Suppose the inverse demand for coal is estimated to be P 75

Suppose the inverse demand for coal is estimated to be P = 75 - 0.6Q, where P is the price of coal and Q is the quantity demanded. The supply of coal is given by P = 0.3Q.

1.  Suppose coal mining produces an external marginal user cost. This cost equals $25 for each unit of production. Calculate and show graphically the socially efficient equilibrium price and quantity of coal.

On your graph of the efficient equilibrium, label and calculate the areas corresponding to

(i) CS

(ii) Scarcity rents

(iii) Quasi-rents

(iv) TVC

(v) Social net benefits (SNB)

Solution

Inverse Demand: P = 75 - 0.6Q

Supply Schedule: P = 0.3Q

Marginal social cost Schedule: Supply + MEC = P = 0.3Q + 25Q = 25.3Q

Solving DD and SS , we get

75 - 0.6Q = 25.3Q

25.9Q = 75

Q = 75/25.9 = 2.9

P = 75 - (0.6*2.9) = 75 - 1.74 = 73.26