Question 1

A monopoly has two production plants with cost functions C₁ = 40 + 0.2Q₁² and C₂ = 50 + 0.1Q₂².The demand it faces is Q = 480 − 5P.What is the profit-maximizing price?

Accepted Answer

The answer of A monopoly has two production plants with...

Question 2

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

Accepted Answer

The price elasticity of demand (E) in a monopoly can be calculated using the formula: E = (P/MR) - 1. Substituting the given values, E = (2/0.5) - 1 = 4 - 1 = 3. Since elasticity is negative for a downward-sloping demand curve, the correct answer is -4/3.

Question 3

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

Accepted Answer

Both formulas D mentions, $ \pi = TR - TC $ and $ \pi = (P - ATC) \times Q $, are correct for calculating the profit of a monopoly. The first formula represents profit as the difference between total revenue (TR) and total cost (TC), while the second formula calculates profit by multiplying the difference between price (P) and average total cost (ATC) by quantity (Q).

Question 4

You are the manager of a monopoly that faces a demand curve described by P = 80 − 5Q.Your costs are C = 10 + 5Q.The revenue-maximizing output is:

Accepted Answer

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Question 5

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

Accepted Answer

The first-order condition for profit maximization in a perfectly competitive market is that the price (P) equals the marginal cost (MC), which is the derivative of the cost function with respect to quantity (Q), hence P − (dC(Q)/dQ) = 0.

Question 6

A monopoly has two production plants with cost functions C₁ = 40 + 0.2 Q₁² and C₂ = 50 + 0.1 Q₂².The demand it faces is Q = 480 − 5P.What is the profit-maximizing level of output?

Accepted Answer

To maximize profit, the firm should equate marginal costs (MC) across plants and set them equal to marginal revenue (MR). Solving the equations derived from the cost functions and demand curve, the optimal outputs are Q1 = 60 and Q2 = 120.

Question 7

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:

Accepted Answer

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Question 8

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:

Accepted Answer

To find the marginal revenue (MR) function, we need to take the derivative of the inverse demand function:

P = 50 - 0.5Q 
MR = dTR/dQ = d(PQ)/dQ = P + Q(dP/dQ)

Substituting P = 50 - 0.5Q, we get:

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

Therefore, the answer is (C) P = 50 - Q.

Question 9

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?

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 10

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

Accepted Answer

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Question 11

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

Accepted Answer

The price elasticity of demand in a monopoly can be calculated using the formula: Elasticity = (Marginal Revenue / Price) + 1. Substituting the given values, we get: Elasticity = (10 / 20) + 1 = 0.5 + 1 = 1.5. However, the correct formula for elasticity in the context of marginal revenue (MR) and price (P) is actually Elasticity = 1 + (MR / P). Given MR = $10 and P = $20, the calculation should be: Elasticity = 1 + (10 / 20) = 1.5. However, my explanation mistakenly calculates the elasticity directly without considering the negative sign that should be present in the formula for elasticity in monopolies, which is actually Elasticity = 1 - (MR / P). Therefore, the correct calculation is Elasticity = 1 - (10 / 20) = 0.5, indicating a mistake in my initial explanation. The correct interpretation of the formula and the negative sign leads to the realization that the elasticity of demand is indeed -2, reflecting the inverse relationship between price and quantity demanded in the context of monopolistic markets.

Question 12

Suppose that initially the price is $20 in a perfectly competitive market.Firms are making zero economic profits.Then the market demand shrinks permanently,some firms leave the industry,and the industry returns to a long-run equilibrium.What will be the new equilibrium price,assuming cost conditions in the industry remain constant?

Accepted Answer

In a perfectly competitive market, the long-run equilibrium price is determined by the minimum point of the average total cost curve. Since cost conditions remain constant, the equilibrium price will remain at $20.

Question 13

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:

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 14

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:

Accepted Answer

In a monopolistically competitive market, the demand curve facing the firm is downward sloping and its marginal revenue (MR) curve lies below the demand curve.

The given demand function is P = 50 − 0.5Q, which can be rewritten in the inverse form as Q = 100 − 2P.

To find the marginal revenue function, we take the derivative of total revenue (TR) with respect to quantity (Q):

TR = P(Q) × Q = (50 − 0.5Q)Q = 50Q − 0.5Q^2

MR = dTR/dQ = 50 − Q

Thus, the firm's marginal revenue function is B) P = 50 − Q, which shows that the price charged by the firm decreases as it produces more output due to diminishing marginal revenue.

Question 15

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

Accepted Answer

In the short run, firms under monopolistic competition can make positive economic profits since they have some market power to set prices above their marginal costs. However, these profits can only be temporary as entry of new firms with similar but slightly differentiated products will drive down demand for existing firms, leading to a decrease in their market share and profits in the long run. In monopolistic competition, P > MC because the firms have some degree of market power to charge a higher price, but P < ATC because they are still subject to competition from similar products. P = MR because the demand curve is downward sloping, and to sell more units of output, the firms must lower their prices, which means that they must also lower the price of their existing units.

Question 16

John provides cheese (H)and milk (M)to the market with the following total cost function C(H,M)= 8 + 0.5H² + 0.1M².The prices of cheese and milk in the market are $3 and $4 respectively.Assume that the cheese and milk markets are perfectly competitive.What output of milk maximizes profits?

Accepted Answer

To find the output of milk that maximizes profits, we need to use the profit maximization rule in a perfectly competitive market, which is to produce at the output level where Marginal Revenue (MR) equals Marginal Cost (MC).

First, we need to calculate the Total Cost (TC) function by plugging in the given prices for cheese and milk into the total cost function:

C(H,M) = 8 + 0.5(3)H + 0.1(4)M
TC = 8 + 1.5H + 0.4M

Next, we need to find the Marginal Cost of producing milk (MC_M). Taking the derivative of the TC function with respect to Milk (M), we get:

MC_M = 0.4

Now, we need to find the Marginal Revenue (MR) of selling milk. In a perfectly competitive market, the price of the good equals the Marginal Revenue, so:

MR_M = 4

To find the profit-maximizing output of milk, we set MR_M equal to MC_M and solve for M:

MR_M = MC_M
4 = 0.4
M = 20

Therefore, the output of milk that maximizes profit is 20. We do not need to consider the output level of cheese, as the problem only asks for the optimal output of milk.

Question 17

Which of the following is true under perfect competition?

Accepted Answer

Under perfect competition, firms are price takers and cannot affect the market price. Therefore, the marginal revenue (MR) curve of a firm is equal to the market price (P). In the short run, a firm will produce where marginal cost (MC) equals MR (which is also equal to P), so P = MC. Option A is incorrect because in the short run, a firm can make zero profits or even negative profits. Option B is not necessarily true as it depends on the shape of the MC curve. Option D is incorrect because profits can be zero or negative in the short run, and there is no guarantee that P > MC in the long run.

Question 18

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

Accepted Answer

In the long-run equilibrium of a perfectly competitive market, all firms end up producing at the minimum point of their long-run average total cost curve (min ATC). At this point, the firm earns normal profits (zero economic profits), which means that marginal revenue (MR) is equal to marginal cost (MC) and also equal to the market price of the good. Therefore, the correct answer is C, MR = MC = min ATC.

Question 19

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

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 20

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.

Accepted Answer

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

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

A monopoly has two production plants with cost functions C₁ = 40 + 0.2Q₁² and C₂ = 50 + 0.1Q₂².The demand it faces is Q = 480 − 5P.What is the profit-maximizing price?

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

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

You are the manager of a monopoly that faces a demand curve described by P = 80 − 5Q.Your costs are C = 10 + 5Q.The revenue-maximizing output is:

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

A monopoly has two production plants with cost functions C₁ = 40 + 0.2 Q₁² and C₂ = 50 + 0.1 Q₂².The demand it faces is Q = 480 − 5P.What is the profit-maximizing level of output?

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:

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:

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

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

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:

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

John provides cheese (H) and milk (M) to the market with the following total cost function C(H,M) = 8 + 0.5H² + 0.1M².The prices of cheese and milk in the market are $3 and $4 respectively.Assume that the cheese and milk markets are perfectly competitive.What output of milk maximizes profits?

Which of the following is true under perfect competition?

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

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

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.

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

A monopoly has two production plants with cost functions C1 = 40 + 0.2Q12 and C2 = 50 + 0.1Q22.The demand it faces is Q = 480 − 5P.What is the profit-maximizing price?

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

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

You are the manager of a monopoly that faces a demand curve described by P = 80 − 5Q.Your costs are C = 10 + 5Q.The revenue-maximizing output is:

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

A monopoly has two production plants with cost functions C1 = 40 + 0.2 Q12 and C2 = 50 + 0.1 Q22.The demand it faces is Q = 480 − 5P.What is the profit-maximizing level of output?

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:

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:

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

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

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:

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

John provides cheese (H) and milk (M) to the market with the following total cost function C(H,M) = 8 + 0.5H2 + 0.1M2.The prices of cheese and milk in the market are $3 and $4 respectively.Assume that the cheese and milk markets are perfectly competitive.What output of milk maximizes profits?

Which of the following is true under perfect competition?

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

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

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 monopoly has two production plants with cost functions C₁ = 40 + 0.2Q₁² and C₂ = 50 + 0.1Q₂².The demand it faces is Q = 480 − 5P.What is the profit-maximizing price?

A monopoly has two production plants with cost functions C₁ = 40 + 0.2 Q₁² and C₂ = 50 + 0.1 Q₂².The demand it faces is Q = 480 − 5P.What is the profit-maximizing level of output?

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:

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:

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:

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:

John provides cheese (H) and milk (M) to the market with the following total cost function C(H,M) = 8 + 0.5H² + 0.1M².The prices of cheese and milk in the market are $3 and $4 respectively.Assume that the cheese and milk markets are perfectly competitive.What output of milk maximizes profits?