Ross derives utility from only two goods, chocolates (x) and donuts (y). His uti
ID: 1216597 • Letter: R
Question
Ross derives utility from only two goods, chocolates (x) and donuts (y). His utility function is as follows: U(x,y) = 2xy. His marginal utility from chocolates (x) and donuts (y) are given as follows: MUx = 2y and MUy = 2x. Ross has an income of $100 and the price of chocolates (Px) and donuts (Py) are both $0.50. a. What quantities of x and y will maximize Ross's utility? Show your work. How much total utility can be achieved by consuming these quantities? (2+6+2 = 10 points) b. Suppose price of donuts (Py) increase to $1.00, price of chocolates and income remain unchanged. How much is the total effect of this price change on Ross's consumption of donuts? Show your work. How much of this total effect is due to income effect and how much is due to substitution effect? Show your work. (1+4+2+4 = 11 points)
Explanation / Answer
a) for maximisation of utility
MUx /MUy = Px/Py
2y / 2x = 0.5/0.5
2y=2x
x=y
according to budget constraint
0.5x + 0.5 y =100
0.5 x + 0.5 x= 100
x=100
y=100 are quantities that maximize ross's utility
U= 2(100)(100) =20000
b)
price of donut increases to 1.00
then budget constarint will be
0.5x + 1y=100
equilibrium condition
2y/2x= 0.5/1
y= 0.5x
x= 2y
inserting this in budget constraint
0.5x + 1y=100
1y +1y=100
2y=100
y=50
x=2(50) =100
consumption of donuts have decreased from 100 to 50 units.
this price effcet is only due to income effect and not due to substitution effect
because spending share on both x and y have remained and there is no change in the quantity of x
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