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.