Question 1

A monopolist will always equate marginal revenue and marginal cost when maximizing profit.

Accepted Answer

A monopolist maximizes profit by producing the quantity of output where marginal revenue (MR) equals marginal cost (MC), as this is the point where the additional revenue from selling one more unit equals the additional cost of producing that unit, ensuring no further profit can be made by increasing or decreasing production.

Question 2

If he produces anything at all, a profit-maximizing monopolist with some fixed costs and no variable costs will set price and output so as to maximize revenue.

Accepted Answer

A profit-maximizing monopolist will set output where marginal revenue equals marginal cost, and then charge the highest price that consumers are willing to pay for that level of output. This will result in maximizing revenue and profits, even if there are fixed costs involved in production.

Question 3

The demand for a monopolist's output is  , where p is the price it charges. At a price of $3, the elasticity of demand for the monopolist's output is

Accepted Answer

D

Question 4

The demand for a monopolist's output is  , where p is its price. It has constant marginal costs equal to $5 per unit. What price will it charge to maximize its profits?

Accepted Answer

The answer of The demand for a monopolist's output is...

Question 5

A monopolist faces a constant marginal cost of $1 per unit. If at the price he is charging, the price elasticity of demand for the monopolist's output is -0.5, then

Accepted Answer

For a monopolist to maximize profits, the price elasticity of demand must be greater than -1 in absolute value. An elasticity of -0.5 indicates inelastic demand, meaning the monopolist can increase total revenue by increasing price, suggesting they are not maximizing profits.

Question 6

A profit-maximizing monopolist faces the demand curve q = 100 - 3p. It produces at a constant marginal cost of $20 per unit. A quantity tax of $10 per unit is imposed on the monopolist's product. The price of the monopolist's product

Accepted Answer

The monopolist will pass part of the tax onto consumers. The demand curve is q = 100 - 3p, which implies p = (100 - q)/3. The monopolist sets marginal revenue equal to marginal cost plus tax. The tax increases the cost by $10, but due to the monopolist's pricing power, the price will rise by less than the full tax amount. The price increase is $5.

Question 7

The demand for a monopolist's output is  , where p is its price. It has constant marginal costs equal to $6 per unit. What price will it charge to maximize its profits?

Accepted Answer

The answer of The demand for a monopolist's output is...

Question 8

A monopolist faces the inverse demand curve p = 64 - 2q. At what level of output is his total revenue maximized?

Accepted Answer

Total revenue is maximized when marginal revenue is zero. The marginal revenue curve has the same intercept as the demand curve but twice the slope. Thus, MR = 64 - 4q. Setting MR = 0 gives q = 16.

Question 9

Since a monopoly makes excess profits beyond the normal rate of return on investment, an investor is likely to get a higher rate of return in the stock market by investing in monopolistic rather than in competitive industries.

Accepted Answer

The answer of Since a monopoly makes excess profits beyond...

Question 10

A monopolist with constant marginal costs faces a demand curve with a constant elasticity of demand and does not practice price discrimination. If the government imposes a tax of $1 per unit of goods sold by the monopolist, the monopolist will increase his price by more than $1 per unit.

Accepted Answer

When a tax is imposed, the monopolist will try to shift the burden of the tax onto the consumers by increasing the price of the good. Since the monopolist faces a constant elasticity of demand, increasing the price by $1 per unit would result in a decrease in quantity demanded by more than one unit, which would result in a decrease in total revenue. To avoid this, the monopolist will increase the price by more than $1 per unit to spread the burden of the tax between consumers and the monopolist. Therefore, the statement is true.

Question 11

A natural monopoly occurs when a firm gains ownership of the entire stock of some natural resource and thus is able to exclude other producers.

Accepted Answer

A natural monopoly occurs when a firm is able to produce at a lower cost than any potential competitors due to factors like economies of scale or control of a scarce resource. It does not necessarily require ownership of the entire stock of a natural resource.

Question 12

The demand for a monopolist's output is 7,000 divided by the square of the price in dollars that it charges per unit. The firm has constant marginal costs equal to 1 dollar per unit. To maximize its profits, it should charge a price of

Accepted Answer

To maximize profits, a monopolist sets marginal revenue (MR) equal to marginal cost (MC). The demand function is Q = 7000/P^2, where Q is quantity and P is price. To find MR, we first find the total revenue (TR) function by multiplying the demand function by price (P * Q = P * 7000/P^2 = 7000/P). Differentiating TR with respect to P gives MR = -7000/P^2. Given that MC = 1, we set MR = MC to find the profit-maximizing price: -7000/P^2 = 1. Solving for P gives P = sqrt(7000), which is not an exact match to any of the options. However, the correct approach involves finding the derivative of the revenue function correctly, which involves applying the inverse demand function to express price as a function of quantity and then differentiating. The mistake in the initial explanation was in the differentiation step and in not correctly applying the relationship between MR and MC. The correct approach involves setting MR equal to MC and solving for P, taking into account the correct form of the MR curve derived from the demand curve. Given the error in the initial calculation, let's correct the approach:First, we need to express the demand equation in terms of P to find the revenue function: P = sqrt(7000/Q). Then, the total revenue (TR) is P*Q, which needs to be expressed correctly and differentiated to find MR. However, without going through the complex calculus, we recognize an error in the initial step of directly finding MR without correctly adjusting for the monopolist's revenue and cost structure.To correctly solve this, we should recognize that the monopolist's decision involves understanding how changes in price affect total revenue and costs. The correct calculation involves more detailed steps that include correctly deriving MR from the demand function and equating it to MC, which was stated as 1. Given the mistake in the initial explanation, the correct answer involves recognizing that the monopolist will not simply charge a price equal to marginal cost (which would be the competitive market outcome) but will instead choose a price that maximizes the difference between total revenue and total costs. This involves correctly applying the principles of marginal analysis, which was not accurately done in the initial explanation.Upon reevaluation, the correct approach to find the profit-maximizing price involves correctly deriving the marginal revenue function from the given demand function and equating it to the marginal cost to solve for the price. However, without the correct mathematical derivation provided in the initial response, the specific choice among the given options was incorrectly justified. The correct method involves detailed calculus that was not accurately represented in the initial explanation.

Question 13

The demand for a monopolist's output is 10,000 divided by the square of the price it charges. The monopolist produces at a constant marginal cost of $5. If the government imposes a sales tax of $10 per unit on the monopolist's output, the monopolist price will rise by

Accepted Answer

The monopolist's inverse demand function is P = 10,000/Q^2, where P is price and Q is quantity. At a marginal cost of $5, the monopolist will choose to produce where MR = MC, which gives:

10,000/Q^2 - 2P(10,000)/Q^3 = 5

Solving for Q, we get Q = (100,000/3)^(1/2), and solving for P, we get P = 10,000/(100,000/3) = $30. Therefore, without the tax, the monopolist's price is $30 and its quantity is (100,000/3)^(1/2).

With the tax, the monopolist's cost is now $15 ($5 in production cost plus $10 in tax), and the monopolist will produce where MR = MC again. The new MR function is:

(10,000/Q^2) - 2(30)(10,000)/Q^3 = 15

Solving for Q, we get Q = (200,000/9)^(1/2), and solving for P, we get P = 10,000/(200,000/9) = $22.50. Therefore, the monopolist's price has risen by $7.50 ($22.50 - $15) due to the sales tax.

Question 14

A monopolist faces the inverse demand function described by p = 50 - 4q, where q is output. The monopolist has no fixed cost and his marginal cost is $5 at all levels of output. Which of the following expresses the monopolist's profits as a function of his output?

Accepted Answer

The monopolist's profit function is total revenue minus total cost. Total revenue is pq = (50 - 4q)q = 50q - 4q^2. Total cost is 5q. Therefore, profit is (50q - 4q^2) - 5q = 45q - 4q^2.

Question 15

If the interest rate is 10%, a monopolist will choose a markup of price over marginal cost of at least 10%.

Accepted Answer

The markup of price over marginal cost that a monopolist chooses is determined by the price elasticity of demand for its product, not directly by the interest rate.

Question 16

The demand for a monopolist's output is  , where p is the price it charges. At a price of $3, the elasticity of demand for the monopolist's output is

Accepted Answer

The formula for elasticity of demand is:

Elasticity = (% change in quantity demanded / % change in price) * (p / q)

To calculate the elasticity at a price of $3, we need to know the price and quantity demanded at another point to calculate the percentage changes. Let's assume that the initial price and quantity demanded are $4 and 10, respectively:

Elasticity = ((10-6)/(6/10)) * (3/6) = -1.20

Therefore, the elasticity of demand at a price of $3 is -1.20.

Question 17

A monopolist faces the inverse demand function described by p = 23 - 5q, where q is output. The monopolist has no fixed cost and his marginal cost is $6 at all levels of output. Which of the following expresses the monopolist's profits as a function of his output?

Accepted Answer

The answer of A monopolist faces the inverse demand function...

Question 18

Since a monopoly charges a price higher than marginal cost, it will produce an inefficient amount of output.

Accepted Answer

A monopoly has the power to set prices higher than marginal cost because it has no competition. As a result, it will produce a lower quantity of output than would be socially optimal, leading to inefficiency in the market. This is known as a deadweight loss.

Question 19

For a monopolist who faces a downward-sloping demand curve, marginal revenue is less than price whenever quantity sold is positive.

Accepted Answer

This is because a monopolist has market power and can influence the price of its product. To sell more units, the monopolist must lower the price, which means the marginal revenue earned on each additional unit sold is less than the price.

Question 20

A monopolist faces the inverse demand curve p = 120 - 6q. At what level of output is his total revenue maximized?

Accepted Answer

Total revenue is maximized when marginal revenue equals zero. The marginal revenue curve has the same intercept as the demand curve but twice the slope. Thus, MR = 120 - 12q. Setting MR = 0 gives 120 - 12q = 0, solving for q gives q = 10.

Quiz 23: Monopoly