Question

There are two distinct sectors: taxidermists (X) and tap dancers (T). It is surprising that there is complete labor mobility between the two sectors. There are 200 equally talented workers who supply their labor inelastically. The demand for taxidermists is EX = 190 – 10 wX, and the demand for tap dancers is ET = 160 – 5 wT. a) What is the competitive equilibrium outcome (equilibrium wage and employment level in each sector) in this labor market? b) What would happen if the government imposed a minimum wage of $12 that covered only the tap dancer sector?

Answer 1

a) Given that labor is 200 units we have EX + ET = 200, LT being tap dancers and LX being taxidermist.

Competitive wage should be same in both industries so that we have wX = 19 - EX/10 and wT = 32 - ET/5

19 - EX/10 = 32 - ET/5

ET/5 - EX/10 = 13

2ET - EX = 130 and that ET + EX = 200

This gives 3ET = 330 or ET = 110 and therefore EX = 200 - 110 = 90. The competitive wage is $10.

b) In the market for tap dancers there is now a minimum wage of 12. The number of tap dancers demanded is 160 - 5*12 = 100 Hence ET = 100. This implies EX = 100.

When EX = 100, they will move to the market for taxidermist, increase supply so that at this rate, all of them are employed but at a lower wage

(190 - 100)/10 = $9. Hence wage rate in the market for Taxidermists will fall to $9 and employment increased to 100 taxisdermists.