A (classic) monopolist faces a demand curve given by Q(P) = 100 – 0.25P and a continuously divisible product in a factory with cost function TC(Q) = 3.5Q^2 + 100Q + 600. a: Calculate the inverse demand curve P(Q), total revenue curve TR(Q), marginal revenue curve MR(Q), and marginal cost curve MC(Q). b: Carefully write out this firm’s profit maximization problem, using the particulars of this problem. c: Give the marginal condition (equation) that characterizes the solution to this problem. Solve this condition for the firm’s optimal quantity Q*.
A (classic) monopolist faces a
a: Calculate the inverse demand curve P(Q), total revenue curve TR(Q), marginal revenue curve
MR(Q), and marginal cost curve MC(Q).
b: Carefully write out this firm’s profit maximization problem, using the particulars of this
problem.
c: Give the marginal condition (equation) that characterizes the solution to this problem. Solve
this condition for the firm’s optimal quantity Q*.
d: Calculate the optimal price.
e: Calculate the firm’s maximized profit.
f: On a graph with quantity on the horizontal axis, neatly plot the marginal revenue curve and
marginal cost curve. Show Q* on your graph.
g: Label areas on your graph using a, b, c, etc. and indicate the areas that correspond to total
revenue, variable cost, and
h: Calculate the firm’s producer surplus at Q*
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