Question

2. Let the willingness to pay for apples at a particular farm be WTP 30 Q/3 and the marginal cost of producing apples be MCQ/3. 1. [10] What is the efficient level of apple production and the net economic benefit?

Answer 1

Demand function:

WTP = P = 30 – Q/3

Supply function:

MC = P = Q/3

Efficient level is (P = MC).

P = MC

30 – Q/3 = Q/3

Q/3 + Q/3 = 30

2Q/3 = 30

2Q = 30 × 3

2Q = 90

Q = 90/2 = 45

Answer: The efficient level is 45 units of production.

Economic benefit is the aggregate of consumer surplus (CS) and producer surplus (PS).

Calculation of CS:

WTP = P = 30 – Q/3

Since (Q = 45), P would be (30 – 45/3 = 30 – 15 =) 15; coordinate (Q, P) is (45, 15)

If (Q = 0), P would be (30 – 0/3 = 30 – 0 =) 30; coordinate (Q, P) is (0, 30)

CS = 0.5 × Difference in Q × Difference in P

      = 0.5 × (45 – 0) × (30 – 15)

      = 0.5 × 45 × 15

      = 337.5

Calculation of PS:

MC = P = Q/3

Since (Q = 45), P would be (45/3 =) 15; coordinate (Q, P) is (45, 15)

If (Q = 0), P would be (0/3 =) 0; coordinate (Q, P) is (0, 0)

PS = 0.5 × Difference in Q × Difference in P

      = 0.5 × (45 – 0) × (15 – 0)

      = 0.5 × 45 × 15

      = 337.5

Economic benefit = CS + PS

                              = 337.5 + 337.5

                              = 675 (Answer)