Question

The annual market marginal demand curve for electricity is MB=400-1.5Q. The annual marginal cost curve is MC=50+Q. The government is considering whether to build one of three plants. The first will have a maximum production capacity of 50 units of Q; the second a maximum capacity of 100 units, and the third, a maximum capacity of 200 units. Plants need to be operated at maximum capacity; otherwise, excess investment cost (not depicted in the diagram) will be incurred. Given this background:

What is the annual benefit of the 50-unit plant?

What is the annual cost?

What is the annual net benefit?

What is the annual benefit of the 100-unit plant?

What is the annual cost?

What is the annual net benefit?

What is the annual benefit of the 200-unit plant?

What is the annual cost?

What is the annual net benefit?

Ignoring investment (capital) cost, if only one plant is to be built, which plant size should be built?

Assume that the investment cost is incurred annually, and the annual cost is equal to 5% of the total investment cost (e.g., if the total investment cost is $1 million, then the annual investment cost would be 0.05*$1million=$50,000). What is the highest total investment cost at which the plant with the highest net benefit (the answer to the previous question) should still be built?

Answer 1

MB=400-1.5Q. and MC=50+Q
a) 50 unit plant
MB = 400 - ( 1.5 * 50 ) = 325
MC = 50 + 50 = 100
Net benefit = 325 - 100 = 225

b) 100 unit plant
MB = 400 - ( 1.5 * 100 ) = 250
MC = 50 + 100 = 150
Net benefit = 250 - 150 = 100

c) 200 unit plant
MB = 400 - ( 1.5 * 200 ) = 100
MC = 50 + 200 = 250
Net benefit = 100 - 250 = -150

d) The 50 unit plant has the highest net benefits and so it should be built.
The 200 unit plant has actually negative net benefits.

e) The annual cost is 5% of the investment cost so,
Investment Cost = ( 100 * 100 ) / 5 = 2000
The investment cost for the plant is 2000.