Question

Linda consumes only two goods, x and y. Her utility function ? = ??. The initial price of x is $9 and the price of y is $1, and her weekly income is $72. Suppose that the price of x subsequently drops to $4. a) Find the initial consumption basket A when the price of x is $9. b) Find the final consumption basket C when the price of x is $4. c) Find the decomposition basket B. d) Find the numerical values of the income and substitution effects on x consumption. e) Graph the results.

Answer 1

U = xy

Utility is maximized when MUx/MUy = Px/Py

MUx = U/x = y

MUy = U/y = x

MUx/MUy = y/x

(a)

MUx/MUy = y/x = 9/1 = 9

y = 9x

Substituting in budget line:

72 = 9x + y

72 = 9x + 9x = 18x

x = 4

y = 9 x 4 = 36

(b)

MUx/MUy = y/x = 4/1 = 4

y = 4x

Substituting in new budget line:

72 = 4x + y

72 = 4x + 4x = 8x

x = 9

y = 9 x 4 = 36

(c)

In case (a), U = 4 x 36 = 144

Keeping utility at 144 and substituting y = 4x in utility function,

x.4x = 144

4x² = 144

x² = 36

x = 6

y = 4 x 6 = 24

(d)

For good x,

Total effect (TE) = 9 - 4 = 5

Substitution effect (SE) = 6 - 4 = 2

Income effect (IE) = TE - SE = 5 - 2 = 3

NOTE: As per Chegg Answering Policy, 1st 4 parts have been answered.