Monopoly earns the highest profit when its MR is equal to MC. To find MR we need TR which is P*Q.
From demand equation, "P = 96- 4*Q"
So, "TR = 96*Q - 4*Q^2". Thus, "MR = 96 - 8*Q".
To caclulate MC we need TC. "TC = AC*Q=100+6*Q+0.5*Q^2"
"MC = 6+Q".
As "MC=MR",
"6+Q = 96 - 8*Q" (i)
Q = 10, P = 56 (ii).
The maximum profit(TP) is the difference between total revenue and total cost.
So, "TR = 560. TC = 100+60+50 = 210."
So, "TP = 560 - 210 = 350"(ii).
(iii) As the firm's average variable cost is "AVC = 100\/Q +0.5*Q = 10+5 = 15" is less than the equilibrium price(P = 56), the firm should continue to operate in short-run.
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