Question

The market for sweet potatoes consists of 1,000 identical firms. The market demand curve is given by Qd = 1000 – 5P. Each firm has a short-run total cost, SRTC = 100 + 100q + 100q^2 , where q is output. In short-run market equilibrium, each individual firm will

a. earn a profit.

b. earn a loss.

c. earn zero economic profit.

d. produce an output of q = 4.

Answer 1

Answer

Option b

The short-run supply curve is equal to the marginal cost curve for an individual firm

MC is a change in the total cost and found by differentiation

MC=dSRTC/dq=100+200q

MC=100+200q

P=100+200q

the individual demand curve is

P=100+200q

200q=P-100

q=0.005P-0.5

the industry supply curve is

Q=q*1000=(0.005P-0.5)*1000=5P-500

Qs=5P-500

the market is in equilibrium at Qd=Qs

1000-5P=5P-500

10P=1500

P=$150

the market price is $150

market quantity is

Qd=1000-5*150=250

each firm produces at MC=P

100+200q=150

q=0.25 units

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Profit=TR-TC

TR=P*Q=0.25*150=37.5

TC=100+100*0.25+100*0.25^2=131.25

Profit=37.5-131.25

Profit=-93.75

each firm will earn a loss of $93.75.