Microeconomics, monopoly, final exam practice problems
(The attached PDF file has better formatting.)
*Question 1.1: Marginal Revenue
Assume the demand curve is linear.
At P = $100, total revenue is $200,000.
At P = $80, total revenue is $240,000.
What is the marginal revenue per unit at P = $120? If you find the demand curve as Q in terms of P, you must convert this to P in terms of Q before finding the marginal revenue curve.
Answer 1.1: B
Solution: The demand curve is Q = α – β × P
At P = $100, total revenue = $200,000, so Q = 2,000
At P = $80, total revenue = $240,000, so Q = 3,000
We use these values to solve for α and β in the demand curve.
2,000 = α – β × 100
3,000 = α – β × 80
A 1,000 = 20 β A β = 50 and α = 7,000
Q = 7,000 – 50P, so at P = 120, Q = 1,000.
P = 7,000 / 50 – 0.02Q = 140 – 0.02Q
The total revenue curve is TR = 140Q – 0.02Q2.
The marginal revenue curve is MR = 140 – 0.04Q.
At P = $120, Q = 1,000, and marginal revenue is 140 – 0.04 × 1,000 = $100
*Question 1.2: Elasticity
The price elasticity of demand facing a monopolist (at its equilibrium price) is which of the following?
–4 to –1
–1 to 0
0 to +1
+1 to +4
Answer 1.2: A
The law of demand says that the quantity demanded falls when the price rises, so the elasticity is negative.
Marginal revenue = price × (1 – 1/|η|), where η is the elasticity.
Marginal revenue = marginal cost at the equilibrium price. Marginal cost can not be negative, so marginal revenue is not negative at the equilibrium price.
The price is not negative, so (1 – 1/|η|) > 0 A 1 > 1/|η| A η < –1.
*Question 1.3: Price Elasticity of Demand Facing a Monopolist
Which of the following is true of the price elasticity of demand η facing a monopolist which prices at its optimal point?
The price elasticity of demand is between –4 and –1.
The price elasticity of demand is between –1 and 0.
The price elasticity of demand is between 0 and +1.
The price elasticity of demand is between +1 and +4.
The price elasticity of demand could be anywhere between –4 and +4.
Answer 1.3: A
The law of demand says that the price elasticity of demand is negative: if the price rises, consumers buy a smaller quantity.
If the market demand curve is flat (perfectly horizontal), the price elasticity of demand is –4 even for a monopolist. In practice, the market demand curve is never perfectly flat, though the demand curve facing a single firm in a competitive industry is flat.
If the demand facing the monopolist is inelastic, or between –1 and 0, a 1% increase in the price causes less than a 1% decrease in the quantity demanded, so revenue increases. The total production cost declines, since fewer goods are sold. The monopolist would raise the price, which causes revenue to increase and cost to decline, so profit increases.
*Question 1.4: Indications of Monopoly
Which is the best indication of monopoly power?
Economies of scale that require at $1 million in capital to compete
Having more patents than its peer companies in a high-tech industry
Ownership of much natural resources within the home country
Barriers to entry that prevent competitors from entering the industry
Game theoretic pricing in a prisoner’s dilemma game
Answer 1.4: D
Statement A: A $1 million capital requirement is not material in most industries.
Statement B: The number of patents is often irrelevant in high-tech industries, since one successful product may be worth 100 unsuccessful products.
Statement C: Ownership of natural resources in the home country is not critical. In developed countries, natural resources are imported from developing countries.
Statement E: The prisoners’ dilemma game occurs in some two firm duo-polies, not in one firm monopolies.
Statement D: Unless an industry has barriers to entry, a monopoly cannot sustain itself.
*Question 1.5: Natural Monopolies
Natural monopolies typically occur when
Fixed costs and marginal costs are both high.
Fixed costs are high and marginal costs are low.
Fixed costs are low and marginal costs are high.
Fixed costs and marginal costs are both low.
Fixed costs are low and marginal costs are highly variable.
Answer 1.5: B
For a municipal utility, such as phone service (before cell phones) or electricity service:
The fixed costs of laying the phone lines or electricity lines through the city requires digging up the streets to lay lines underground, which is a large cost.
Once these lines have been laid, adding an additional consumer requires connecting another home to the street lines, which is a small cost.
For a software maker (like Microsoft):
The fixed costs are research and development for a new product, which are high.
The marginal cost is the cost of burning a CD, which is small.
*Question 1.6: Supply Curves for Monopolists
A monopolist’s supply curve
Is the part of its marginal cost curve that lies above its minimum average costs.
Is the part of its marginal cost curve that lies above its minimum average variable costs.
Does not exist.
Coincides with its marginal revenue curve.
Is the part of its marginal revenue curve that lies above its minimum average costs.
Answer 1.6: C
A supply curve gives the quantity produced at each price. But the monopolist’s quantity depends on the demand curve, so it has no supply curve. Know the distinction:
A competitive firm’s output does not depend on the demand curve.
A monopolist’s output depends on the demand curve.
*Question 1.7: Monopoly and Demand Elasticity
A monopolist sells at price P*, where the price elasticity of demand is η*. If |η*| < 1, the percentage change in output is less than the percentage change in price. In this case,
The monopolist should increase output at least until demand becomes elastic.
The monopolist should decrease output at least until demand becomes elastic.
The monopolist should increase output at least until demand becomes inelastic.
The monopolist should decrease output at least until demand becomes inelastic.
The monopolist should increase its price at least until demand become inelastic.
Answer 1.7: B
Output (quantity) decreases but price increases more than proportionally, so total revenue increases.
Output (quantity) decreases A variable cost decreases A total cost decreases.
Revenue increases and cost decreases A total profit increases.
A monopolist always operates on the elastic part of the demand curve.
When demand is inelastic, marginal revenue is negative, since an increase in quantity demanded requires a greater (pricing) decrease in price.
Since marginal cost is always positive, this cannot be the optimal (equilibrium) point of production.
By decreasing output, the monopolist moves to a more elastic part of the demand curve.
Jacob: The question asks about a monopolist. Does this apply to a competitive firm as well?
Rachel: The demand curve facing a competitive firm is always infinitely elastic.
*Question 1.8: Competition vs Monopoly
Suppose 20 firms operate in a competitive market for wine. If the twenty firms merge and create a monopoly, but marginal costs do not decrease, all but which of the following are true? Assume the market demand curve is downward sloping, the marginal cost curve is upward sloping, the monopolists marginal cost curve is the market supply curve before the merger, and all firms maximize profits.
Consumers’ surplus decreases
Producers’ surplus increases
Social welfare remains the same
The equilibrium price increases
The equilibrium quantity decreases
Answer 1.8: C
The monopolist reduces quantity to increase price. This creates dead weight loss, so social welfare decreases.
Jacob: How do we know that producers’ surplus increases? Social welfare is consumers’ surplus plus producers’ surplus. If social welfare decreases, perhaps both consumers’ surplus and producers’ surplus decrease.
Rachel: If producers’ surplus decreased, the monopolist would charge the competitive price and produce the competitive quantity.
Jacob: How do we know that consumers’ surplus decreases?
Rachel: Social welfare decreases and producers’ surplus increases, so consumers’ surplus decreases even more than producers’ surplus increases.
*Question 1.9: Profit Maximization
Which of the following is true for any firm that maximizes profits and has an upward sloping marginal cost curve?
Producers’ surplus exceeds consumers’ surplus
Consumers’ surplus exceeds producers’ surplus
It produces at a point where the price elasticity of demand facing it is elastic
It produces at a point where the price elasticity of demand facing it is inelastic
It produces at a point where the price elasticity of demand facing it is –1
Answer 1.9: C
If the price elasticity of demand is –1 or more, the firm could produce less, raises prices by an equal or greater percentage amount, and have less costs of production.
If the firm operates in a competitive market, it faces a price elasticity of demand of –4
if the firm is a monopolist, it faces an elastic demand curve.
Jacob: What if the price elasticity of demand is –1 at all points? This is true if the demand curve is Q = k / P, where k is a constant.
Rachel: We can write such demand curves, but they are not realistic. Suppose that when P = $10, the firm sells 10,000,000 units of the good. This demand curve implies that if the firm offers only 100 units for sale, some consumers will pay $1,000,000 apiece, and if it offers only 1 unit for sale, some consumer will pay $100,000,000 for it. This is silly; in real life, the value of good to the consumer does not change by a factor of ten million.
*Question 1.10: Profit Maximization
Which of the following is true for any firm that maximizes profits and has an upward sloping marginal cost curve?
Price equals marginal revenue
Marginal revenue equals marginal cost
Marginal cost is minimized
Price equals average cost
Average cost is minimized
Answer 1.10: B
The equimarginal principle says that marginal revenue equals marginal cost for all firms, both competitive firms and monopolists. Choices A, D, and E are true for competitive firms but not for monopolists. Choice C is never true.
*Question 1.11: Dead Weight Loss of Monopoly
In a competitive market, the equilibrium price is $70 and the equilibrium quantity is 100. To increase their profits, the suppliers merge and form a monopoly. The monopoly price is $80 and the monopoly quantity is 80. The dead weight loss from the monopoly is $200. Both the demand curve and the marginal cost curve are sloped.
To offset the monopoly, the government imposes a $2.50 per unit excise tax on the monopolist, so that 80 × $2.50 = $200. What is the effect of the excise tax on the dead weight loss?
The dead weight loss after the tax, considering consumers’ surplus, producers’ surplus, and the tax revenue, is zero.
The tax reduces producers’ surplus and increases consumers’ surplus, leaving a smaller (but not zero) dead weight loss.
The tax has no effect on the dead weight loss.
Both producers’ surplus and consumers’ surplus increase because of the tax.
Both producers’ surplus and consumers’ surplus decrease because of the tax.
Answer 1.11: E
We can solve this problem from the relations in the textbook. We can also solve it by assuming the demand curve and supply curve are linear. The excise tax raises the supply curve by $2.50 at every point. This raises the monopoly price and lowers the monopoly quantity.
*Exercise 1.12: Copper Monopoly
Copper is produced by a profit-maximizing monopoly. The marginal cost to produce copper is constant at $40 a pound. The price elasticity of demand is constant at –2. What is the price charged for copper?
$10 a pound
$20 a pound
$40 a pound
$80 a pound
$160 a pound
Answer 1.12: D
We use the relation that marginal revenue = P × (1 – 1/|η|), where η is the price elasticity of demand. At equilibrium, the marginal revenue equals the marginal cost.
Marginal revenue = marginal cost = P × (1 – 1/|η|) A $40 = P × (1 – ½) A $40 = P × ½ A P = $40 / ½ = $80.