The total marginal cost functions of a competitive firm are tv+1800+2q^2 and mc=

Question

The total marginal cost functions of a competitive firm are tv+1800+2q^2 and mc=4q, where tv and mc are total cost respectively, and q is the firms total output. There are currently 100 identical firms. The demand function is p=180-.02q. P is price, q is aggregate quantity demanded

A.) fine equilibrium price and quantity. Explain
B.) is this long run equilibrium. Explain
C.) suppose what actually happens in the damand condition so that the new function is p=240-.02q. Find short run and long run effect of this change on the equilibrium price, quantity, and the number of firms in the industry. Explain The total marginal cost functions of a competitive firm are tv+1800+2q^2 and mc=4q, where tv and mc are total cost respectively, and q is the firms total output. There are currently 100 identical firms. The demand function is p=180-.02q. P is price, q is aggregate quantity demanded

A.) fine equilibrium price and quantity. Explain
B.) is this long run equilibrium. Explain
C.) suppose what actually happens in the damand condition so that the new function is p=240-.02q. Find short run and long run effect of this change on the equilibrium price, quantity, and the number of firms in the industry. Explain

A.) fine equilibrium price and quantity. Explain
B.) is this long run equilibrium. Explain
C.) suppose what actually happens in the damand condition so that the new function is p=240-.02q. Find short run and long run effect of this change on the equilibrium price, quantity, and the number of firms in the industry. Explain

Explanation / Answer

TC=1800+2Q^2

MC=4Q

Market demand : p=180-.02q

1.

Firms demand:

Qi= (180-P)/.02*100= 90-P/2

MR for each firm= P*Qi

Revenue=(180-2Q)*Q

MR=180-4Q

MC=4Q

Profit maximization MR=MC

180=8Q

Q=22.5

P=135

Profit=225

b.

No, as the firm is making positive profit, new firm will enter into market. As a result price will fall due to competition. AT long run

P will be equal to ATC

C.

P=240-.02Q

Firm demand curve

Q=120-P/2

MR=240-4Q

MC=4Q

Profit maximization point MR=MC

240=8Q

Q=30

P=180

Profit=0

This is both short run and lonf run equilibrium. As in short run firm is having zero profit so no new firm will enter into market. number of firm will remain same at 100.

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