Assume that there are a large number of identical firms in a competitive industr
ID: 1254078 • Letter: A
Question
Assume that there are a large number of identical firms in a competitive industry, each
with the cost function:
TC = 25+4q+q2
a. What is the minimum price at which firms will continue operating in the short
run? In the long run?
b. Assume that there are n firms in the industry. What is the short-run industry
supply function?
c. Industry (inverse) demand is given by P = 40-Q/5. If there are 20 firms in the
industry, is the industry in long-run equilibrium? What is the market price?
Calculate and graph (dont worry about graph) the profits of an individual firm (along with AC, AVC, and
MC curves).
d. How many firms will serve the market in long-run equilibrium
Explanation / Answer
AC=TC' AC=4+2q q=1/2 Plugging this in to TC and solving TR-TC gives us the answer to A Pq-(25+4q+q^2) 1/2p-25-2-1/2 1/2p=55/2 p=55 This is our P in SR for LR we first find ATC this is TC/Q =25/Q+4+Q now we plug in 1/2 =50+4+1/2=109/2 For B we take derivative of AC to obtain MC and MC is our supply curve for a firm MC=4 since there are n firms our maarket supply is 4n For C P=40-Q/5 n=20 we set this equal to LRATC 40-Q/5=25/Q+4+Q 40-4=25/Q+Q-Q/5 36=25/Q+4Q/5 multiply everything by 5 180=125/Q+4Q 125/Q+4Q-180 Multiply by Q 125+4Q^2-180Q divide by 4 Q^2-45Q=-125/4 add 2025/4 to both sides Q^2-45Q+2025/4=475 factor left side (Q-45/2)^2=475 square both sides (Q-45/2)=5sqrt(19) now solve for Q Q=5sqrt(19)+45/2 Plug Q into function and solve for P =71/2+sqrt(19) For D we know our p and Q We multiply our P by 20 =71/2+sqrt(19)*20=aprox 798 firms