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