- Question 4 20 Marks P Q Can Be Written As A Function Of Suppose That For A Certain Product The Market Price P The Ma 1 (109.37 KiB) Viewed 35 times
market price P = P(Q) can be written as a function of the market
demand quantity Q ∈ (0, 100). (a) Suppose the demand function is
P(Q) = 500−Q and the current market demand is Q0 = 80. Showing all
steps of your working, evaluate the consumer surplus (CS) defined
by CS = Z Q0 0 P(Q)dQ − P0Q0, where P0 is the current market price.
Round off your result to 4 decimal places. (b) For the demand
function P(Q) = 600 − 1 2Q2 , evaluate the consumer surplus CS =
CS(Q0) as a function of Q0 ∈ (0, 100). Show that CS(Q0) is strictly
increasing with Q0 by checking the sign of its derivative. (c) Show
that CS(Q0) is strictly increasing for any demand function
satisfying P 0 (Q) < 0 for all Q ∈ (0, 100). Note that P0 is a
function of Q0 denoted as P0 = P(Q0).
Question 4 (20 marks) P(Q) can be written as a function of Suppose that for a certain product, the market price P 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 = = / (Q– , P(Q)dQ – P.Qo, where Po is the current market price. Round off your result to 4 decimal places. (b) For the demand function P(Q) = 600 – ?Q?, 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 QE (0, 100). Note that Po is a function of Qo denoted as Po = P(Qo). =