Question

A representative firm with total cost given by TC=20+20q+5q² operates in a competitive industry where the short-run market demand and supply curves are given by Q_D=1400-40P and Q_S=-400+20P. Please answer questions

1. Calculate the equilibrium quantity of output in the market

2. Calculate the quantity of output of the individual firm.

3. How many firms are operating in the market in the short run?

Answer 1

Answer to the question no. 1:

To find the market equlibrium quantity nd price we will equalise the Qs and Qd as:

Thus the merket equlibrium price is 30. And the equilibrium quantity (Q) will be:

Answer to the question no. 2:

Under perfect competition the price=MR=MC. Thus, the firm will produce the quantity at a level where the Price (=30)=MC. Let us derive the MC from the TC as:

Thus the firm will produce at a level where the P=MC as:

Thus, one firm will produce a quantity q=1.

Answer to the question no. 3:

The market equlibrium quantity is Q=200, and we find that each firm is producing q=1. Thus, there will be 200 firms in the market which collectively will produce Q=200.

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