parts (b) and (d), find the total number of firms in a short run equilibrium.
6. (4 points) In the long run, would you expect to see firms enter or exit the industry? Explain your reasoning. What effect will entry or exit have on market equilibrium (in terms of market price and quantity)?
7. (6 points) Given the cost curve above, what is the long run equilibrium price in the industry? What is the number of firms in a long run equilibrium?

Answer 1

a) Firm's total cost function is = fixed cost+variable cost= 45+(q^2)/5

b)To find short run equilibrium, we equate the Q^d and Q^s:

1600 – 150P = 250P

Price= 1600/400=4

Quantity = 250*4= 1000

c)To find Marginal cost function, we differentiate the total cost function with respect to quantity. So, marginal cost function is:

d) At short run, to determine equilibrium quantity, firms equate marginal cost to market price. So:

2/5q=4; q= 10

Profit or loss is defined by following formula: (Price-marginal cost)*quantity sold. But, since this is a competitive market, price and marginal costs are the same. So, essentially the firms make zero profit.

e) Total number of firms in industry= total industry output/output produced by each firm= 1000/10=100

So, there are 100 industries in the short run.

f) average cost of a firm at quantity 10 is 45/q+q/5= 45/10+10/5= 6.5. It is less than the prevalent market price. Hence, we expect firms to exit from this industry in the long run. Since supply is reducing, we expect total output of the industry to fall and prices to rise.

g) In the long run, economic profit is zero, which means that price is equal to average cost. It means that long run price is where average cost is the minimum, i.e. price =AC=MC. So, given the cost curve, we get AC function as: 45/q+q/5.

AC=MC is when =

q= 15. At, this q, AC is= 45/15+15/5= 6

So, long run price is 6. At this price, quantity demanded is  1600 – 150*6= 700. Quantity supplied by each firm in long run is 15. So, total number of firms in long run is 700/15= 46.6666 or approximately 46 firms.