Please explan how you arrived at your answers :) Georgia consumes only grapefrui
ID: 1187551 • Letter: P
Question
Please explan how you arrived at your answers :)
Georgia consumes only grapefruits and pineapples. Her utility function is U(x,y)=x^2y^8, where x is the number of grapefruits consumed and y is the number of pineapples consumed. Georgia's income is $105, and the prices of grapefruits and pinapples are $1 and $3, respectively.
a) write down Georgia's budget constraint. What is the slope of the budget line?
b) What is Georgia's marginal rate of substitution at the point (x,y)?
c) How many grapefruits will she consume?
d) how many pineapples will she consume?
e) If her income increases to $120, how many grapefruits will she consume? Are grapefruits a normal or inferior good?
Explanation / Answer
Georgia's income is $105, and the prices of grapefruits and pinapples are $1 and $3, respectively.
Let, x is the number of grapefruits consumed and y is the number of pineapples consumed.
(a) Georgia's budget constraint:
So, x+3y= 105 ;slope= 1/3;
(b)Georgia's marginal rate of substitution at the point (x,y) is 4
(c) utility function is U(x,y)=x^2y^8 = (105-3y)^2*y^8 ;So,for max satisfaction, dU/d x=0;
10y^9-630y^8+9800y^7=0;
y^2-63y+980=0;
y=35,28 ;x=0,21;
(x,y)=(21,28) is solution.
She will consume 21 grapefruits.
(d)She will consume 28 pineapples