Question

The market for computers is characterized by perfect competition. Firms and consumers are price takers and in the long run there is free entry and exit of firms in this industry. All firms are identical in terms of their technological capabilities. Thus the cost function as given below for a representative firm can be assumed to be the cost function faced by each firm in the industry. The total cost function for the representative firm is given by the following equation: TC = q2 + 5q+ 36 Suppose that the market demand is given by: P = 1025 - 2Q Note: Q represents market values and q represents firm values. The two are different.

a) Determine the equation for average total cost for the firm (1 Mark)

b) What is the long-run equilibrium price in this market? (Hint: since the market supply is unknown at this point, it’s better not to think of trying to solve this problem using demand and supply equations. Instead you should think about this problem from the perspective for a firm)

c) What is the long-run output of each representative firm in this industry? (1 Mark)

d) When this industry is in long-run equilibrium, how many firms are in the industry?

e) How will the graph look like for the entire industry in the long run? (Mark the equilibrium industry price and quantity) (1 Mark)

f) How will the graph for the firm look like in the long run? (Mark the equilibrium price and quantity produced by the firm and mark any profit or loss being made by it)

Answer 1

a) We are given:

Total cost function of the firm:

Therefore, the Average Cost function is given by:

b) In the long run, the equilibrium occurs at the point where Long Run Marginal Cost Curve and Long Run Average Cost Curve intersects:

Therefore, equilibrium is given by:

Now since Market Price is equal to Marginal Cost at optimum level of output

Therefore, Long Run Equilibrium Price in the market is

c) Long Run Equilibrium quantity of a firm is  

d) The Industry is in the long run Equilibrium when all the firms in the industry are making zero economic profits i.e. all firms are producing at P = MC level of output

Let there be firms in the market.

Since all the firms are identical, they will produce the same quantity

Therefore, the Market Output level will be given by

We know the equilibrium output of a firm and Equilibrium price of the market:

,

Therefore, there are 84 identical firms in the Industry.