Answer to Question #148513 in Economics for Luke Williams

Question

Consider a town with two neighbors. They are considering planting some trees in their town. There is a public good in this economy from the trees in the form of fresh air, an increase in the bird population, and shade. Neighbor-A demand for trees is given by P1 = 500-2Q. Neighbor-B demand for trees is given by P2 = 250 -3Q. The marginal cost of planting trees in the town is given by MC = 150. How many trees will be planted in the town? What is the price paid by each neighbor for the trees?

Answer 1

P1 = 500 - 2Q and P2 = 250 - 3Q, so $MR1 = TR'(Q) = 500 - 4Q,$

MR1 = MC,

500 - 4Q = 150,

Q = 87.5 units,

P = 500 - 2×87.5 = 325.

MR2 = 250 - 6Q,

MR2 = MC,

250 - 6Q = 150,

Q = 16.67 units,

P = 250 - 3×16.67 = 200.