Labor economics: problem 5.2
Consider the demand for and supply of risky jobs : a. Derive the algebra that leads from equations (5.4) and (5.5) to equation (5.6).
(5.4) π0=pα0E*- w0 E*
(5.5) π1=pα1E*- w1 E*
It is given that a profit-maximizing firm offers a risky environment if π1>π0 (when the profits the firm can earn when it chooses to be a risky firm exceed the profits the firm can earn when it chooses to be a safe firm) and a profit-maximizing firm offers a safe environment if π1<π0 (when the profits the firm can earn when it chooses to be a safe firm exceed the profits the firm can earn when it chooses to be a risky firm). Offering a safe working environment: | Offering a risky working environment: | π1<π0↔pα1E*- w1 E* < pα0E*- w0 E*↔pα1- w1 < pα0- w0 ↔pα1-pα0- w1 < - w0 ↔pα1-pα0 < w1 - w0 ↔θ<w1-w0 ↔ w1-w0 > θ (5.6) | π1>π0↔pα1E*- w1 E* > pα0E*- w0 E*↔pα1- w1 > pα0- w0 ↔pα1-pα0- w1 > - w0 ↔pα1-pα0 > w1 - w0 ↔θ>w1-w0 ↔ w1-w0 < θ (5.6) |

b. Describe why the supply curve in figure 5.2 is upward sloping. How does you explanation incorporates θ? Why?
Figure 5.2 illustrates the supply curve to risky jobs in a particular labor market. The supply curve indicates how many workers are willing to execute a risky job as a function of the wage differential between the risky job and the safe job (also known as the reservation price or ∆w=w1-w0).
When it is assumed that all workers dislike risk, no worker would be willing to work at the risky job when the wage differential is zero. As the wage differential rises, there will come a point where the worker who dislikes risk the least is bought off and decides to work in the risky job. As the wage differential between the risky job and the safe job keeps increasing, more and more workers are bribed into the risky occupation and the number of workers who