Question 1

You are the manager of a monopoly firm with (inverse) demand given by P = 50 - 0.5Q. Your firm's cost function is C = 40 + 5Q². Your firm's marginal revenue is: A) P = 50 - 0.5Q. B) P = 100 - Q. C) P = 50 - Q. D) There is insufficient information to determine the firm's marginal revenue.

Accepted Answer

For a monopoly firm, marginal revenue (MR) is given by: 
MR = P + Q(dP/dQ)

Here, P = 50 - 0.5Q 
So, dP/dQ = -0.5

Therefore, MR = (50 - 0.5Q) + Q(-0.5) 
= 50 - 0.5Q - 0.5Q 
= 50 - Q

Hence, the correct answer is C, i.e., MR = 50 - Q.

Question 2

In a monopoly where the marginal revenue and price are, respectively, given by $10 and $20, the price elasticity of demand is:
A) -1.
B) -2.
C) -0.5.
D) Cannot be determined based on the information in the question.

Accepted Answer

Price elasticity of demand ($E_d$) is defined as the percentage change in quantity demanded ($Q$) in response to a percentage change in price ($P$). Mathematically, $E_d = \frac{\% \Delta Q}{\% \Delta P} \cdot \frac{P}{Q}$.

In a monopoly, the marginal revenue ($MR$) is always less than the price ($P$) because the monopolist must lower the price to sell more units. Therefore, $MR = P \cdot (1 + \frac{1}{E_d})$.

Plug in $MR = 10$ and $P = 20$ to solve for $E_d$: 
$10 = 20 \cdot (1 + \frac{1}{E_d})$
$\frac{1}{E_d} = \frac{1}{2}$
$E_d = -2$

Note that the negative sign indicates the inverse relationship between price and quantity demanded.

Question 3

Clark Industries currently spends 5 percent of its sales on advertising. Suppose that the elasticity of advertising for Clark is 0.25. Determine the optimal profit margin over price (P - MC)/P.
A) 15 percent.
B) 20 percent.
C) 25 percent.
D) None of the answers is correct.

Accepted Answer

The answer of Clark Industries currently spends 5 percent of...

Question 4

In a monopoly where the marginal revenue and price are, respectively, given by $3 and $6, the price elasticity of demand is:
A) -0.5.
B) -1.
C) -1.5.
D) -2.

Accepted Answer

The price elasticity of demand in a monopoly is given by the formula: Elasticity = (P - MR) / MR. Substituting the given values, Elasticity = (6 - 3) / 3 = 1. Since elasticity is negative for demand, it is -2.

Question 5

Which of the following formulas correctly measures the profit of a monopoly?
A) π = TR - TC
B) π = (P - ATC)Q
C) π = (P - AVC)Q
D) π = TR - TC and π = (P - ATC)Q

Accepted Answer

Profit (π) for a monopoly is calculated as total revenue (TR) minus total cost (TC), which is option A. It can also be expressed as (P - ATC)Q, where P is price, ATC is average total cost, and Q is quantity, which is option B. Therefore, both A and B are correct, making option D the correct choice.

Question 6

Consider a monopoly where the inverse demand for its product is given by P = 80 - 2Q. Total costs for this monopolist are estimated to be C(Q) = 100 + 20Q + Q². At the profit-maximizing combination of output and price, deadweight loss is: A) $30. B) $50. C) $80. D) Cannot be determined with the given information.

Accepted Answer

The answer of Consider a monopoly where the inverse demand...

Question 7

The first-order condition for a firm maximizing its profit operating in a monopolistically competitive market is:
A) (dMR/dQ) = (dMC/dQ).
B) P - (dC(Q)/dQ) = 0.
C) (dR(Q)/dQ) - (dC(Q)/dQ) = 0.
D) (dMR/dQ) < (dMC/dQ).

Accepted Answer

The first-order condition for a firm maximizing its profit in a monopolistically competitive market is (dR(Q)/dQ) - (dC(Q)/dQ) = 0. This is because the firm maximizes profit by producing where marginal revenue (dR(Q)/dQ) equals marginal cost (dC(Q)/dQ), just as in a perfectly competitive market. However, in a monopolistically competitive market, the firm faces a downward-sloping demand curve and thus has some market power, causing marginal revenue to be less than price. Therefore, the first-order condition in a monopolistically competitive market is slightly different from that in a perfectly competitive market, but still involves setting marginal revenue equal to marginal cost.

Question 8

The second-order condition for a firm maximizing its profits operating in a perfectly competitive market is: A) (d²π/dQ²) < 0. B) - (d²C(Q)/dQ²) < 0. C) - (dMC/dQ) < 0. D) All of the statements associated with this question are correct.

Accepted Answer

The second-order condition for a firm maximizing its profits operating in a perfectly competitive market is that the second derivative of the profit function with respect to output is negative. This means that the marginal cost curve must be upward sloping.

Question 9

In a competitive industry with identical firms, long-run equilibrium is characterized by:
A) P > min ATC.
B) P < AVC.
C) MR = MC = min ATC.
D) MR < P.

Accepted Answer

In a competitive industry with identical firms, long-run equilibrium occurs when each firm is producing at minimum average total cost (min ATC) and earning normal profits. At this point, the marginal cost (MC) of production is equal to the marginal revenue (MR) of selling each additional unit of output, and both are equal to the market price (P). Therefore, the answer choice that correctly identifies this equilibrium condition is C: MR = MC = min ATC. The other choices are either incorrect or incomplete.

Question 10

Which of the following is true under monopolistic competition in the long run?
A) Profits are always zero.
B) P > MC.
C) P = MR.
D) All of the choices are true in monopolistic competition.

Accepted Answer

The answer of Which of the following is true under...

Question 11

You are the manager of a firm that produces output in two plants. The demand for your firm's product is P = 96 - 15Q, where Q = Q₁ + Q₂. The marginal costs associated with producing in the two plants are MC₁ = 6Q₁ and MC₂ = 3Q₂. How much output should be produced in plant 2 in order to maximize profits? A) 1 B) 2 C) 3 D) 4

Accepted Answer

To maximize profits, we need to find the level of output that equates marginal revenue with marginal cost in each plant. First, we can rewrite the demand equation as follows: Q = (96 - P)/15 Substituting this into the expression for Q, we get: Q = (96 - P)/15 = Q₁ + Q₂ Simplifying, we get: Q₂ = (96 - P)/15 - Q₁ Now we can express profits as: Profit = (P - MC₁)Q₁ + (P - MC₂)Q₂ Substituting the expressions for P and MC₂, we get: Profit = (96 - 15Q - 6Q₁)Q₁ + (96 - 15Q - 3Q₂)Q₂ Taking the derivative of profit with respect to Q₁ and Q₂ and setting them equal to zero, we get: dProfit/dQ₁ = 96 - 15Q - 12Q₁ + 3Q₂ = 0 dProfit/dQ₂ = 96 - 15Q - 6Q₂ + 2Q₁ = 0 Solving these two equations simultaneously, we get Q₁ = 2 and Q₂ = 4. Therefore, the optimal level of output for plant 2 is 4 units.

Question 12

Compute the marginal revenue when the price elasticity of demand is -0.10.
A) -9P, meaning marginal revenue is negative and 9 times greater than price.
B) 9P, meaning marginal revenue is positive and 9 times greater than price.
C) -3P, meaning marginal revenue is negative and 3 times greater than price.
D) 3P, meaning marginal revenue is positive and 3 times greater than price.

Accepted Answer

The marginal revenue (MR) can be calculated using the formula MR = P(1 + 1/E), where P is the price and E is the price elasticity of demand. Given E = -0.10, substituting into the formula gives MR = P(1 + 1/-0.10) = P(1 - 10) = -9P, indicating that marginal revenue is negative and 9 times greater than the price.

Question 13

The second-order condition for a monopoly maximizing its profit is: A) (d²R(Q)/dQ²) - (d²C(Q)/dQ²) < 0. B) (d²R(Q)/dQ²) - (d²C(Q)/dQ²) = 0. C) (dMR/dQ) < (dMC/dQ). D) (d²R(Q)/dQ²) - (d²C(Q)/dQ²) < 0 or (dMR/dQ) < (dMC/dQ).

Accepted Answer

The second-order condition for profit maximization in a monopoly involves ensuring that the marginal revenue's rate of change with respect to quantity is less than the marginal cost's rate of change with respect to quantity. This ensures that the profit-maximizing quantity is at a point where profit is maximized, not minimized. The complex expressions in the other options are not standard representations of this condition.

Question 14

Which of the following is true under monopolistic competition in the short run?
A) Profits are always zero.
B) P > MC.
C) P = MR.
D) All of the choices are true in monopolistic competition.

Accepted Answer

In monopolistic competition, firms can earn positive economic profits in the short run due to their unique product differentiation. Therefore, P > MC is true in the short run. However, profits will eventually be driven to zero in the long run due to the entry of new firms attracted by the positive profits. P = MR is not necessarily true as the demand curve is downward-sloping and the marginal revenue curve is below the demand curve. Therefore, the best choice is B.

Question 15

You are the manager of a firm that sells its product in a monopolistically competitive market with (inverse) demand given by P = 50 - 0.5Q. Your firm's cost function is C = 40 + 5Q². Your firm's marginal revenue is: A) P = 50 - 0.5Q. B) P = 50 - Q. C) P = 100 - Q. D) There is insufficient information to determine the firm's marginal revenue.

Accepted Answer

In a monopolistically competitive market, a firm's marginal revenue is given by the slope of the demand curve at the quantity produced, multiplied by (1 - 1/η), where η is the price elasticity of demand.
The inverse demand curve for the market is P = 50 - 0.5Q, which can be rewritten as Q = 100 - 2P. Taking the derivative of this with respect to Q gives -2, which is the slope of the demand curve.
Using the formula for marginal revenue, we get:
MR = (-2) * (1 - 1/η)
We do not have information on the price elasticity of demand, but we do know that in the short run, demand is relatively inelastic due to the presence of product differentiation. Therefore, we can assume a value of η < 1, which means that (1 - 1/η) is greater than 0 and less than 1.
Thus, the marginal revenue will be negative and less than the price, which is consistent with monopolistic competition. 
Simplifying the expression for MR, we can see that it is equal to -2 + 2/η. Again, we do not have information on η, but we can assume a value of η = 0.5 for illustrative purposes (which is consistent with the fact that demand is relatively inelastic in the short run). Plugging this into the formula gives:
MR = -2 + 2/0.5 = -2 + 4 = 2
Therefore, the marginal revenue for the firm is P = 50 - Q, which is equivalent to 2Q = 100 - 2P.

Question 16

You are the manager of a firm that sells its product in a competitive market with market (inverse) demand given by P = 50 - 0.5Q. The market equilibrium price is $50. Your firm's cost function is C = 40 + 5Q². Your firm's marginal revenue is: A) $50. B) MR(Q) = 10Q. C) MR(Q) = 50 - Q. D) There is insufficient information to determine the firm's marginal revenue.

Accepted Answer

CIn a competitive market, the firm's marginal revenue (MR) is equal to the market price, which is given as $50, hence option A is correct. Additionally, the given information does not provide a direct formula for marginal revenue based on quantity (Q), making option C also a correct interpretation under the assumption that the firm perceives its marginal revenue as decreasing with quantity, aligning with the inverse demand function's structure, albeit not directly calculable from the provided information.

Question 17

The first-order condition for a monopoly maximizing its profit is: A) P - (dC(Q)/dQ) = 0. B) (dR(Q)/dQ) - (dC(Q)/dQ) = 0. C) (dR(Q)/dQ) - (dC(Q)/dQ) < 0. D) (d²R(Q)/dQ²) - (d²C(Q)/dQ²) < 0.

Accepted Answer

The first-order condition for a monopoly maximizing its profit is (dR(Q)/dQ) - (dC(Q)/dQ) = 0 where R(Q) is the revenue function and C(Q) is the cost function. This condition states that the marginal revenue should equal the marginal cost at the profit-maximizing level of output. Therefore, the best choice is B.

Question 18

The first-order conditions for profit maximization in a perfectly competitive market are: A) P - (dC(Q)/dQ) = 0. B) (dR(Q)/dQ) - (d²C(Q)/dQ²) < 0. C) P - (d²C(Q)/dQ²) = 0. D) P > (dC(Q)/dQ).

Accepted Answer

The first-order condition for profit maximization in a perfectly competitive market is P - MC = 0, where MC is the marginal cost. This can also be written as P - (dC(Q)/dQ) = 0, since MC equals the derivative of the cost function with respect to quantity.

Question 19

Which of the following is true under perfect competition?
A) Profits are always positive.
B) P > MC.
C) P = MR.
D) All of the choices are true for perfect competition.

Accepted Answer

Under perfect competition, price is determined by the market and individual firms have no control over it. Therefore, they can only maximize profits by producing at a level where marginal revenue (MR) equals marginal cost (MC), which also means that price equals MR. Option A is incorrect because profits can be zero in the long run in perfect competition. Option B is incorrect because P = MC only in the short run and not necessarily in the long run. Option D is incorrect because option A is false.

Question 20

In a monopoly where the marginal revenue and price are, respectively, given by $0.50 and $2, the price elasticity of demand is:
A) -0.75.
B) -1.
C) -5/4.
D) -4/3.

Accepted Answer

The answer of In a monopoly where the marginal revenue...

Quiz 8: Managing in Competitive, Monopolistic, and Monopolistically Competitive Markets

You are the manager of a monopoly firm with (inverse) demand given by P = 50 - 0.5Q. Your firm's cost function is C = 40 + 5Q². Your firm's marginal revenue is:

In a monopoly where the marginal revenue and price are, respectively, given by $10 and $20, the price elasticity of demand is:

Clark Industries currently spends 5 percent of its sales on advertising. Suppose that the elasticity of advertising for Clark is 0.25. Determine the optimal profit margin over price (P - MC) /P.

In a monopoly where the marginal revenue and price are, respectively, given by $3 and $6, the price elasticity of demand is:

Which of the following formulas correctly measures the profit of a monopoly?

Consider a monopoly where the inverse demand for its product is given by P = 80 - 2Q. Total costs for this monopolist are estimated to be C(Q) = 100 + 20Q + Q². At the profit-maximizing combination of output and price, deadweight loss is:

The first-order condition for a firm maximizing its profit operating in a monopolistically competitive market is:

The second-order condition for a firm maximizing its profits operating in a perfectly competitive market is:

In a competitive industry with identical firms, long-run equilibrium is characterized by:

Which of the following is true under monopolistic competition in the long run?

Compute the marginal revenue when the price elasticity of demand is -0.10.

The second-order condition for a monopoly maximizing its profit is:

Which of the following is true under monopolistic competition in the short run?

You are the manager of a firm that sells its product in a monopolistically competitive market with (inverse) demand given by P = 50 - 0.5Q. Your firm's cost function is C = 40 + 5Q². Your firm's marginal revenue is:

You are the manager of a firm that sells its product in a competitive market with market (inverse) demand given by P = 50 - 0.5Q. The market equilibrium price is $50. Your firm's cost function is C = 40 + 5Q². Your firm's marginal revenue is:

The first-order condition for a monopoly maximizing its profit is:

The first-order conditions for profit maximization in a perfectly competitive market are:

Which of the following is true under perfect competition?

In a monopoly where the marginal revenue and price are, respectively, given by $0.50 and $2, the price elasticity of demand is: