Ambrose, whom you met in the last chapter, continues to thrive on nuts and berries. You saw two of his indifference curves. One indifference curve had the equation x2 = 20 ˆ’ 4ˆš x1, and another indifference curve had the equation x2 = 24 €“ 4 ˆš x1, where x1 is his consumption of nuts and x2 is his consumption of berries. Now it can be told that Ambrose has quasilinear utility. In fact, his preferences can be represented by the utility function U(x1, x2) = 4ˆš x1 + x2.
(a) Ambrose originally consumed 9 units of nuts and 10 units of berries.
His consumption of nuts is reduced to 4 units, but he is given enough berries so that he is just as well-off as he was before. After the change, how many units of berries does Ambrose consume? _____
(b) On the graph below, indicate Ambrose€™s original consumption and sketch an indifference curve passing through this point. As you can verify, Ambrose is indifferent between the bundle (9,10) and the bundle (25,2). If you doubled the amount of each good in each bundle, you would have bundles (18,20) and (50,4). Are these two bundles on the same indifference
curve_____

(c) What is Ambrose€™s marginal rate of substitution, MRS(x1, x2), when he is consuming the bundle (9, 10)? (Give a numerical answer.) _____ What is Ambrose€™s marginal rate of substitution when he is consuming the bundle (9, 20)? _____
(d) We can write a general expression for Ambrose€™s marginal rate of substitution when he is consuming commodity bundle (x1, x2). This is
MRS(x1, x2) = _____ Although we always write MRS(x1, x2)as a function of the two variables, x1 and x2, we see that Ambrose€™s utility function has the special property that his marginal rate of substitution does not change when the variable x2 changes.

Transcribed Image Text:

Berries 20 10 (9.10) 10 20 Nuts 15