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.

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Asked Apr 10, 2019
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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.

 

  1. b) calculate his income and substitution effects of a decrease in the price of food to $6.
  2. c) calculate the compensating variation of the price change. 
  3. d)calculate the equivalent variation of the price change. 
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Expert Answer

Step 1

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.

Step 2

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)

Step 3

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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