The domestic supply and demand curves for left-handed backscratchers (LHBs) are

Question

The domestic supply and demand curves for left-handed backscratchers (LHBs) are given by P = 10 + Q and P = 100 - 2Q, respectively, where P is the price in dollars per LHB, and Q is the quantity in LHBs per year. Canada produces and consumes only a trivial fraction of the world’s output of LHBs, so the current world price of $30/LHB is unaffected by events in the Canadian market. Transportation costs are negligible.
a. How much will Canadian consumers pay for LHBs and how many LHBs per year will they consume?
b. How will your answers to (a) change if the government imposes a tariff of $20/back-scratcher?
c. What total effect on domestic producer and consumer surplus will the tariff have? How much revenue will the tariff raise?

Explanation / Answer

(a)

The world price of LHB is $30/LHB.

Canada is a small country in international trade of LHB. So, world price will prevail in Canada.

Canadian consumer will pay $30/LHB.

Demand curve is as follows -

P = 100 - 2Q

2Q = 100 - P

2Q = 100 - 30

2Q = 70

Q = 35

Canadian consumers will consume 35 LHBs per year.

(b)

Imposition of tariff of $20/LHB will raise the price of LHB in Canada to $50/LHB ($30 + $20).

So, after imposition of tariff, Canadian consumers will pay $50/LHB.

Demand curve is as follows -

P = 100 - 2Q

2Q = 100 - P

2Q = 100 - 50

2Q = 50

Q = 25

After imposition of tariff, Canadian consumers will consume 25 LHBs.

(c)

Consumer surplus before tariff = 1/2 * (100 - 30) * 35 = $1,225

Consumer surplus after tariff = 1/2 * (100 - 50) * 25 = $625

So, consumer surplus will decrease by ($1,225 - $625) $600 after imposition of tariff.

Producer surplus before tariff = 1/2 * (30 - 10) * 20 = $200

Producer surplus after tariff = 1/2 * (50 - 10) * 40 = $800

So, producer surplus will increase by ($800 - $200) $600 after imposition of tariff.

Price after tariff = $50/LHB

Calculate demand after tariff -

P = 100 - 2Q

50 = 100 - 2Q

Q = 25

Calculate supply after tariff -

P = 10 + Q

50 = 10 + Q

Q = 40

After imposition of tariff, domestic supply exceeds domestic demand.

This implies that imports will be reduced to zero.

With zero imports, tariff revenue will also be $0.

Thus, the tariff will raise $0 as revenue.

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