Question

Olga makes her own trail mix at home and likes to have a particular ratio of dried fruit (d) to peanuts (n). Her utility is represented by the following Leontief preferences over bags of dried fruits and peanuts:

u(d,n)=min[6d,18n]

The price of a bag of dried fruit is pd, the price of a bag of peanuts is pn, and Olga's income is represented by m.

a. Setup Olga's utility maximization problem. Then find the demand functions for goods d and n (show work)

b. Write the formulas and calculate the following elasticities for demand of dried fruit (d)
(show work)
Price elasticity of demand:

Cross price elasticity of demand:

Income elasticity of demand:

c. Setup expenditure minimization problem and solve for the compensated demand functions (show work):

d. Graph and label the demand function for d*(Pd, Pn,m) when Pn=3 and m=20 (place d on the x-axis and Pd on the Y-axis)

e. Graph the compensated demand function for d^c(Pd,Pn,U-bar) when Pn =3 and U-bar=72 (place d on the x-axis and Pd on the y-axis

Answer 1