Problem 1: Labor supply & demand with a mandated benefit

A small economy's labor market is perfectly competitive, with supply described by the equation w=8+0.2L^S and demand described by w=38-0.1L^D.Assume that decimal (not just integer) answers are possible throughout your analysis.

a. Compute the competitive equilibrium hourly wage rate and quantity of labor employed.

b. The government passes a new law requiring employers to set aside $2 per hour in retirement savings for all employees (something that no employers had previously done), in addition to paying the regular hourly wage. How will this affect the equilibrium wage rate and the quantity of labor employed if workers value this new benefit as equivalent to $2 extra in hourly pay? Be numerically precise; illustrate your answers to parts a and b in a hand-drawn labor supply - labor demand diagram.

c. Repeat your analysis from part b), now assuming that workers appreciate the new benefit, but they only value it as highly as $1 per hour in extra pay (since they assign a higher value to current income rather than funds they'll receive in the future). Draw a new diagram showing your answers to parts a) and c).