Question

1) Suppose there are 100 workers in the economy in which all workers must choose to work a risky or a safe job. Worker 1’s reservation price for accepting the risky job is $1; worker 2’s reservation price is $2, and so on. Because of technological reasons, there are only 15 risky jobs.

a) What is the equilibrium wage differential between safe and risky jobs?

b) Which workers will be employed at the risky firm? (i.e., worker #X – worker #Y)

c) Suppose now that an advertising campaign, paid for by the employers who offer risky jobs, stresses the excitement associated with “the thrill of injury,” and this campaign changes the attitudes of the work force toward being employed in a risky job. Worker 1 now has a reservation price of -$10 (that is, she is willing to pay $10 for the right to work in the risky job); worker 2’s reservation price is -$9, and so on. There are still only 15 risky jobs. What is the new equilibrium wage differential?

Answer 1

a) The labour supply curve can be calculated using the given data. The reservation price for the first worker is $1, second worker is $2 and so on. Total workers in the economy are 100. Therefore, the supply curve will be upward slopping with slope equals to 1.

Calculation for supply curve: Step 1: As the curve is linear, Identify any two points on the line. Lets take first point (1,1) and second point (2,2).

Equation of line is y = m*x + c.

Step 2: Solving the above equation for these two points, calculate slope and constant c. Using this two points equation of line becomes y = x + 1 . (Slope m = 1 and c = 0)

Now, the demand curve is inelastic and therefore the demand curve will be a vertical line with equation x= 15. Now the wage equillibruim will be attend with Demand curve = Supply curve. By solving the equation of demand and supply curve, we get x = 15 and y = 15 as a solution. Therefore, the equillibrium wage differential between risky and safe job is $15

b) Since equillibrium wage differential is $15, so all the workers whose reservation price is less than $16 will be hired. Therefore, worker 1, 2, ...15 will be hired

c) Now if workers preference shifts as mentioned, then the supply curve will shift down as shown in figure. The first point will be (-10,1) and second point will be (-9,2). From this, the slope of the line is 1 and constant c = -10. Therefore equation of supply curve will be now y = x - 10 and demand curve will be x = 15. Solving these two equation, we get y = 5. Therefore, the new equillibrium wage differential will be $5 dollars.