GS
Answered
Consider a competitive market with supply and demand curves expressed as:
Supply P = 5 + 0.036Q Demand P = 50 - 0.04Q,
where P represents unit price in dollars and Q represents sales rate in units per day.
a. Determine the equilibrium price and sales rate.
b. If this were the labor market for low skilled workers, what would be the loss in consumer surplus (purchaser surplus) when the minimum wage is set at $40 per day (an eight hour day)?
c. What is the loss or gain in producer surplus (seller surplus) in part b. above?
On Jul 09, 2024
a.Equilibrium price (wage rate) and sales rate (employment rate) are computed as follows:
5 + 0.036Q = 50 - 0.04Q
0.076Q = 45
Q = 592.11 units per day
Wage rate = P = 50 - .04(592.11) = $26.32 per day
b.Consumer surplus lost would be the area bounded by the minimum wage $40, the market equilibrium wage $26.32, the employment rates, before and after wages, and zero employment. We have a trapezoid made up of a rectangle and a triangle. The rectangle is bounded by the two wages, zero sales, and sales rate at the minimum wage.Height of rectangle = WM - WE = 40 - 26.32 = 13.68
Base of rectangle = QM = ?
PM = 50 - 0.04QM
40 = 50 - 0.04QM
QM = 250
Area of rectangle = b ∙ h = (250)(13.68) = 3,420.
Area of triangle with base measured on the vertical.
Base length = PM - PE = 13.68
Height = QE - QM = 592.11 - 250 = 342.11
Area = (1/2)b ∙ h = (0.5)(13.68)(342.11) = 2,340
Thus, consumer surplus lost = 3420 + 2340 = $5760 per day.
c.The producer surplus also has two parts. Producers gain the surplus in the rectangle lost by consumers in part b.Area = 3,420. But, the loss in employment (sales) represents a loss in surplus. This loss is a triangle bounded by supply, equilibrium wage rate, and the two levels of employment (sales rates). The only thing left to compute is the height of the supply curve at
QM = 250.
Supply P = 5 + 0.036(250) = 14.
The area of the triangle of loss is (1/2)(b ∙ h).
Base = b = 342.11 (measured horizontally)
Height = h = 26.32 - 14 = 12.32
Area of triangle = (0.5)(342.11)(12.32) = 2,107.40
Net change in producer surplus = $3420 - 2107.40 = $1,312.60