1. Draw an indifference map for a typical person’s preferences over five-dollar bills
( ) 1 x and ten-dollar bills ( ) 2 x . Explain why the marginal rate of substitution is what you
say it is.
2. Construct a representative indifference curve for the following cases: The two
goods are right gloves and left gloves, and (1) the consumer has two hands; and (2) the
consumer has only one (say left) hand.)
3. Emily gets utility from compact discs (c), movies (m), and pizza (p). If her utility
function is u(c,m, p) = 2cm2 + 4p + cp2 , which of the following bundles of compact
discs, moves, and pizza does Emily prefer?
(i) (2, 3, 4)
(ii) (5, 1, 2)
(iii) (3, 3, 0)
(iv) (0, 10, 0)
4. Let money income be $10 while the price of good 1 is $2 and the price of 2 is $1.
Draw a budget line. Now draw the new budget lines according to each of the following
changes in prices and income.
(i) The price of good 1 decreases from $2 to $1
(ii) The price of good 2 increases from $1 to $2 and income increases to $20
(iii) Both prices are doubled but income is tripled
5. The only two goods that give Bart utility are soap and calculators. When
calculators cost $8 each and soap costs $2 per bar, his optimal consumption bundle is 8
bars of soap and 4 calculators. What is his income? Now the price of soap rises to $3 and
the price of calculators falls to $6, so he can afford a combination of 10 soaps and 3
calculators if he so desires. Would it make any sense for him to consume this new
combination? (hint: Draw a graph)
6. Abe’s marginal utility of apples is 12 and his marginal utility of bananas is 5. If
apples cost $2 each and bananas cost $1 each, is Ape consuming at an optimum? If not,
which fruit should Ape consumes more of?
7. Suppose that income ism =102, and prices are 2 p1 = and 5 p2 = , and consider
the following utility function:
( , ) ( 2)( 1) u x1 x2 = x1 + x2 +
(i) Find the utility-maximizing quantities of 1 x and 2 x .
(ii) What is the maximum utility level that this consumer can achieve?
8. Brendan’s utility function is u(x1, x2 ) = x1x2 . The prices of x1 and x2 are $2 and
$2 respectively. Brendan has an income of $20.
(i) How many of each good will he consume to maximize his total utility?
(ii) What the maximum utility level does he receive? (Hint: For the utility
functionu(x1, x2 ) = x1x2, you have theMU1 = x2 and MU2 = x1).
(iii) Suppose that Brendan’s income increases to $32 but a tax is placed on 1 x
so that 1 x costs Brendan $4 each while the price of 2 x stay the same, how
many 1 x and 2 x will he consume now? What the maximum utility level
will he receive in this case?
al)
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