Asked by Jeanette Avila on Jul 06, 2024
Verified
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?
Equilibrium Price
Equilibrium price is the price at which the quantity of a good demanded by consumers equals the quantity supplied by producers, leading to market stability.
Consumer Surplus
The difference in the total expected payment consumers are ready to make for a good or service and their actual expenditures.
Producer Surplus
The difference between the actual amount received by sellers for a product and the least amount they would be willing to accept, representing the net benefit to producers.
- Analyze the resting price and quantity levels in both regulated and unregulated market environments.
- Recognize the concept of producer and consumer surplus, and elucidate the changes in these surpluses following interventions in the market.
- Analyze the impacts of minimum wage policies on the labor market.
Verified Answer
GS
Gurdeep Singh-GuriJul 09, 2024
Final Answer :
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
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
Learning Objectives
- Analyze the resting price and quantity levels in both regulated and unregulated market environments.
- Recognize the concept of producer and consumer surplus, and elucidate the changes in these surpluses following interventions in the market.
- Analyze the impacts of minimum wage policies on the labor market.