Question

Consider a consumer with a utility function u(x1, x2) = min{21, 222}. Suppose the prices of good 1 and good 2 are p1 = P2 = 4. The consumer's income is m = 120. (a) Find the consumer's preferred bundle. (b) Draw the consumer's budget line. (c) On the same graph, indicate the consumer's preferred bundle and draw the indifference curve through it. (d) Now suppose that the consumer gets a discount on good 1: each unit beyond the 4th comes at a reduced price of 1. In a separate graph draw the new budget constraint. Find the consumer's optimal bundle. (One way to do this is to draw his indifference curves through different points)

Answer 1

utility: uomin&a, 282}. x and az are complements and consumed jointly such that 4 = 222 at equilibrium. Budget: 124 + 4x2=120 a, 9 (27) + 4x2=120 1234 : 120 3.82=10 } preferred bundle 24 = 20 ) b) consumers budget line: 421 +422= 120 e intercept: 120 = 30 2x2 - - - - uzo - consumers preffere preferred bundle is EC 20,5). 10 The corresponding utility: ū= min $20,20}=20 d) Thee budget line now has kink at 4= 4. from this point the line become flatter. The highest amount of a bought : 4+ (120-4*4)=108 At new equilibrium : 2 =222 27 2-222 As old equilibrium = 574 New equilibrium lies in the flatter part. jo! 4= 90

The equation of the budget line: . Az + 4x2 = 120 for xust 24 + 4*, = 120 " X,>4 If the consumer consumes at the flatter part; for any bundle {2, ²2} total expenditure : 4x4+ (â - A) + A2= 120 on hi - 4 tah= 109 :. + , - 108 Then for 24 = 22; 22 +422= 108 ar, 62 = 108 :.X2 = 18? Ez :. = 36 2