Question 4 Suppose that for a certain product, the market price P = P(Q) can be written as a function of %3D the market demand quantity Q € (0, 100). (a) Suppose the demand function is P(Q) = 500 -Q and the current market demand is Qo = 80. Showing all steps of your working, evaluate the consumer surplus (CS) defined by Qo CS = "P(Q)dQ – PoQo. where P, is the current market price. Round off your result to 4 decimal places. (b) For the demand function P(Q) = 600 –0, evaluate the consumer surplus CS = CS(Qo) as a function of Qo € (0, 100). Show that CS(Qo) is strictly increasing with Qo by checking the sign of its derivative. (c) Show that CS(Qo) is strictly increasing for any demand function satisfying P'(Q) < 0 for all Q (0, 100). Note that P, is a function of Qo denoted as Po = P(Qo). %3D
Question 4 Suppose that for a certain product, the market price P = P(Q) can be written as a function of %3D the market demand quantity Q € (0, 100). (a) Suppose the demand function is P(Q) = 500 -Q and the current market demand is Qo = 80. Showing all steps of your working, evaluate the consumer surplus (CS) defined by Qo CS = "P(Q)dQ – PoQo. where P, is the current market price. Round off your result to 4 decimal places. (b) For the demand function P(Q) = 600 –0, evaluate the consumer surplus CS = CS(Qo) as a function of Qo € (0, 100). Show that CS(Qo) is strictly increasing with Qo by checking the sign of its derivative. (c) Show that CS(Qo) is strictly increasing for any demand function satisfying P'(Q) < 0 for all Q (0, 100). Note that P, is a function of Qo denoted as Po = P(Qo). %3D
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section5.3: The Natural Exponential Function
Problem 44E
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Transcribed Image Text:Question 4
Suppose that for a certain product, the market price P = P(Q) can be written as a function of
%3D
the market demand quantity Q € (0, 100).
(a) Suppose the demand function is P(Q) = 500 - Q and the current market demand is Qo = 80.
Showing all steps of your working, evaluate the consumer surplus (CS) defined by
P(Q)dQ – P.Qo:
CS
where P, is the current market price. Round off your result to 4 decimal places.
(b) For the demand function P(Q) = 600 –0, evaluate the consumer surplus CS = CS(Q.) as
a function of Qo € (0, 100). Show that CS(Qo) is strictly increasing with Qo by checking the
sign of its derivative.
(c) Show that CS(Qo) is strictly increasing for any demand function satisfying P'(Q) < 0 for all
Q (0, 100). Note that P, is a function of Qo denoted as Po = P(Qo).
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