1. Danny’s Dump Truck sells its output in both the domestic and the foreign mark
ID: 1204238 • Letter: 1
Question
1. Danny’s Dump Truck sells its output in both the domestic and the foreign markets. Because of import and export restrictions, there is not possibility of a purchase in one market that could then be sold in the other market. The demand function associated with each market is as follows:
P1 = 20,000 - 2Q1 P2 = 25,000 – 50Q2
Danny’s marginal cost is $10,000 in both markets. (assume AC= MC) Suppose the firm can engage in third degree price discrimination.
a. Find the price and output in each market. Find Danny’s total profits through price discrimination.
b. Graphically show how Danny charges different prices in different markets.
c. Calculate the price elasticity of demand for each market.
Explanation / Answer
a. Domestic Market
P1 = 20,000 - 2Q1
TR1 = P1*Q1 = [ 20,000 - 2Q1 ]*Q1
MR1 =dTR1/dQ1 = 20,000 - 4Q1
MC = 10,000
Equating MR = MC, to find the profit maximizing output
20,000 - 4Q1 = 10,000
Q1 = 10,000/4 = 2,500
P1 = 20,000 - 2Q1 = 20,000 - 2*25,00 = $15,000
Profit = TR - TC = P*Q1 - AC*Q1
Profit = 15,000*2,500 - 10,000*2,500
= $12,500,000
Foreign Market
P2 = 25,000 – 50Q2
TR2 = P2*Q2 = [ 25,000 - 50Q2 ]*Q2
MR2 =dTR2/dQ2 = 25,000 - 100Q2
MC = 10,000
Equating MR = MC, to find the profit maximizing output
25,000 - 100Q2 = 10,000
Q2 = 15,000/100 = 150
P2 = 25,000 - 100Q2 = 25,000 - 2*150 = $24,700
Profit = TR - TC = P*Q1 - AC*Q1
Profit = 24,700*150 - 10,000*150
= $2,205,000
Danny’s total profits through price discrimination = $2,205,000 + $12,500,000
= $14,705,000
b. Show cann't upload the image of graphs, but its simple just plot MR curve derived here , Show its Interaction with the MC and then for that quantity look for price in Demand curve.
c. For Domestic Market
E1 = % change change in Quantity demanded/% change in Price = Slope of demand curve
E1 = 1/2 = 0.5
E2 = 1/50 = 0.02
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