Question

Consider your tastes for $5 bills and $10 bills. Suppose that all you care

about is how much money you have, but you don't care whether a par-

ticular amount comes in more or fewer bills (and suppose that you could

have partial $10 and $5 bills).

(a) With the number of $5 bills on the horizontal axis and the number

of $10 bills on the vertical, illustrate 3 indierence curves from your

indierence map. Write down a utility function that represents the

tastes you graphed.

(b) What is your marginal rate of substitution of $10 bills for $5 bills?

(c) Are averages strictly better than extremes? How does this relate to

whether your tastes exhibit diminishing marginal rates of substitu-

tion?

(d) Are these tastes quasilinear?

(e) Are either of the goods on your axes \essential"?

Answer 1

let x1 = five dollar bills

    x2 = ten dollar bills

b ) According to prefrences given , we can assume that ,this person has cobdouglas utility

U=x1x2

MRS = MUx1/MUX2 = x2/x1 =10/5 = 2

c) MRS =x2/x1 = 5/10 = 0.5

d) Yes averages are stricly better than extremes , implying strict convexity .

differentiating mrs with respect to x1

dmrs/dx1 = - x2/x1² <0

quasi concavity with diminishing mrs

similarly for x2.

e) yES , these prefrences are homothetic