Question

4. (50%) Maggie's demand function for bagels. Assume that U(CB) = CSB-S and that the price of bagels is Pa, the price of chalis Pc, and income is I (do not assign numerical values to the variables!). a. Use the three steps from lecture to find the chal demand function, C(pc.1), and the bagels demand function, B(P8.1). You must show how you derive the tangency condition from the given utility function (hint: calculate MU, MUe, etc.)! b. Given the demand functions from (a), calculate and interpretpol and PP: apa OB(PB.) C. Given the demand functions from (a), calculate and interprete a. If Maggie has $6, the price of bagels is $1.50, and the price of chair is $3, how much of each good does she consume?

Answer 1

U=Ch Bir muc du = 1 Bill 12 MUB - dy dB Slope of Indifference curme = MR S ce - Muc MUB a c/2 cl2 Slope of Budget line - Pe (a) At equilibrium Slope of Indifference curne - Slope of Budget in line

[PB B = Pc c) - Cu - Put (1) in budget constraint, e Pe. C + PB B = I Pe c & P. c = I » QPC . c = I >> - Chair demand from 6 - (1) we have; PB B = Pec В - Гас B = B = I Bagel demand 2PB Function

I so and pe o This means that the demand for chair is inversely related to its own price ice As the price of Chair increases, the demand for chair will decrease and vice-versa assuming other things (I) to be constant. B - I Lo Io , Pozo The demand for bagel is also inversely related to its own price assuming other things (I) to be constant.

- ac 2 I 0 [ Pe >o] This means that increasing the income cuill increase the demand for chair while keeping the price of chair constant. Hence Chair is a normal Good. B = 2PB [ PB >o >o This means increasing the income will increase the demand for Bagels and vice-versa while keeping the - price of Bagel constant. Honce . Bagel is also a normal Crood. o Criven, I= $6 ;PB = $1.50 and Pc = $3. care ang = 1 and Barbulis = 2