b. Suppose his monthly income is $1,800 and X and Y both cost $1 per unit. What

Question

b. Suppose his monthly income is $1,800 and X and Y both cost $1 per unit. What is his best choice?
c. Suppose the price of good X rises to $2 per unit. What is his new best choice?

    What is the total uncompensated change in X?

    What is the corresponding substitution effect?

     What is the corresponding income effect?

What is his compensating variation for the price change?

d. If you measured the change in consumer surplus from the price change in part (c) using Antonio's uncompensated (i.e., ordinary) demand curve for good X, would you overstate, understate, or get exactly correct the compensating variation?

Explanation / Answer

b.

Income = 1800 = Px*X + Py*Y

Px = $1 / unit    

Py = $1 / unit

1800 = X + Y   ------------------------------ (1)

Marginal utility of X / Marginal Utility of Y = Px / Py

(1/X1/2)/ (1/Y1/2) = 1/1

X = Y

Putting the value of X in equation 1

1800 = Y+Y = 2Y

Y = 900

X = 1800 – Y = 1800-900

X= 900

Thus best choice is to purchase 900 units of each X and Y.

C.

1.

Px = $2

Then

1800 = 2X+Y

(1/X1/2)/ (1/Y1/2) = Px/Py = 2/1

Y1/2/ X1/2 = 2/1

Y1/2 = 2* X1/2

Squaring both sides in above equation

Y = 4X

1800 = 2X+4X = 6X

X = 300 units

Y = 1200 units

Thus, the best choice is:

X = 300 units

Y = 1200 units

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