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Social Scienceloui's preferences over pizza (x) and other goods (y) are given by U(X,Y)=XY^2, with associated marginal utilities. his income is $240.question d@) calculate his optimal basket when Px=8 and Py=1. b) calculate his income and substitution effects of a decrease in the price of food to $6.c) calculate the compensating variation of the price change. d)calculate the equivalent variation of the price change.
loui's preferences over pizza (x) and other goods (y) are given by U(X,Y)=XY^2, with associated marginal utilities. his income is $240.
question d
@) calculate his optimal basket when Px=8 and Py=1.
- b) calculate his income and substitution effects of a decrease in the price of food to $6.
- c) calculate the compensating variation of the price change.
- d)calculate the equivalent variation of the price change.
Expert Answer
Utility:
The utility is the power or ability of the goods and services that satisfy the consumers want. Alternatively, the satisfying power of commodity is called utility.
The Optimal basket when Px =8 and Py = 1
Budget Line = I = PxX + PyY
240 = PxX + PyY
Utility function , U(X,Y)=XY^2
MUx = Y^2
MUy = 2XY
MUx / MUy = Px/Py
Y^2 / 2XY = 8 / 1
Y = 16x
Insert Y =16x, in budget line, I = PxX + PyY
240 = 8 * X + 1 * 16X
X = 10
Now, put value of X = 10 in Y = 16x
Hence, Y = 16 * 10 = 160
The Optimal basket when Px =8 and Py = 1, (X,Y) = (10,160)
The income and substitution effects of a decrease in the price of food to $6.
In general, Y/X = Px/Py
PyY =PxX
From budget line, I = PxX + PyY
X = I / 2Px
Y = I / 2Py
New budget line, 6x + y = 240
Now, MRS = Px /Py
Y/X = 6/1
Y = 6X
Hence, value of X= 20, Y = 60 (using new budget line, 6x + y = 240)
Now find the new income, delta I = X *delta Px
M – 240 = 10(6-8)
M = 220 (Note-...
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