Choice Theory Practice Questions
1. Assume a consumer has a utility function over two goods given by U (x, y) = 3 ln(x) + 4 ln(y). For
each of the following utility functions, decide whether it represents the same preferences as the given
function. If it does, provide a function that transforms the original function into the new function. If it
does not, provide a counterexample (i.e. two bundles (x,y) where one bundle is preferred in the original
utility function, but the other bundle is preferred in the new utility function).
(a) 6 ln(x) + 2 ln(y)
(b) 10x3/7 y 4/7
(c) x3 + y 4
(d) 3x + 4y
2. Assume a consumer has a utility function over two goods given by U (x, y) = x + 2y
(a) Draw an indifference curve for this utility function that shows all combinations of x and y that give
this consumer 10 units of utility. Draw a second indifference curve on the same graph showing all
combinations that give 20 utility.
(b) What is the marginal rate of substitution of x for y? How does this relate to the slope of the
indifference curves you drew above?
(c) Assume the consumer currently has 10 units of good x and 5 units of good y. Show this point on
the graph with your indifference curves. For each of the following potential trades, calculate the
consumer’s utility after the trade, plot their new consumption on the graph, and state whether the
consumer would be better or worse off if they accepted the trade. How could you use the MRS to
decide whether the consumer would be better off or worse off?
i. Give up 1 unit of good y and receive two units of good x
ii. Give up 2 units of good y and receive 1 unit of good x
iii. Give up 3 units of good x and receive 1 unit of good y
iv. Give up 1 units of good x and receive 1 unit of good y
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