Question

The lamp industry is perfectly competitive. The price of a lamp is $50. A representative firm’s cost function is TC=1000+20Q+5Q².

a. What is MR for firms in this industry?
b. What is η of demand for firms in this industry?
c. What output Q will maximize profit for a representative firm?
d. What is the representative firms profit at this output?
e. What is the representative firms ATC at this output?
f. What is the representative firms AVC at this output?
g. Should the representative firm shut down in the short run? Why or why not?
h. What output for the representative firm will minimize ATC? (hint: use solver or find by solving MC=ATC, or if you are calculus whiz find ATC’=0)
i. Is the lamp industry in equilibrium? Why or why not?
j. Suppose total industry demand at P=$50 is 3000. How many firms are operating in the industry?
k. What would you expect to happen to future firm population in the lamp industry?
l. What would you expect to happen to future price in the lamp industry?
m. What industry price will result in LR industry equilibrium?

Answer 1

a)

P = 50

TR = PQ

= 50Q

dTR/dQ = MR = 50

b)

= (dQ/dP)(P/Q)

P = 50

dP/dQ = 0  

dQ/dP =    

Thus   =    which means perfectly elastic

c)

TC = 1000 + 20Q + 5Q2

MC = 20 + 10Q

P = MC  

50 = 20 + 10Q  

50 - 20 = 10Q

30 = 10Q

Q = 3

d)

Profit = PQ - TC

= 50(3) - 1000 - 20(3) - 5(3)2

= 150 - 1000 - 60 - 45

= - 955 which means firm is making a loss of 955

e)

ATC = TC/Q

=  (1000 + 20Q + 5Q2 )/Q

= 1000/Q + 20 + 5Q

Q = 3  

ATC = 1000/3 + 20 + 5(3) = 368.33

f)

AVC = TVC/Q

TVC =   20Q + 5Q2

AVC = (20Q + 5Q2 )/Q

= 20 + 5Q

= 20 + 5(3)

= 35

g)

Since firm is making loss in short run but P = 50 > AVC = 35 which means firm is earning operating profit therefore firm will continue to produce despite of loss in short run