The production of lumber creates many externalities. Suppose that the perfectly competitive market supply and demand equations are respectively:

QS(P) = (5/4) P - 25

QD(P) = 225 - (5/4)P

Units are $/ log for prices and costs and logs for quantities.

* assume all benefits, costs and surplus and related efficiency concepts are measured using money which is not equity-weighted.

a) Find the inverse demand and inverse supply equations and plot on a graph. name it Fig 1

b) Set the marginal consumer benefit equal to the marginal producer cost to find the market equilibrium quantity and substitute back into either the inverse demand or supply equation to find the market equilibrium price. Show your work and label Pmarket and Qmarket on Fig. 1.

c) Suppose that the marginal external cost is: MCexternal = 20 + Q.

d) Write down an equation for the marginal social cost as a function of output (Q). Redraw the marginal benefit consumer and marginal cost producer curves and then plot the marginal external cost and the marginal social cost curves on the graph.

e) Calculate the socially efficient equilibrium price and quantity (show your work). Label on your graph.

i) For the socially efficient allocation, label the following. i) total external costs

ii) total social costs

iii) total social benefits iv) total social surplus

f) total consumer benefits

g) Calculate the gain in total social surplus due to reducing lumber from the perfectly competitive

market level to the socially efficient level. Label the deadweight loss of the market.

h) Label the socially efficient quota.