Suppose a monopolist has two segmented markets, domestic (1) and foreign (2). Th
ID: 1198415 • Letter: S
Question
Suppose a monopolist has two segmented markets, domestic (1) and foreign (2). The demand functions for both markets and the total cost function are as follows: P1 = 100 - Q1 P2 = 80 - 2Q2 2 2 TC = Q1 + 2Q1Q2 + Q2 Find the output the firm would produce and sell in each market in order to maximize profit. What price will the firm charge in each market Explain, with quantitative evidence, the relevance of price elasticity of demand in the determination of the relative prices charged in each market. (Hint: Estimate the price elasticity of demand in each market. The market with a more elastic demand should be charged a lower price. Do the results obtained conform with this principle) Explain why a firm needs thorough knowledge of ATC, AVC and MC. Indicate the key market decision(s) associated with each variable. Explain the basic features of the various market structures discussed in class. What is product differentiation How is it that in a perfectly competitive market long run economic profit is zeroExplanation / Answer
Soln :
a) Domestic market demand function i.e P 1 = 100 - Q1 & foreign market demand function P2 = 80 - 2Q2
Total cost = Q12 + 2Q1 Q2 + Q22
For a monopolist , profit is maximum when marginal revenue = marginal cost
revenue for domestic firm = Price X quantity
R1 = (100 - Q1 ) Q1
marginal revenue dr1/dq1 = 100 - 2Q1
Total cost for firm 1 = Q12 + 2Q1 Q2 + Q22
Marginal cost with respect to Q1 = 2Q1 + 2Q2
Equating marginal revenue and marginal cost
100 - 2Q1 = 2Q1 + 2Q2
4Q1 + 2Q2 = 100 - (1)
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Marginal revenue for foreign firm = 80 - 4Q2
Marginal cost with respect to Q2 = 2Q1 + 2Q2
2Q1 + 2Q2 = 80 - 4Q2
2Q1 + 6Q2 = 80 - (2)
Solving equation 1 & 2
4Q1 + 2Q2 = 100
2Q1 + 6Q2 = 80
multiply equation 2 by 2
4Q1 + 2Q2 = 100
4Q1 + 12Q2 = 160
Subtracting
- 10Q2 = - 60
Q2 = 6 units
Q1 = 88/4
Q1 = 22 units
Price of domestic firm = 100 - 22
P1 = $ 78
Price of foreign firm P2 = 80 - 2 X 6
P2 = $ 68
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b) For domestic firm P 1 = 100 - Q1
Q1 = 100 - P1
when P1 = $ 78
Q1 = 22 units
when P1 = $ 76
Q1 = 24 units
Price elasticity of demand for domestic firm = % change in quantity demanded / % change in price
Ep1 = 9.09/2.56
Ep1 = 3.54 ( Elastic demand)
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For foreign firm P2 = 80 - 2Q2
2Q2 = 80 - P2
Q2 = 40 - 0.5P2
when p2 = 68
Q2 = 6 units
when p2 = $ 66
Q2 = 7 units
Price elasticity of demand for foreign firm = % change in quantity demanded / % change in price
Ep2 = 16.66 / 2.94
Ep2 = 5.66 ( Elastic demand)
Thus a market with elastic demand should charge a lower price and the results obtained conform with this principle .
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