The market supply function is P = 10 + Q and the market demand function is P = 70 - 2Q. What is the change in consumer surplus associated with a minimum floor price of $40?

Question

Quizplus · Accepted Answer

To find the change in consumer surplus, we need to first find the equilibrium price and quantity, which is where the market supply and demand curves intersect.

Setting the market supply function equal to the market demand function:

10 + Q = 70 - 2Q

Solving for Q:

3Q = 60

Q = 20

Substituting Q = 20 into either the market supply or demand function gives us the equilibrium price:

P = 70 - 2(20) = 30

Now, if there is a minimum floor price of $40, that means the price cannot go below $40. We need to find the new equilibrium quantity, which is where the market supply and demand curves intersect at a price of $40:

10 + Q = 40 - 2Q

Solving for Q:

3Q = 30

Q = 10

So the new equilibrium is at a price of $40 and a quantity of 10.

To find the change in consumer surplus, we first need to calculate the original consumer surplus:

Consumer Surplus = (1/2)(Base)(Height)

Base = 20 (quantity at the original equilibrium price of $30)

Height = (70 - 30) = 40 (difference between the original equilibrium price and the maximum price consumers were willing to pay)

Consumer Surplus = (1/2)(20)(40) = $400

Now, with the new equilibrium price of $40 and quantity of 10, the new consumer surplus is:

Base = 10 (quantity at the new equilibrium price of $40)

Height = (70 - 40) = 30 (difference between the new equilibrium price and the maximum price consumers are willing to pay)

Consumer Surplus = (1/2)(10)(30) = $150

So the change in consumer surplus is:

Change in Consumer Surplus = New Consumer Surplus - Original Consumer Surplus

Change in Consumer Surplus = $150 - $400 = -$250

Thus, the answer is C, which is a decrease in consumer surplus of -$175.

The Market Supply Function Is P = 10 + Q