Question

Suppose Hinterland has been a closed economy (meaning there is no immigration from foreign countries and no international trade). The current labor force has 4 million skilled workers and 8 million unskilled workers. Both types of labor have perfectly inelastic supply curves, and the current skilled-unskilled wage ratio is 2.5. The elasticity of demand of skilled labor is -0.4, while the elasticity of demand of unskilled labor is -0.1. Suppose Hinterland allows a brief period of immigration, during which time 50,000 skilled workers and 200,000 unskilled workers migrate to Hinterland. Suppose there are no other changes to the economy. Approximately what is the new skilled-unskilled wage ratio? (Hint: The percent change in the wage ratio is approximately equal to the percent change in the skilled wage minus the percent change in the unskilled wage.)

Answer 1

With migration (in both kinds of labor markets) the supply curve will simply shift right by that amount. Given that the supply curves are perfectly inelastic, using the elasticity of labor demand and such change in quantity of labor, we can find the new wage levels as follows:

For skilled workers:

Initial level = 4 million or 4,000,000 workers

Increase in workers = 50,000 workers, thus, percentage change in workers = (50000/4000000)*100 = 1.25%

So, with elasticity of demand as -0.4, using elasticity formula: ed = percentage change in quantity/percentage change in wage

Percentage change in wage = 1.25/-0.4 = -3.125%

For unskilled workers:

Initial level = 8 million or 8,000,000 workers

Increase in workers = 200,000 workers, thus, percentage change in workers = (200000/8000000)*100 = 2.5%

So, with elasticity of demand as -0.1, we have percentage change in wage = 2.5/-0.1 = -25%

Percentage change in the wage ratio = percent change in the skilled wage - percent change in the unskilled wage

= -3.125 - (- 25) = 21.875% (approximately)

So, new skilled-unskilled wage ratio = 2.5*(1 + 21.875%)

= 2.5*(1.21875) = 3.047 (approximately)