Question

Suppose in the market for corn the demand function is modeled by Qd=-5P+700 and in the short run the market is supplied by your firm and 99 other firms with exactly the same cost schedule as you. Find the equilibrium market price P*, the equilibrium market quantity Q*, your firm's profit-maximizing quantity q*, and your firm's profit at this price and quantity in the short run. Note: the quantity produced increases in increments of 1 and the fixed cost is 20.

Quantity Total Cost

0 20

1 60

2 80

3 120

4 180

5 260

Answer 1

We can develop Marginal Cost schedule for each level of output as under

Quantity, Q	Total Cost, TC	Marginal Cost=Change in TC/Change in Q	Qd=-5P+700	Qs=100*Q
0	20
1	60	40
2	80	20	600	200
3	120	40	500	300
4	180	60	400	400
5	260	80	300	500

In a competitive market, Marginal Cost (MC)=P. It represents supply curve of a competitive firm. We consider only increasing section of marginal cost or supply curve of a firm.

Since there are 100 firms in market. Market Supply schedule can be made as Qs=100*Q (Refer above table)

Quantity demanded can be calculated with the help of given demand curve and MC as Price. (Please refer the given table)

We can observe that Qs=Qd=400 at P=MC=$60

So, equilibrium price is $60

Equilibrium market quantity is 400 units

Optimal output of a firm=4 units

Total Cost at optimal quantity=TC=$180 (Please refer above table)

Total Revenue=TR=P*Q=60*4=$240

Profit of a firm=TR-TC=240-180=$60