Heterogeneous consumers
A monopolist offers a single price to two consumers with the following demand functions:
p1(q1) = 120 − q1
p2(q2) = 45 − 1/2 q2.
The firm experiences a constant marginal cost of production, c = 10.
a) Graph aggregate demand, marginal revenue and marginal cost on a single graph
b) Find the optimal price and resulting demands of consumers 1 and 2 (P ∗ , q∗ 1 and q ∗ 2 ).
Quantity effect of a specific tax
A regulator plans to impose a specific tax on a previously unregulated monopolist. Before imposing the tax, they want to know what the change in quantity produced will be from such a tax. The proposed specific tax is τ = 10 and the following are the inverse demand and total cost functions:
P(Q) = 100 − 1/8Q
C(Q) = 20 + 10Q + 1/8Q^2 .
Find the change in quantity from a $10 increase in the tax.