Question

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?

A) -$25

B) -$150

C) -$175

D) -$200

Please provide a explanation! thank you!

Answer 1

In the above question

Market Demand is P = 70 - 2Q

Market Supply is P = 10 + Q

First we need to find equilibrium price and quantity

70 - 2Q = 10 + Q

3Q = 60

Q = 20

Hence equilibrium quantity is 20 units

Now we can find equilibrium price by putting equilibrium quantity in any of the two equations

P = 10 + Q

P = 10 + 20

P = $30

Now consumer surplus represents the shaded area which is a triangle in the graph. So to find area of the shaded region we will use

Area = 1/2 x base x height

Area = 1/2 x 20 x 40

Area = 400

Hence consumer surplus will be 400 at equilibrium

Now, if there is a price floor of $40 then

Price = $40 and to find quantity demanded at this price we will insert this price in demand equation to find quantity demanded.

P = 70 - 2Q

40 = 70 - 2Q

Q = 15

Now the shaded area represents the new consumer surplus when there is a price floor.

Area = 1/2 x base x height

Area = 1/2 x 15 x 30

Area = 225

Hence consumer surplus will be 225 at a price floor of $40

Change in consumer surplus is

225 - 400

= -175

Thus option C is correct