Question

Imagine a monopsony labor market with the following labor supply and marginal revenue product of labor (MRPL) curves; W(l)=10+5l²

and MRPL=70.
1. Find the firm's profit maximizing labor hired and the equilibrium wage.
2. Plot the supply of labor, marginal expenditure, and labor demand curves and show the equilibrium. Clearly mark the intercepts, curves, and the equilibrium wage and labor with correct numbers.
3. Calculate the deadweight loss and mark the area on your plot. Hint:
|ˡ₁ ₗ₀ (a+bx+cx²) dx=(ax+ bx²/2 + cx³/3) |ˡ₁ ₗ₀ = (al₁ + bl²₁ /2 + cl³₁ /3) - (al₀ + bl²₀ /2 + cl³₀ /3) where l₀, l₁,a,b,c are numbers 4. Explain why there is a deadweight loss.

Answer 1

1. The firm's profit-maximizing labor hired is
`\( (5)/(2) \)`units and the equilibrium wage is $17.50.

2. The plotted supply of labor intersects the labor demand curve and marginal expenditure curve at \
`( (5)/(2) \)` units of labor with an equilibrium wage of $17.50.

3. The deadweight loss is 12.92 units².

Explanation:

In a monopsony labor market, the profit-maximizing level of labor hired is found where marginal expenditure (the wage rate plus the marginal cost of hiring an additional worker) equals the marginal revenue product of labor. This occurs at
`\( (5)/(2) \)` units of labor hired and an equilibrium wage of $17.50.

Plotting the supply of labor, marginal expenditure, and labor demand curves illustrates their intersection at the profit-maximizing level of labor and equilibrium wage. The deadweight loss calculation reveals the area of inefficiency caused by the monopsonistic power, resulting in a gap between the efficient equilibrium quantity and the quantity actually hired. This inefficiency arises because the monopsonist restricts employment below the level that would prevail under perfect competition, leading to a loss in potential surplus.

This deadweight loss represents the foregone gains from mutually beneficial transactions that would have occurred if the market were perfectly competitive. It symbolizes the loss in overall welfare due to the market power of the single buyer of labor.