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Asked by Rainn Cline on May 16, 2024

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A firm's demand curve is given by P = 500 - 2Q. The firm's current price is $300 and the firm sells 100 units of output per week.
a. Calculate the firm's marginal revenue at the current price and quantity using the expression for marginal revenue that utilizes the price elasticity of demand.
b. Assuming that the firm's marginal cost is zero, is the firm maximizing profit?

Price Elasticity Of Demand

Percentage change in quantity demanded of a good resulting from a 1-percent increase in its price.

Marginal Revenue

The extra revenue received from the sale of an additional unit of a product or service.

  • Comprehend the method by which a monopolist ascertains the level of output and price that maximizes profits.
  • Comprehend the connection among demand elasticity, marginal revenue, and the strategies for setting prices in a monopoly.
  • Explain the circumstances in which monopolies operate and the impact of variations in marginal costs and demand elasticity on their production.
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Eduardo CastilloMay 21, 2024
Final Answer :
a.Begin by calculating the price elasticity of demand, ED: a.Begin by calculating the price elasticity of demand, ED: = ∙ To find solve for Q in terms of P. P = 500 - 2Q P - 500 = -2Q Q = 250 - 0.5P = -0.5; = ∙ = -0.5 ∙ = -1.5 MR = P + P MR = 300 + 300 MR = 300 - 200 = 100 b.If MC = 0, the firm is not maximizing profit since MR should be equal to MC. The firm should expand output. MR = 500 - 4Q = 0 4Q = 500 Q = 125 = a.Begin by calculating the price elasticity of demand, ED: = ∙ To find solve for Q in terms of P. P = 500 - 2Q P - 500 = -2Q Q = 250 - 0.5P = -0.5; = ∙ = -0.5 ∙ = -1.5 MR = P + P MR = 300 + 300 MR = 300 - 200 = 100 b.If MC = 0, the firm is not maximizing profit since MR should be equal to MC. The firm should expand output. MR = 500 - 4Q = 0 4Q = 500 Q = 125 ∙ a.Begin by calculating the price elasticity of demand, ED: = ∙ To find solve for Q in terms of P. P = 500 - 2Q P - 500 = -2Q Q = 250 - 0.5P = -0.5; = ∙ = -0.5 ∙ = -1.5 MR = P + P MR = 300 + 300 MR = 300 - 200 = 100 b.If MC = 0, the firm is not maximizing profit since MR should be equal to MC. The firm should expand output. MR = 500 - 4Q = 0 4Q = 500 Q = 125 To find a.Begin by calculating the price elasticity of demand, ED: = ∙ To find solve for Q in terms of P. P = 500 - 2Q P - 500 = -2Q Q = 250 - 0.5P = -0.5; = ∙ = -0.5 ∙ = -1.5 MR = P + P MR = 300 + 300 MR = 300 - 200 = 100 b.If MC = 0, the firm is not maximizing profit since MR should be equal to MC. The firm should expand output. MR = 500 - 4Q = 0 4Q = 500 Q = 125 solve for Q in terms of P.
P = 500 - 2Q
P - 500 = -2Q
Q = 250 - 0.5P a.Begin by calculating the price elasticity of demand, ED: = ∙ To find solve for Q in terms of P. P = 500 - 2Q P - 500 = -2Q Q = 250 - 0.5P = -0.5; = ∙ = -0.5 ∙ = -1.5 MR = P + P MR = 300 + 300 MR = 300 - 200 = 100 b.If MC = 0, the firm is not maximizing profit since MR should be equal to MC. The firm should expand output. MR = 500 - 4Q = 0 4Q = 500 Q = 125 = -0.5; a.Begin by calculating the price elasticity of demand, ED: = ∙ To find solve for Q in terms of P. P = 500 - 2Q P - 500 = -2Q Q = 250 - 0.5P = -0.5; = ∙ = -0.5 ∙ = -1.5 MR = P + P MR = 300 + 300 MR = 300 - 200 = 100 b.If MC = 0, the firm is not maximizing profit since MR should be equal to MC. The firm should expand output. MR = 500 - 4Q = 0 4Q = 500 Q = 125 = a.Begin by calculating the price elasticity of demand, ED: = ∙ To find solve for Q in terms of P. P = 500 - 2Q P - 500 = -2Q Q = 250 - 0.5P = -0.5; = ∙ = -0.5 ∙ = -1.5 MR = P + P MR = 300 + 300 MR = 300 - 200 = 100 b.If MC = 0, the firm is not maximizing profit since MR should be equal to MC. The firm should expand output. MR = 500 - 4Q = 0 4Q = 500 Q = 125 ∙ a.Begin by calculating the price elasticity of demand, ED: = ∙ To find solve for Q in terms of P. P = 500 - 2Q P - 500 = -2Q Q = 250 - 0.5P = -0.5; = ∙ = -0.5 ∙ = -1.5 MR = P + P MR = 300 + 300 MR = 300 - 200 = 100 b.If MC = 0, the firm is not maximizing profit since MR should be equal to MC. The firm should expand output. MR = 500 - 4Q = 0 4Q = 500 Q = 125 a.Begin by calculating the price elasticity of demand, ED: = ∙ To find solve for Q in terms of P. P = 500 - 2Q P - 500 = -2Q Q = 250 - 0.5P = -0.5; = ∙ = -0.5 ∙ = -1.5 MR = P + P MR = 300 + 300 MR = 300 - 200 = 100 b.If MC = 0, the firm is not maximizing profit since MR should be equal to MC. The firm should expand output. MR = 500 - 4Q = 0 4Q = 500 Q = 125 = -0.5 ∙ a.Begin by calculating the price elasticity of demand, ED: = ∙ To find solve for Q in terms of P. P = 500 - 2Q P - 500 = -2Q Q = 250 - 0.5P = -0.5; = ∙ = -0.5 ∙ = -1.5 MR = P + P MR = 300 + 300 MR = 300 - 200 = 100 b.If MC = 0, the firm is not maximizing profit since MR should be equal to MC. The firm should expand output. MR = 500 - 4Q = 0 4Q = 500 Q = 125 = -1.5
MR = P + P a.Begin by calculating the price elasticity of demand, ED: = ∙ To find solve for Q in terms of P. P = 500 - 2Q P - 500 = -2Q Q = 250 - 0.5P = -0.5; = ∙ = -0.5 ∙ = -1.5 MR = P + P MR = 300 + 300 MR = 300 - 200 = 100 b.If MC = 0, the firm is not maximizing profit since MR should be equal to MC. The firm should expand output. MR = 500 - 4Q = 0 4Q = 500 Q = 125 MR = 300 + 300 a.Begin by calculating the price elasticity of demand, ED: = ∙ To find solve for Q in terms of P. P = 500 - 2Q P - 500 = -2Q Q = 250 - 0.5P = -0.5; = ∙ = -0.5 ∙ = -1.5 MR = P + P MR = 300 + 300 MR = 300 - 200 = 100 b.If MC = 0, the firm is not maximizing profit since MR should be equal to MC. The firm should expand output. MR = 500 - 4Q = 0 4Q = 500 Q = 125 MR = 300 - 200 = 100
b.If MC = 0, the firm is not maximizing profit since MR should be equal to MC. The firm should expand output.
MR = 500 - 4Q = 0
4Q = 500
Q = 125

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