Ch. 15 & 16 Worksheet — Answer Key

Step 1 — MR = MC: 60 − 2Q = Q → 3Q = 60 → Q = 20 Step 2 — Price off demand: P = 60 − Q = 60 − 20 = $40 Step 3 — Profit: TR = 40 × 20 = $800. TC = 60 + 0.5(400) = $260. Profit = 800 − 260 = $540 Common mistake: reading P off MR instead of demand. MR at Q=20 is 60 − 40 = 20, but buyers pay the demand price of $40.

P = MC: Since P = 60 − Q (demand) and MC = Q, set 60 − Q = Q → Q = 30 Price: P = 60 − 30 = $30 Profit: TR = 30 × 30 = $900. TC = 60 + 0.5(900) = $510. Profit = 900 − 510 = $390 Comparison: moving from monopoly to perfect comp, Q rises (20 → 30), P falls ($40 → $30), profit falls ($540 → $390). Society is better off; the firm is worse off.

Demand = MC: 130 − 2Q = 10 + Q → 3Q = 120 → Q = 40 Price: P = 130 − 2(40) = $50 At this Q, the marginal buyer’s willingness to pay ($50) exactly equals marginal cost ($50). No beneficial trade is left unmade — the efficient outcome.

MR = MC: 130 − 4Q = 10 + Q → 5Q = 120 → Q = 24 Price from demand: P = 130 − 2(24) = 130 − 48 = $82 The trap: reading P off MR gives MR(24) = 130 − 96 = $34, which is way too low. The monopolist charges the demand price, not the MR value.

CS (triangle above P=82, below demand, Q = 0 to 24): Demand intercept = 130. Height = 130 − 82 = 48. Base = 24. CS = ½ × 24 × 48 = $576 PS (trapezoid above MC, below P = 82, Q = 0 to 24): MC(0) = 10, MC(24) = 34. Heights: 82 − 10 = 72 and 82 − 34 = 48. PS = ½ × (72 + 48) × 24 = ½ × 120 × 24 = $1,440 DWL (triangle between demand and MC, Q = 24 to 40): At Q = 24: demand = 82, MC = 34 (gap = 48). At Q = 40: they meet at 50. Base = 16, height = 48. DWL = ½ × 16 × 48 = $384

TC at Q = 24: 15 + 10(24) + 24² = 15 + 240 + 576 = $831 ATC: 831 / 24 ≈ $34.63 Profit: (P − ATC) × Q = (82 − 34.625) × 24 = 47.375 × 24 ≈ $1,137 Cross-check: TR − TC = (82 × 24) − 831 = 1,968 − 831 = $1,137 ✓

The government creates monopoly power by granting exclusive rights — patents (drugs, inventions), copyrights (books, software), and special licenses. One of the three barriers to entry from Mankiw Ch 15.

Profit-max quantity is where MR = MC, which is Q = O. Read the price UP from O to the demand curve (not MR) → price = B The classic trap: reading the price off MR instead of demand would give a lower value, undershooting the true monopoly price.

Profit-max rule: produce where MR = MC. MR crosses MC at quantity O. At N, MR > MC (produce more). At P, MR < MC (produce less).

Profit = (Price − ATC) × Quantity At Q = O: price (from demand) is B; ATC (from ATC curve) is Z. So profit = (B − Z) × O Option D (0.5 × base × height) is the formula for a TRIANGLE — that’s deadweight loss, not profit.

Every firm maximizes profit where MR = MC. For a monopolist, the price is read from the demand curve, which sits strictly above MR. So P > MR = MC at the profit-max quantity. This inequality is exactly why monopoly creates deadweight loss.

The monopolist produces where MR = MC, but the efficient level is where D = MC. Since MR < D, Qm < Qe. The units between Qm and Qe have P > MC (beneficial trades) but don’t happen — the DWL triangle.

Price discrimination is generally legal and widespread: student discounts, senior discounts, airline tickets, coupons, hardcover vs paperback, quantity discounts. Antitrust restricts only narrow forms meant to harm competitors. In Mankiw’s framing, price discrimination often actually raises efficiency — it increases both profits AND total output relative to uniform-price monopoly.

Defining feature visible in the graph: ATC is still declining across the relevant output range, and MC lies below ATC (as it must when ATC is falling). A single firm can supply the entire market at lower cost than several firms could. You can’t tell a patent monopoly from a figure — that’s a legal fact, not a geometric one.

Profit-max rule: MR = MC. Reading from Figure 15-10, MR crosses MC at approximately Q = 3. The price (read off demand at Q = 3) is about $7. Q = 7.5 would be the socially efficient output (where D = MC), not the monopolist’s choice — a classic trap answer.

Every profit-max firm — competitive, monopoly, monopolistic comp — produces where MR = MC. For a monopolistically competitive firm, MR < P (downward-sloping demand), so P > MC at profit-max. Choices C and D describe perfect competition.

Profit-max Q: MR = MC at Q ≈ 30. Price: read UP from Q = 30 to the demand curve → $70 $40 would be the value on MR at Q = 30 — the classic mistake of reading the price off MR instead of demand.

CS is the triangle above price, below demand, from Q = 0 to Q = 30. Demand intercept = $100. Price = $70. Base = 30. Height = 100 − 70 = 30. CS = ½ × 30 × 30 = $450

Profit = (P − ATC) × Q At Q = 30: P = $70, ATC ≈ $50. Profit = ($70 − $50) × 30 = $600 If this were long-run equilibrium, demand would be tangent to ATC and profit = 0. Here they cross, signaling positive short-run profit that would attract entry.

Like a monopoly, a monopolistically competitive firm faces downward-sloping demand, so MR < P. Setting MR = MC gives P > MC. Every unit beyond the profit-max Q would benefit buyers (P > MC) but isn’t produced. Options B, C, D are wrong: output is not excessive (quite the opposite); long-run profits are zero under free entry; and monopolistic competition has NO barriers to entry.

The statement has them backwards. Monopolistic competition = many sellers offering differentiated products (restaurants, clothing brands, books). Oligopoly = a few sellers, often similar products (airlines, wireless carriers, oil refiners).

The view of advertising is still debated. Critics: ads manipulate preferences, impede competition, act as a barrier to entry. Defenders: ads provide information and intensify competition. There’s no consensus that advertising is efficiency-enhancing.

In long-run equilibrium, P = ATC (zero economic profit, demand tangent to ATC). But P > MC — the firm produces on the downward-sloping part of ATC, not at the minimum. So P = ATC but P ≠ MC. Perfect competition: P = MC = min ATC (all equal). Monopolistic comp: P = ATC > MC.

Both face downward-sloping demand curves, so MR < P. Setting MR = MC then gives P > MC. Shared by all firms with market power — monopoly, monopolistic competition, oligopoly.