1. You must answer this question: Using graphical analysis contrast and compare
ID: 1091865 • Letter: 1
Question
1. You must answer this question: Using graphical analysis contrast and compare the short run equilibrium in the competitive market with the short and long run equilibrium in a monopoly. You will need to explain your graphs and analysis. You may answer one of the following questions:
2. Competition: Assume market clearing price is $25 and TC = 2000 + 10Q + .002Q2 Find, profit max Q, TR, TC, and Profit.
3. Monopoly: Assume P = 100- 2Q TC = 10 + 2Q Find Profit max price and Quantity, profit, and elasticity at profit max.
Explanation / Answer
I chose to answer the 3 rd ques
The profit maximising price and quantity for a monopolist occur where marginal cost = marginal revenue.
P = 100- 2Q
total revenue (TR) = PQ = (100-2Q)Q = 100Q - 2Q^2
marginal revenue = d TR / dQ = 100-4Q
total cost (TC) = 10 + 2Q
marginal cost = d TC / dQ = 2
MR = MC
100-4Q = 2
4Q = 98
Q = ( 24.5)
At Q =24.5
P= 100-2Q = 100-49 = 51
Hence profit maxima occurs at Profit max price = 51 and quantity = 24.5
Profit = ( P*Q) = ( 51*24.5) =1249.5
MR = 100-4Q = ( 100-4*24.5) = 2
Hence elasticity at profit max = ( TR/TC) =( 100Q - 2Q^2 )/(10+2Q) = 49/59 = 0.83
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