Solution
Price: ¥10000
Total Cost: 200000 + 4q2
Marginal Cost: 8q
(a)
Revenue function = Pq = 10000*q
Profit Function (π) = Revenue - Cost
= 10000q - 200000 -4q2
(b)
On differentiating profit Function with respect to q
dπ/dq = 10000 - 0-8q
dπ/dq = 0
10000 - 8q =0
8q = 10000
q = 10000/8 = 1250
Total Revenue (R) = pq = 10000*1250 =12500000
Total Cost = 200000 + 4q2 = 20000 +4(1250)2 =6450000
π = R - C = 12500000 - 6450000 =6050000
Yes the firm is earning profit.
(c)
In short run a firm's shut down condition is given by
P > AVC
AVC = 4q2 /q =4q
AVC|q=1250 = 4*1250=5000
P = ¥10000
The firm should continue to operate as P>AVC
(d)
As it is clear from the above calculation shown that
P> AVC. Therefore,firm must continue to operate in long run as well as price is greater than AVC
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