Question

3. Suppose your utility function (e. level of satisfaction from consuming a and b) is given by U(a, b)=a 1/32/3 where a represents apple and b represents banana. Your total income is $500. The price of apple is $5 and the price of banana is $10. (a) Write your Budget Constraint (BC). What is the Marginal Rate of Transformation? (b) Find the Marginal Rate of Substitution. (c) Find the consumption combination of bananas and apples that maximizes your utility given your budget constraint. (d) From your answer on (c), what is the utility (or level of satisfaction) that you get? Now, suppose the price of apple increases to $10. (e) Find the consumption combination of bananas and apples that maximizes your satisfaction given your new budget constraint. What is your new utility?

Answer 1

- I = $500 (a) Budget constraint ? Pat P B = I SA ISAT lob=5ool

Marginal rate of transformation, Th) Marginal rate of substitution MRS, mua MUA MRS IMPS I b (c At optimal consumption bundle

MRT - MRS Put this into budget constraint, Sa sat lob- 500 Sat loa -500 a = 500 Ta= 33.33

TU-33.33 Total utility from the optinal bundle (e) - Suppose, la increases to $16. Now, budget constraint is & lo at lob= 500 Ast optimal dundle - MRT - l = MRS - MUX Now put this into new budget constraint, we get i- lo a tlo(2a) - 500

30a - 500 Ta = 16.67 . U = (1626 7)*/3333343 - (1642"o ( 16.6.2)*243 = 16.67) (2 % U= (1667) (1:59) go" 26.50 New utility