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Sem 5 Prep
← Intl TradeTariff welfare and effective protection

Formulas for this chapter

Consumer surplus loss from a tariff

Loss = (units still consumed x price rise) + 1/2 x (fall in consumption) x (price rise)

Always in two parts: the rectangle on the units still bought, plus the triangle for the buyers who drop out. The class's numbers give 50 x $1 + 1/2 x 20 x $1 = $60.

Units still consumed
Consumption after the tariff
Fall in consumption
Consumption before minus consumption after
Price rise
New domestic price minus the world price

Producer surplus gain from a tariff

Gain = (units previously produced x price rise) + 1/2 x (rise in production) x (price rise)

Also called the subsidy effect of the tariff. Two parts again: the old output at the higher price, plus the triangle on the new output under the rising supply curve. The class's numbers give 10 x $1 + 1/2 x 10 x $1 = $15.

Units previously produced
Domestic production at the free trade price
Rise in production
Production after minus production before
Price rise
New domestic price minus the world price

Deadweight loss, two ways

DWL = consumer loss - producer gain - government revenue = 1/2 x (rise in production) x (price rise) + 1/2 x (fall in consumption) x (price rise)

Compute it both ways and check they agree; if they do not, one of the four box numbers is wrong. The first triangle is the production or protection cost, the second the consumption cost.

Consumer loss
Area AGHB, the two-part figure
Producer gain
Area AGJC, the two-part figure
Government revenue
Imports after the tariff x the duty per unit

Total consumer or producer surplus as a triangle

Consumer surplus = 1/2 x quantity x (choke price - price paid) Producer surplus = 1/2 x quantity x (price received - supply intercept)

To cross-check the two-part loss and gain. On the class's curves, consumer surplus falls from $122.50 to $62.50, a fall of $60, and producer surplus rises from $5 to $20, a rise of $15.

Choke price
Price at which quantity demanded falls to zero, $4.50 on the class's curve
Supply intercept
Price at which domestic supply falls to zero

Rate of effective protection

g = (t - a_i x t_i) / (1 - a_i)

Whenever a question gives an input cost as well as a tariff on the finished good. If a_i = 0 then g = t. g exceeds t when t_i is below t, equals t when t_i equals t, and turns negative when a_i t_i exceeds t. Extend it to several inputs by summing a_i t_i on top and a_i below.

g
Effective rate of protection to producers of the final commodity
t
Nominal tariff rate on the final commodity, as a decimal
a_i
Cost of the imported input divided by the final commodity's free trade price
t_i
Nominal tariff rate on the imported input, as a decimal

Cost per domestic job saved

Cost per job = loss of consumer surplus / number of jobs saved

When a question gives a consumer cost and an employment figure. Use the consumer surplus loss on top, not the deadweight loss, because the question is what the policy costs the people who pay for it.

Loss of consumer surplus
The full consumer cost of the tariff, area AGHB
Jobs saved
Employment in the industry attributable to the protection
Step 1 of 28
The ideaTheory

Somebody paid for that toll booth

The toll booth raised money for the council and helped local farmers. Both are real gains. But nobody handed over that money for nothing.

Townspeople paid twice: once on the rice they still buy at the higher price, and once by giving up the rice they no longer buy at all.

This chapter adds the money up. It turns out the losers lose more than the winners win, and the gap has a name.

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