Suppose the total cost equation for a competitive firm is
given by:
TC=1,000 + 10Q – 2Q2...

Question

Suppose the total cost equation for a competitive firm is
given by: 
TC=1,000 + 10Q – 2Q2 +
0.5Q3
(A)
At
what output is the average variable cost (AVC) at a minimum?

(B)
If
the market price of the firm’s output is $7.5 per unit, should the firm produce
or shut down?

David · Accepted Answer

TC = 1000 +10Q-2Q2+0.5Q3  
TVC = 10Q-2Q2+0.5Q3 
AVC  = TVC/Q = 10-2Q+0.5Q2
a) 
Minimum AVC where dAVC/dQ = 0 
Therefore dAVC/dQ = -2 + Q 
Equating it to 0 gives Q = 2 
At Q=2,  
AVC = 10-2(2)+0.5(2)2 = 8
b) 
Since minimum AVC at Q=2 is more than the market price of $7.5 per unit,

Suppose the total cost equation for a competitive firm is given by: TC=1,000 + 10Q – 2Q 2 + 0.5Q 3 (A) At what output is the average variable cost (AVC) at a minimum? (B) If the market price of the...

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