A perfectly competitive firm has the following total cost schedule: TC = 2Q^2 -

Question

A perfectly competitive firm has the following total cost schedule: TC = 2Q^2 - 6Q +16. Answer the following: 1. What level of output minimizes the average total cost (ATC)? a. Q=8 b. Q=4 c. Q=2.83 d. None is correct. 2. If P=$2, how much output does the firm produce in the short-run? a. Q=2 b. Q=2.83 c. Q=4 d. Q=8 3. If P=$2, how much profits is the firm making at the profit maximizing level of output? a. Profit=0 b. Profit=-16 c. Profit= -8 d. Profit=2 4. Find the short run supply for this firm. a. Q= P + 3 b. Q=(P/4) +3 c. Q=4P-6 d. Q=(P/4)+(3/2) 5. Suppose there is another firm in the market with identical cost curves. Find the industry supply. a. Q=8P-12 b. Q=(P/2)+3 c. Q=2P+6 d. Q=(P/2)+6

Explanation / Answer

Ans)

#.
c. 2.83
TC = 2Q^2 - 6Q +16
ATC=TC/Q
ATC=2Q-6+16/Q
dATC/dQ=2-16/Q2
Let dATC/dQ=0
2=16/Q2
Q2=8
Q=2.83
#
a. Q=2
P=2
MC=dTC/dQ=4Q-6
P=MC
2=4Q-6
4Q=2+6
4Q=8
Q=2
#
c. Profit= -8
Profit=TR-TC
=(2*2)-(2*4-6*2+16)
=-8
#
d. Q=(P/4)+(3/2)
MC=dTC/dQ=4Qs-6
P=4Qs-6
P+6=4Qs
Qs=P/4+3/2

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