June buys both ham (x) and cheese (y) for her sandwiches. Her preferences over t
ID: 1169599 • Letter: J
Question
June buys both ham (x) and cheese (y) for her sandwiches. Her preferences over these two goods can be represented by the utility function u(x, y) = min{x, 2y}. That is, ham and cheese are perfect complements. Suppose June has income I = 60 to spend on ham and cheese. The price of a slice of ham is px = 2 and price of a slice of cheese is py = 1. Use the utility function given above to find her best consumption bundle (x*,y*). Suppose now that the price of a slice of ham is px = 1 and price of a slice of cheese is py = 2. Find the new optimal consumption bundle (x*,y*). Comparing your result in part (a) and (b), does it imply an upward sloping demand curve for cheese (y)?Explanation / Answer
u = min [x, 2y]
This utility function signifies that x and y are perfect complements (L-shaped indifference curves].
(a) Budget line: I = xpx + ypy
60 = 2x + y
For perfect complements, optimal consumption bundle is when x = 2y
Substituting in budget line,
60 = 2 x 2y + y = 5y
y = 12
x = 2y = 24
(x*, y*) = (24, 12)
(b)
Revised budget line:
60 = x + 2y
Optimum bundle stays the same at x = 2y.
60 = 2y + 2y = 4y
y = 15
x = 2y = 30
(x*, y*) = (30, 15)
(c)
When py = 1, y = 12
When py = 2, y = 15
As price increases, quantity of y increases. This suggests an upward sloping demand curve.
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.