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3. A consumers preferences over a and y are given by the utility function u(x,y) - 2vr 2/y. The individuals income is I $100. The price of a unit of good c is $2, while the price of a unit of good y is S1. a) Graphically describe: i. the consumers preferences for r and y ii. the budget constraint (b) Find the optimal x that the consumer would choose. You may assume (c) What is the consumers MRS at (x, y) (d) Suppose that the consumers income increases by S50. an interior solution and that preferences are convex (which they are) (10, 80? Interpret. Why is this not an optimal choice of r and y? i. Graphically describe the effect of this increase in the budget con- straint. ii. Calculate the optimal level of x. What level of utility does the con- sumer reach with the new level of income? (e) Suppose now that for every unit of good a that the consumer buys, her employer provides her with an additional dollar to be spent on that good. Repeat question 3d under this assumption

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D O EC ake Convex to oidgin, bwith- de 1&1 50 MAS 6 3 sxy= thus at (ago), MRS not , equad to fAice Ratio, Hence duk not aw ogポWald en ce interpsetation. tMRS ua slope af fe, ft J defined as the人are oodx, to get ow Mone ut of, ephg utlity level 익 at wtun a consumes ouig to ive up a numbeu ofuuh chonged((0,9o), toget ono Mobe Y, lve ((o,9%), to get ono Mose y, give up D wdtl Now at point Hue 이x, d.) Mi=C+ 50=150。 56 y↑ Ty Soy=4x 1a I 15 G X -150 X150 45part a) graph of IC

Dr different levels of utility:

15000 10000 5000 5000 Good

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