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PROBLEM IV. Ambrose's utility function is U ($1.32) = xix; where :1 is his consumption of good 1 and 1'2 is his consumption of good 2. The price of good 1 is 3, the prioe of good 2 is 4, and Ambmse's income. is 20. Q17. Ambrose'a marginal rate of substitution at a bundle (11,19) is m% (b) 7%:- ma (r1) E%i on' Q18. At Ambrose's optimal consumption bundle (run), the marginal rate of subatitution must equal the slope of the budget line, i e, rm/pg = 3;'4. Thin condition can be written as cw75=7i (m%=-% M-%=% (d1 \"$4, = -% mih= Q19. At Ambrose's optimal consumption bundle (:51' mg), he will use his entire income for purchasing the bundle. In other words, the bundle ($1.13) hon on the budget Line. This condition can be Written as (a) 3;, + 412 s 20. (b) 7% = 20. 1 (c) % a 20. (d) J's\"; = 20, (e) xiii = 20' Q20. What is Amhmsc's optimal consumption bundle ($1432)? (a) (6.0) lb) (2.3) {c} (El-5) {d} (3,3) (8} (4-2) Q21, Suppose that than: in another consumer. Beatrice, whose utility func is given by [1"(21, 2;) = 21:; + (in. When the price of good 1 '5 3, price of good 2 is 4, and Beatrice's income is 36, her optimal consumption bundle is (a) (5:5) 0?) (0:9) (C) (4:5) (d) (8'3) (9) (12,0) Q22. Suppose that there in yet another consumer, Charlie. whose utility func- tion is given by Wynn) : min{1'1'4:rg}. When the price of good 1 is 3' the price of good 2 is 4, and Charlie's income in 32, her optimal oonsnmptiun bundle is in) (0.8) (b) (4-5) (C) (9. 1} (d) (3.2) 0*) (5:6)