Question

Consider the following supply and demand equations in the market for labour.

Supply: w=L

Demand: w= 500−L.

Use these equations to respond to the following questions.

(a) What is the market equilibrium price and quantity?

(b) Under a free market, what is the Total Surplus?

(c) Suppose that the government enacts a minimum wage of w= 400. What is theTotal Surplus?

(d) What is the Surplus amount of labour under the minimum wage?

Answer 1

Answer a

At equilibrium, Ls = Ld

Hence w =500 - L

or, w = 500- w (replacing L from w as per supply function)

or w+w = 500

or 2w = 500

or, w =250

w =500-L

or, 250 =500-L

or, L = 500-250

or, L = 250

Hence Equilibrium Labor Quantity is 250 and wage is $250

Answer b

Total Surplus will be given by a area of a triangle with base 250 (equilibrium quantity) and height 500 (wage at quantity 0). Hence surplus = 1/2 * 250 *500 = 250*250 = $62500

Answer c

At wage 400, supply will be given by, w=L i.e Ls = 400 and Labor demanded will be given by, w =500-L i.e. 400 = 500-L, or, L= 500-400 =100

New Total Surplus = Old Total Surplus - Dead weight Loss

Dead weight loss is given by area of shaded triangle with base 250-100 =150 and height 400-100=300. Hence dead weight loss = 1/2*150*300 = 150*150 = $22500

Hence New Total Surplus = 62500 -22500 = $40000

Answer d

Since the Labor demanded is 100 while the labor supply is 400 hence the labor surplus amount is 400-100 = 300.

Hence 300 is answer