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Chapter 9: Problem 12

The domestic supply and demand curves for hula beans are as follows: \\[ \begin{aligned} \text {Supply:} & P=50+Q \\ \text {Demand:} & P=200-2 Q \end{aligned} \\] where \(P\) is the price in cents per pound and \(Q\) is the quantity in millions of pounds. The U.S. is a small producer in the world hula bean market, where the current price (which will not be affected by anything we do) is 60 cents per pound. Congress is considering a tariff of 40 cents per pound. Find the domestic price of hula beans that will result if the tariff is imposed. Also compute the dollar gain or loss to domestic consumers, domestic producers, and government revenue from the tariff

Short Answer

Expert verified
The domestic price for hula beans will be 100 cents per pound after the tariff. Domestic consumers will lose \$400 million while domestic producers will gain \$200 million. The government will generate revenue of \$2400 million from the tariff.

Step by step solution

01

Analyze the Supply Curve

The initial supply curve is \(P = 50 + Q\). Since the world hula bean market price is 60 cents per pound and the US does not influence this price, we need to find out the quantity supplied at this price. Setting \(P = 60\) in the supply equation we get \(Q = 60 - 50 = 10\) million pounds.
02

Analyze the Demand Curve

The demand curve is \(P = 200 - 2Q\). To find the quantity demanded at the world price of 60 cents per pound, we set \(P = 60\) in the demand equation, giving \(Q = (200 - 60)/2 = 70\) million pounds.
03

Determine the domestic price after the tariff

When a tariff of 40 cents per pound is imposed, the domestic price will rise by the amount of the tariff. The new domestic price \(P'\) is \(P + \text{tariff} = 60 + 40 = 100\) cents per pound. This shifts the supply curve to \(P' = 50 + Q + 40\), which can be simplified to \(P' = 90 + Q\). At this new price, the quantity supplied is \(Q = 100 - 90 = 10\) million pounds and the quantity demanded is \(Q = (200 - 100)/2 = 50\) million pounds.
04

Calculate Changes to Consumer and Producer Surplus

The gain or loss to domestic consumers can be represented by the decrease in consumer surplus, which is the area of the triangle formed by the demand curve, the horizontal line at the initial price, and the vertical line at the quantity after the tariff. With a base of \(70 - 50 = 20\) and a height of \(100 - 60 = 40\), the loss of consumer surplus is \(\frac{1}{2}.base.height = 0.5.20.40 = \$400\) million. The gain to domestic producers is the increase in producer surplus, which is the area of the triangle formed by the supply curve, the horizontal line at the new price, and the vertical line at the quantity after the tariff. This equals to \(\frac{1}{2}.base.height = 0.5.10.40 = \$200\) million.
05

Calculate Government Revenue

The government revenue from the tariff is \(price.quantity = 40. (70 - 10) = \$2400\) million.

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Most popular questions from this chapter

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