Question

Andrea loves to eat donuts with coffee. In fact, she cannot enjoy coffee (x) unless she has two donuts (y). She gets no additional enjoyment from eating more donuts, unless she has the coffee to go with it.
(a) Write the utility function that represents her preferences.
(b) Graph her indifference curves when U = 2 and U = 6, labeling the nodes on the x- and y-axes.
(c) Suppose donuts each cost $2 and cups of coffee each cost $1. Her weekly budget for coffee and donuts is $25. Add the budget constraint to your graph.
(d) What is her utility maximizing bundle of coffee and donuts? What is her level of utility?
(e) Now, suppose that she moves to the Bay Area, where donuts are still $2, but the price of coffee is now $3. Add a new budget line that represents this price change, with the original budget of $25. What is her new level of utility?
(f) How much would her coffee & donut budget need to increase in order for her to maintain her original level of utility from part d)?

Answer 1

a)

Given, Andrea cannot enjoy coffee (x) unless she has two donuts (y). She gets no additional enjoyment from eating more donuts, unless she has the coffee to go with it => Andrea has Leontief preferences.

U(x,y) = min {x, y/2)

To enjoy 1 unit of utility, Andrea needs 1 coffee and 2 donuts.

b)

c)

Given p_x = 1, p_y = 2 and income I = 25

Budget constraint: p_x. x + p_y. y = 25 => x + 2y = 25

d)

Andrea's optimization problem:

max u(x,y) = min{x, y/2} s.t. x + 2y = 25

Given the nature of leontief preferences, and as evident from the graph,

utility maximizing bundle is given at the "kink" i.e.

x* = y*/2 => y* = 2x*

Substituting this in budget constraint:

x* + 2y* = 25 => 5x* = 25 => x* = 5

thus y* = 2*5 = 10

(5,10) is utility maximizing bundle.

Utility level U = min{5, 10/2} = 5