Question

4. An individual has preferences over two goods (x and y) that are represented by function U = min{x,y}. The individual has income $60, the price of x is $4 and the price of good y is $2. (a) What kind of goods are these to the individual? (i.e. what "special case” is this?) (b) What is this individual's budget constraint? (c) What is this individual's optimal bundle of x and y? [HINT: You can't take the derivative of this utility function, but you know something about the "relationship between x and y" that has to hold at the optimal bundle (d) What is the new optimal bundle when the price of x decreases to $2? (e) Draw a graph (with x on the horizontal axis, and y on the vertical axis) that shows the Income and Substitution Effects of this price decrease. (Hint: one of these effects is zero.)

Answer 1

47 u = min {x, y} . Income = $60 ; Pa = $4 and ly = $2. a) As the utility function is a min function of goods. Hence its a cade of perfect complements 5) budget contraint :- bix + ly . Y = Income . = 42 + 2y = 60 c) oftimal bundle for u = min fa, y } . = 12= y → for fagfeet complements i 4X + 24 = 60 68 - 60 a* = 60/6 = 10; As y* = 10 (2*,y*) - (10,10) – ethimedele u-

: - d) # P = $ 2. do, budget Constiaint becomes 2a + 2y = 60.. > 20 + 20 = 60.. 49 - 60 2 = 60/4 = 15:- - y - Br=15 (2*, 4*) - (15,15) - New Optimal Bundle .
As per HOMEWORKLIB POLICY I can solve only till part (d). So, Request you to please post part (e) so that I can solve it.