12.07.2022 - 05:02

# Suppose that you are the vice president of operations of a manufacturing firm that sells an industrial lubricant in a competitive market. Further, suppose that your economist gives you the following supply and demand functions. Demand: Q_D = 50 – 2P Suppl

Question:

Suppose that you are the vice president of operations of a manufacturing firm that sells an industrial lubricant in a competitive market. Further, suppose that your economist gives you the following supply and demand functions.

Demand: {eq}Q_D = 50 – 2P {/eq}

Supply: {eq}Q_S = -10 + P {/eq}

A. What is the consumer surplus in this market?

B. What is the producer surplus?

A. To calculate the consumer surplus, we first need to find the equilibrium price and quantity. We can do this by setting the quantity demanded equal to the quantity supplied: 50 - 2P = -10 + P Solving for P: 3P = 60 P = 20 Plugging this back into either the demand or supply function, we can find the equilibrium quantity: Q = 50 - 2(20) = 10 Now, to find the consumer surplus, we need to calculate the area between the demand curve and the equilibrium price, from 0 to the equilibrium quantity (10). This is the area of a triangle with a base of 10 (the quantity) and a height of (50-20) = 30 (the difference between the highest price consumers are willing to pay and the equilibrium price): Consumer Surplus = 0.5 x 10 x 30 = 150 Therefore, the consumer surplus in this market is $150. B. To find the producer surplus, we need to calculate the area between the supply curve and the equilibrium price, from 0 to the equilibrium quantity (10). This is also the area of a triangle with a base of 10 (the quantity) and a height of (20 - (-10)) = 30. Producer Surplus = 0.5 x 10 x 30 = 150 Therefore, the producer surplus in this market is also$150.