Question

Maeby has $20 to spend between movies and clothing. The price of movies is $1 and the price of clothing is $4. Suppose Mary’s utility function is given by the equation U = XY, where U is the level of utility measured in utils and X and Y refer to movies and clothing respectively. The marginal utility of movies can be expressed as MUx = Y; and the marginal utility of clothing can be expressed as MUy = X. a) Graph the budget line. b) Solve for the utility maximizing bundle which Maeby should choose. What is her utility from choosing this bundle?

Answer 1

(a) Budget line: $20 = $1 x X + $4 x Y

20 = X + 4Y

When Y = 0, X = 20 (Vertical intercept) and when X = 0, Y = 20/4 = 5 (Horizontal intercept). In following graph, AB is the budget line.

(b) Utility is maximized when MUX/MUY = PX/PY = $1/$4 = 1/4

MUX = U/X = Y

MUY = U/Y = X

MUX/MUY = Y/X = 1/4

X = 4Y

Substituting in budget line,

20 = X + X = 2X

X = 10

Y = X/4 = 10/4 = 2.5

U = XY = 10 x 2.5 = 25