Question

Consider an aggregate supply curve described by MC =5 + Q and an aggregate demand curve described by MWTP = 20 –2 Q.
2a. What is the consumer surplus in the market equilibrium?
2b. What is the producer surplus in the market equilibrium?

Answer 1

Equilibrium:

Demand = Supply

20 – 2Q = 5 + Q

Or, 20 – 5 = Q + 2Q

Or, 15 = 3Q

Or, 15/3 = Q

Or, Q = 5

Now by putting this value in either the demand function or supply function we will get price.

MWTP = P = 20 – 2Q

   = 20 – 2 × 5

   = 20 – 10

   = 10

2a.

Consumer surplus (CS) is on the demand function.

P = 20 – 2Q

The P has to be searched (maximum price) where (Q = 0).

If (Q = 0); P = 20 – 2 × 0 Or, P = 20 – 0 Or, P = 20; the coordinate (Q, P) is (0, 20).

Equilibrium coordinate (as calculated above) is (5, 10).

Therefore,

CS = 0.5 × Difference in P × Difference in Q

      = 0.5 × (20 – 10) × (5 – 0)

      = 0.5 × 10 × 5

      = 25 (Answer)

Note: 0.5 is the part of formula.

2b.

Producer surplus (PS) is on the supply function.

P = MC = 5 + Q

The P has to be searched (minimum price) where (Q = 0).

If (Q = 0); P = 5 + 0 Or, P = 5; the coordinate (Q, P) is (0, 5).

Equilibrium coordinate (as calculated above) is (5, 10).

Therefore,

PS = 0.5 × Difference in P × Difference in Q

      = 0.5 × (10 – 5) × (5 – 0)

      = 0.5 × 5 × 5

      = 12.5 (Answer)

Note: 0.5 is the part of formula.