Practice Worksheet

Chapter 15 — Monopoly

Part 1

Short Answer — Smartphone Monopoly

Given Consider a market for smartphones with a single firm (monopoly). The market demand is given below, along with the monopolist's cost and revenue curves.

Demand: Q_d = 60 − P TC = 60 + 0.5Q² MC = Q MR = 60 − 2Q

Question a

Find the profit-maximizing quantity, price, and profit for this monopolist.

Quantity (Q)

Price (P)

Profit ($)

Hint Three-step monopoly recipe: (1) Set MR = MC and solve for Q. (2) Plug that Q into the demand curve to find P (never read P off MR). (3) Profit = TR − TC = P Q − (60 + 0.5Q²).

Explanation Step 1: MR = MC → 60 − 2Q = Q → 3Q = 60 → Q = 20.
Step 2: From demand, Q = 60 − P so P = 60 − Q = 60 − 20 = $40.
Step 3: TR = 40 × 20 = $800. TC = 60 + 0.5(20)² = 60 + 200 = $260.
Profit = 800 − 260 = $540.

Question b

Now suppose the firm behaves as if this were a perfectly competitive market — producing where P = MC. Find the quantity, price, and the firm's profit under that rule.

Quantity (Q)

Price (P)

Profit ($)

Hint Under perfect competition the firm produces where P = MC, with P determined by where that Q intersects the demand curve. Since MC = Q and P = 60 − Q (from demand), set them equal: Q = 60 − Q. Then compute profit with the same TC formula.

Explanation Step 1: P = MC → 60 − Q = Q → 2Q = 60 → Q = 30.
Step 2: P = 60 − 30 = $30.
Step 3: TR = 30 × 30 = $900. TC = 60 + 0.5(30)² = 60 + 450 = $510.
Profit = 900 − 510 = $390.

Notice: compared to part (a), quantity rose from 20 → 30 (more output), price fell from $40 → $30 (better for consumers), but profit fell from $540 → $390. The monopolist captures less, but society produces the efficient amount.

Part 2

Short Answer — Prescription Drug Monopoly

Given A new prescription drug is protected by a patent, so the market is a monopoly. Demand, marginal cost, and marginal revenue are given below.

Demand: P = 130 − 2Q MC = 10 + Q MR = 130 − 4Q

Question c

What is the socially optimal level of production? Find the quantity and price where demand equals marginal cost.

Q (efficient)

P (efficient)

Hint Social optimum is where the last unit's benefit (P on demand) equals its cost (MC). Set 130 − 2Q = 10 + Q and solve for Q, then plug back into demand to get P.

Explanation Set demand = MC: 130 − 2Q = 10 + Q → 3Q = 120 → Q = 40.
P = 130 − 2(40) = 130 − 80 = $50.

At this quantity, the benefit to the marginal consumer ($50) exactly equals the cost of producing that unit (MC = 10 + 40 = $50). No mutually beneficial trade is left unmade — the socially efficient outcome.

Question d

What is the monopolist's profit-maximizing quantity and price? (Set MR = MC.)

Q (monopoly)

P (monopoly)

Hint MR = MC: 130 − 4Q = 10 + Q. Solve for Q. Then plug into the demand curve (not MR) to get P.

Explanation Set MR = MC: 130 − 4Q = 10 + Q → 5Q = 120 → Q = 24.
From the demand curve: P = 130 − 2(24) = 130 − 48 = $82.

The monopolist produces 24 units (less than the efficient 40) and charges $82 (far more than the efficient $50). This is the source of every welfare problem in Part (e).

Question e

At the monopoly outcome from (d), compute consumer surplus, producer surplus, and the deadweight loss.

Consumer Surplus

Producer Surplus

Deadweight Loss

Hint CS is the triangle above P = 82 and below demand, from Q=0 to Q=24. PS is the area above MC and below P = 82 from Q=0 to Q=24 (a trapezoid, since MC starts at 10 and rises to 34). DWL is the triangle between demand and MC from Q = 24 (monopoly) to Q = 40 (efficient).

Explanation Consumer Surplus: triangle with base 24, height 130 − 82 = 48.
CS = ½ × 24 × 48 = $576.

Producer Surplus: trapezoid above MC, below P = 82, from Q = 0 to Q = 24.
MC at Q = 0 is 10; MC at Q = 24 is 34. Heights: 82 − 10 = 72 and 82 − 34 = 48.
PS = ½ × (72 + 48) × 24 = ½ × 120 × 24 = $1,440.

Deadweight Loss: triangle between demand and MC from Q = 24 to Q = 40.
At Q = 24: demand = 82, MC = 34 (gap of 48). At Q = 40: they meet at 50.
DWL = ½ × (40 − 24) × (82 − 34) = ½ × 16 × 48 = $384.

Question f

Given the total cost curve TC = 15 + 10Q + Q², what is the monopolist's average total cost at Q = 24, and what is the monopolist's profit?

ATC at Q = 24

Profit

Hint Plug Q = 24 into TC to get total cost. ATC = TC / Q. Profit = (P − ATC) × Q, or equivalently TR − TC.

Explanation TC = 15 + 10(24) + (24)² = 15 + 240 + 576 = $831.
ATC = 831 / 24 ≈ $34.63.

Profit = (P − ATC) × Q = (82 − 34.625) × 24 = 47.375 × 24 = $1,137.
Or equivalently: TR − TC = (82 × 24) − 831 = 1,968 − 831 = $1,137.

Part 3

Multiple Choice

Question 1

A government-created monopoly arises when:

government spending in an industry gives rise to monopoly power the government encourages competition among sellers the government gives a firm the exclusive right to sell some good or service the government collects taxes in a particular industry

Hint A government-created monopoly is one where the government deliberately creates a barrier to entry by law. Patents and copyrights are the classic examples.

Explanation Answer: C. The government creates monopoly power by granting exclusive rights — patents (drugs, inventions), copyrights (books, software), and special licenses. Spending and taxation (A, D) don't create monopolies, and encouraging competition (B) is the opposite of creating one.

Question 2 — Refer to Figure 15-4

What price will the monopolist charge in order to maximize profit?

X Z B C

Hint Step 1: find the Q where MR = MC. Step 2: read the price straight up on the demand curve (not MR) at that Q.

Explanation Answer: B. MR intersects MC at quantity O. Going straight up from O to the demand curve gives the monopoly price = B. Students who mistakenly read the price off the MR curve would pick a lower level — that's the classic error this question is designed to catch.

Question 3 — Refer to Figure 15-4

How much output will the monopolist produce in order to maximize profit?

0 N O P

Hint The profit-maximizing rule for any firm is produce where MR = MC. Find where those two curves cross in the figure and read down to the quantity axis.

Explanation Answer: O. MR crosses MC at quantity O. That's the profit-maximizing output. At N, MR > MC (produce more). At P, MR < MC (produce less). Only at O is MR = MC exactly.

Question 4 — Refer to Figure 15-4

What area measures the monopolist's profit?

(B − Z) × O (C − X) × N (B − Y) × O 0.5 × [(B − Z) × (P − N)]

Hint Profit = (Price − ATC) × Quantity. The price is read from the demand curve at Q = O. The ATC is read from the ATC curve at Q = O. Multiply that vertical gap by the quantity.

Explanation Answer: (B − Z) × O. At Q = O, the monopoly price (from demand) is B, and ATC is Z. The profit rectangle has height (B − Z) and width O, so area = (B − Z) × O.

Option D is the formula for a triangle — that would be the deadweight loss, not profit. Option B uses the wrong price, ATC, and quantity. Option C uses Y instead of Z for ATC.

Question 5

Why is marginal revenue less than price for a monopolist, but equal to price for a competitive firm?

A monopolist has no supply curve, so MR is meaningless To sell one more unit, a monopolist must lower the price on all units; a competitive firm can sell more at the going price without cutting it Monopolies face higher marginal costs than competitive firms Competitive firms face downward-sloping demand while monopolies face horizontal demand

Hint Think about the two effects of selling one more unit. A monopolist gets the price for the new unit (output effect, good), but also has to lower the price on every unit already being sold (price effect, bad). A competitive firm doesn't have the second effect.

Explanation Answer: B. A competitive firm is a price taker on a horizontal demand curve — it can sell any quantity at the market price. A monopolist faces the entire downward-sloping market demand curve, so raising Q by one unit forces the price down on every existing unit too. The resulting price effect pulls MR below P: MR = P + Q(ΔP/ΔQ), with ΔP/ΔQ < 0.

Option D has the two firms' demand curves backwards.

Question 6

Which of the following is NOT a source of monopoly power?

A single firm owns a key resource required for production The government grants one firm exclusive rights to produce the good One firm can supply the entire market at lower average total cost than two or more firms could A firm undercuts competitors' prices to attract more customers

Hint Monopoly requires barriers to entry — something that keeps competitors out. Mankiw lists three: resource ownership, government grant, and natural monopoly. Which option is normal competitive behavior?

Explanation Answer: D. Undercutting competitors' prices is the behavior of competitive firms — it's exactly what entry and competition look like. Options A (key resource), B (government grant / patent), and C (natural monopoly / economies of scale) are Mankiw's three barriers to entry that create monopoly power.

Question 7

A natural monopoly exists when:

the monopoly was created without any government intervention a single firm can supply the entire market at lower cost than two or more firms could, because ATC is still declining at the market's output the product sold by the monopolist comes from natural resources the government regulates the industry's prices

Hint "Natural" here has nothing to do with natural resources. It's about cost structure — specifically whether one firm can beat any group of firms on cost.

Explanation Answer: B. A natural monopoly arises from cost structure: when average total cost is still declining at the level of output the market demands, a single firm can serve the whole market more cheaply than several competing firms. Classic examples: water pipes, electrical grids, subway systems. The word "natural" refers to the natural (cost-driven) tendency toward one firm, not natural resources.

Part 4

True or False

Question 8

A monopolist produces where P > MC = MR.

Hint The profit-max rule is MR = MC. At that quantity, where does the monopolist read the price from? The demand curve, which sits above MR.

Explanation True. Every firm maximizes profit where MR = MC. For a monopolist, the price is then read from the demand curve, which sits strictly above MR. So P > MR = MC. This is a core identity of monopoly pricing and also explains why there's deadweight loss: the marginal buyer would pay more than the marginal cost, but the monopolist still won't sell that unit.

Question 9

A monopoly creates a deadweight loss to society because it produces less output than the socially efficient level.

Hint Socially efficient quantity is where demand meets MC (every beneficial trade gets made). A monopolist stops at a smaller Q. What happens to the units in between?

Explanation True. A monopolist produces where MR = MC, but the socially efficient level is where D = MC. Since MR < D, the monopoly Q is smaller. The units between Qm and Qe have P > MC (beneficial trades), but they never happen. The lost surplus is the deadweight loss — a triangle between D and MC from Qm out to Qe.

Question 10

Price discrimination is prohibited by antitrust laws.

Hint Think about movie theater student discounts, senior citizen discounts, airline tickets, coupons. All of those are forms of price discrimination. Are any of those illegal?

Explanation False. Price discrimination is generally legal and in fact widespread: student discounts, senior citizen discounts, airline tickets (with different fares for business vs leisure travelers), quantity discounts, coupons, hardcover vs paperback books. Antitrust laws only restrict certain narrow forms meant to harm competitors (predatory pricing or clearly discriminatory wholesale pricing under the Robinson-Patman Act). In Mankiw's framing, price discrimination often actually improves efficiency — it raises both profits and total output relative to uniform-price monopoly.

Question 11

A monopolist can charge any price it wants without losing customers.

Hint A monopolist faces the market demand curve — and the market demand curve slopes downward. If the monopolist doubles the price, what happens to quantity demanded?

Explanation False. This is a common misconception. A monopolist is a price maker, not a price fixer. It faces the entire market demand curve, which slopes down — higher price means fewer customers. The monopolist picks the price/quantity combination on the demand curve that maximizes profit (by setting MR = MC). If it charged an arbitrarily high price, quantity demanded would fall, possibly to zero.

Part 5

Refer to Figure 15-10

Figure 15-10 A firm faces the demand, MR, MC, and ATC curves shown below. Use the figure to answer the next two questions.

The declining ATC curve intersected by demand while still falling is the classic signature of a natural monopoly.

Question 12 — Refer to Figure 15-10

What type of monopoly is shown in the figure?

A competitive firm (not a monopoly at all) A natural monopoly A government-created monopoly from a patent A perfectly price-discriminating monopoly

Hint Look at the ATC curve. Is it U-shaped, or is it still declining where demand crosses it? A declining ATC across the relevant range is the signature of what kind of monopoly?

Explanation Answer: B — a natural monopoly. The defining feature visible in the graph: ATC is still declining all the way across the relevant output range, and MC lies below ATC (as it must when ATC is falling). This is a cost structure in which a single firm can supply the whole market more cheaply than several firms could. You can't identify a patent monopoly from a figure — that's a legal fact, not a geometric one.

Question 13 — Refer to Figure 15-10

If the firm profit-maximizes, what amount of output will it produce?

Q = 1 Q = 3 Q = 5 Q = 7.5 (where demand meets MC)

Hint The profit-maximizing rule is the same as for any firm: produce where MR = MC. Find where the MR curve crosses the MC curve in the figure, not where demand crosses MC.

Explanation Answer: Q = 3. The profit-max rule is MR = MC. Reading from the figure, MR crosses MC near Q = 3. At that quantity, price (read off demand, not MR) is about $7. Q = 7.5 would be the socially efficient output (where D = MC), not the monopolist's choice — a classic trap answer.

Your Score

0 / 13

Keep Practicing

Return to Lesson