please need an answer A competitive firm has estimated its average variable cost
ID: 1131177 • Letter: P
Question
please need an answer
A competitive firm has estimated its average variable cost function as A 1 = 20-00AO + 0.0000502 its total fixed cost is $500 a. The marginal cost function associated with this AVC function is SMC= " (4 points) b. AVC reaches its minimum at forecasted price is P- $23.60. c.To maximize its profit the firm should produce units of output at which AIC= (6 points )The units of output. Profit (loss) is (6 points) Suppose the forecasted price is P-310. d. The firm should produce 6 points) units of output for a profit (loss) of SExplanation / Answer
a. TVC = AVC (Q)
TVC = 20Q - 0.04Q2 + 0.00005Q3
SMC is derived by differentiating TVC w.r.t Q.
SMC = 20 - 0.08Q + 00.00015Q2
b. BY seeing when AVC reaches its minimum , firstly differentiating AVC w.r.t Q and then equate it zero. Then we get,
-0.04 + 0.0001Q = 0
Q = 400
And AVC = 20 - 0.04(400) + 0.00005(400)2
AVC = 20- 16 + 0.08
AVC = 4.08
Hence, AVC reaches its minimum at 400 units of output at which AVC = 4.08.
For maximise profit equate P= $23.60 with SMC .
Similarly when P=$10 then equate this with SMC.
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