Suppose that the demand function of Japanese car in the US is given D(p) = 250 -
ID: 1201464 • Letter: S
Question
Suppose that the demand function of Japanese car in the US is given D(p) = 250 - 2p where p is the price of Japanese cars. If the supply schedule is horizontal at a price of $5, what will be the equilibrium number of Japanese cars sold in the US? How much money will people spend in total on Japanese cars? Due to the pressure from American car manufacturers, the US imposes an import duty on Japanese cars in such a way that for every car exported to the US the Japanese manufacturers must pay a tax to the US government of $2. How many Japanese cars will now be sold in the US? At what price? How much revenue will the US government collect with this tariff? Suppose that instead of imposing an import duty, the US government persuades the Japanese government to impose "voluntary export restrictions" on their exports of cars to the US. Suppose that the Japanese agree to restrain their exports by requiring that every car exported to the US must have an export license. Suppose further that the Japanese government agrees to issue only 236,000 export licenses and sells these licenses to the Japanese firms. If the Japanese firms know the American demand curve and if they know that only 236,000 Japanese cars will be sold in America, what price will they be able to charge in America for their cars? How much will a Japanese firm be willing to pay the Japanese government for an export license? To see it, think about what it costs to produce a car and how much it can be sold for if you have an export license. How much will be the Japanese government's total revenue from the sale of export license? How much money will Americans spend on Japanese cars? Why might the Japanese "voluntarily" submit to export controls?Explanation / Answer
1.
D(p) = Q = 250 – 2P
250 – 2P = Q
2P = 250 – Q
P = 125 – 0.5Q
TR = PQ = 125Q – 0.5Q^2
MR = Derivative of TR with respect to Q
= 125 – Q
MC = $5
Equilibrium condition is MR = MC
125 – Q = 5
Q = 120
Putting Q = 120 in P
P = 125 – 0.5Q
= 125 – 0.5 × 120
= 125 – 60
= 65
Total spending = Q × P
= 120 × 65
= 7,800
Answer: Equilibrium number of cars = 120 and the total spending is $7,800.
2.
New MC = $5 + $2 = $7
Equilibrium condition is MR = New MC
125 – Q = 7
Q = 118
Putting Q = 118 in P
P = 125 – 0.5Q
= 125 – 0.5 × 118
= 125 – 59
= 66
Answer: 118 numbers of cars would be sold now at $66 price.
3.
Government collects tax = Tax rate per car × Number of car supplied
= $2 × 118
= $236 (Answer)
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