Question

4. consider the following utility functions

a) for each of these utility function what is the equation of an indifference curve ?

c) for each utility function show weather the function exhibits the diminishing rate of substitution property

d) do the above utility function represent the same preference ordering? why or why not?

c) Suppose the price of beer doubles, but the price of pizza and Tom's income stay the same. How much beer is Tom consuming as a percentage of his previous beer consumption? How much pizza is Tom consuming as a function of his previous pizza consumption? (d) Would Tom be willing to switch bundle A (4,2) for bundle B (2,4)? Why or why not? 4. Consider the following utility functions: i u(i,2) (1/3)712, with MU (1/3)2 and MU2 (1/3)1 ii u(1,r2) 7(12), with MU 14zian and MU 14x32 (a) For each of these utility functions, what is the equation of an indifference curve? (b) For each of these utility functions, compute the MRS. (c) Diminishing marginal rate of substitution occurs when the MRS decreases (in absolute value) as we increase 1. Note that only strictly convex preferences exhibit this property. For each of the utility functions above, show whether the function exhibits the diminishing marginal rate of substitution property. (d) Do the above utility functions represent the same preference ordering? Why or why not? 5. Suppose Peter has $800,000 to spend on a house and "other goods" (denominated in dollars). The price of 1 square foot of housing is $300, and Peter chooses to purchase a house of 2,000 square feet in size. Assume that houses do not differ in quality: their price is solely determined by their size. Also, assume throughout that Peter spends money on housing solely for its consumption value, not as part of his investment strategy, and that Peter has well-behaved, strictly convex preferences. Page 2

Answer 1

Equation of IC is found by writing X2 as a function of X1, for a given constant utility level

2%

D) if MRS is same, then two utility function will exhibit same preferences. Thus all consumers will rank the difference consumption bundles in same way

Bcoz each utility function is strict monotonic transformation of one other