Question

how to solve this?!

Section III Longer Problems (4 points each - 68 points total). Show your work. 1. Consider Mary's utility function u(x1, +2) = [min{2x1, x2}]} (a) Draw Mary's indifference curve that yields u = 1 and u = 2. Mark the kink clearly. (b) Derive Mary's optimal demand function for each of the goods, i.e., find ai (P. P. m) and (P1, P2, m). (C) If Pi = 1, P2 = 1 and m 6, what is her optimal consumption bundle (1 ) (a) Suppose the price of good 1 increases, P = 4, 12 = 1 and m= 6. Find her optimal consumption bundle (xi ) given the new prices. (c) Given the new prices, how high must be for Mary to be as happy as having the original comsumption bundle in point d? (1) Given the hypothetical income and new prices, what is her optimal consumption bundle ) () Find the income and substitution effects based on the consumption bundles (1 (31',-) and (312)

Answer 1

b.

given u (x1,x2)= min(2x1, x2)

the optimal demand function is given at the kink, hence

2x1= x2.................(1)

now consider a budget constraint given as M= p1x1 + p2x2............(2)

put the value of x2 in Eqn (2) from Eqn (1)e

we get m= p1x1+2p2x2

x1= m/p1+2p2

so, x2= 2m/p1+2p2

c.

if p1 = 1 , p2 =1 and m = 6

then (x1,x2) = (2,4)

D.

if p1 = 4 then

the demand will be changed to x1 = 1 and x2 = 2 (since it is the complementary goods hence change in p1 will also reduce the demand for good 2 i.e.x2)

E. marry needs to increase it m (income to 12) i.e. doubles the original so as to derive the same demand. it can verify by putting m=12 in the derived demand functions x1 and x2.