# The demand curve for labor is  Q=100-5P. The supply curve is Q=5P. Helpful hint. The indirect (inverse) demand curve is P=20-0.2Q a) What is the equilibrium price and quantity. b) What is the consumer surplus? c) What is the producer surplus? d) What is the total surplus?

Tushar Chandra | Certified Educator

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The demand curve for labor is  Q=100-5P and the supply curve is Q=5P.

At the equilibrium point, the demand curve and the supply curve intersect each other. If the equilibrium price is Pe, the quantity buyers are willing to buy at Pe is equal to the quantity sellers are willing to sell.

To determine Pe, solve 100 - 5Pe = 5*Pe.

100 = 10*Pe

Pe = 100/10 = 10

The equilibrium price is 10.

At this price on the demand curve, the quantity demanded is equal to 100 - 5*10 = 50. On the supply curve, the quantity supplied is also equal to 50.

Consumer surplus is a way to quantify consumer benefit. It is equal to the difference between the amount that consumers are willing to pay for a service and the amount that they actually pay for it.

The demand curve we are given is Q=100-5P. If the price of labor is 0, the quantity demanded is 100. Consumer surplus is the area below the demand curve for which price is greater than the equilibrium price.

This is equal to (1/2)*(20-10)*(100-50) = 0.5*10*50 = 250

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