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, whereP is the price of coal and Q is the quantity demanded. The supply of coal is given by P = 0.3Q.

1. (3 points) Graph inverse demand and inverse supply. Calculate and show graphically the price and quantity of coal in a competitive equilibrium in which producers do not consider the future impacts of their actions (i.e., the marginal user cost is external). Also graph the equilibrium values of:

(i) MWTA by producers

(ii) MC of production

(ii) WTA by producers

(iii) Total variable costs (TVC)

(iv) Total revenue

(v) PS (what kind of rent is this?)

(vi) CS

Solution

P = 75 - 0.6Q

P = 0.3Q.

In equilibrium Demand = supply

75 - 0.6Q = 0.3Q

0.9Q = 75

Q =75/0.9 = 83.33

P = 25

Perfect competition equilibrium is where MR = MC = AR = P = $25.

Total revenue = P*Q = 25*83.33 = $2083.25

Consumer surplus =area under the demand curve, over the price

CS = 0.5*83.33*(75-25) = $6249.75

Producer surplus is zero in perfect competition.

Since no information about cost is given, if MC = 25, AC = 25 and TC =25Q