7. A monopoly firm faces a demand curve given by L(p) = 40 – 2 p. The firm has constant МC-$12. (A) Find the firm's marginal revenue and use this to find the firm's profit-maximizing output and price. Draw a diagram. Hint: first figure out how express the firm's total revenue in terms of Q. Then if you know calculus, take the derivative of this expression with respect to Q to find marginal revenue. If you don't know calculus, recall that for a linear demand curve, (1) the slope of the marginal revenue curve is twice (in absolute value) the slope of the demand curve; and (2) the marginal revenue curve intersects the vertical (price) axis at the same point as the demand curve; and (3) the marginal revenue curve hits the quantity axis at half the distance of the demand curve. (B) Find the price elasticity of demand at the profit-maximizing output and price. Is demand elastic?
7. A monopoly firm faces a demand curve given by L(p) = 40 – 2 p. The firm has constant МC-$12. (A) Find the firm's marginal revenue and use this to find the firm's profit-maximizing output and price. Draw a diagram. Hint: first figure out how express the firm's total revenue in terms of Q. Then if you know calculus, take the derivative of this expression with respect to Q to find marginal revenue. If you don't know calculus, recall that for a linear demand curve, (1) the slope of the marginal revenue curve is twice (in absolute value) the slope of the demand curve; and (2) the marginal revenue curve intersects the vertical (price) axis at the same point as the demand curve; and (3) the marginal revenue curve hits the quantity axis at half the distance of the demand curve. (B) Find the price elasticity of demand at the profit-maximizing output and price. Is demand elastic?
Chapter14: Monopoly
Section: Chapter Questions
Problem 14.5P
Related questions
Question
![7. A monopoly firm faces a demand curve given by 2(P) = 40 – 2p. The firm has constant
MC=$12.
(A) Find the firm's marginal revenue and use this to find the firm's profit-maximizing output
and price. Draw a diagram. Hint: first figure out how express the firm's total revenue in terms of
Q. Then if you know calculus, take the derivative of this expression with respect to Q to find
marginal revenue. If you don't know calculus, recall that for a linear demand curve, (1) the slope
of the marginal revenue curve is twice (in absolute value) the slope of the demand curve; and (2)
the marginal revenue curve intersects the vertical (price) axis at the same point as the demand
curve; and (3) the marginal revenue curve hits the quantity axis at half the distance of the
demand curve.
(B) Find the price elasticity of demand at the profit-maximizing output and price. Is demand
elastic?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd41ba8ac-446b-4e82-9810-88f2d7f85809%2F6d89b04b-58c7-4735-a11a-fb49048149ff%2Fc17zogu_processed.png&w=3840&q=75)
Transcribed Image Text:7. A monopoly firm faces a demand curve given by 2(P) = 40 – 2p. The firm has constant
MC=$12.
(A) Find the firm's marginal revenue and use this to find the firm's profit-maximizing output
and price. Draw a diagram. Hint: first figure out how express the firm's total revenue in terms of
Q. Then if you know calculus, take the derivative of this expression with respect to Q to find
marginal revenue. If you don't know calculus, recall that for a linear demand curve, (1) the slope
of the marginal revenue curve is twice (in absolute value) the slope of the demand curve; and (2)
the marginal revenue curve intersects the vertical (price) axis at the same point as the demand
curve; and (3) the marginal revenue curve hits the quantity axis at half the distance of the
demand curve.
(B) Find the price elasticity of demand at the profit-maximizing output and price. Is demand
elastic?
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