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A consumer’s utility function is U(x, y) = 2xy2 . The price of x is Px, theprice of y is Py, and the consumer’s income is I. (x and y do not have to be integers.)a) Derive the equation of the...

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A consumer’s utility function is U(x, y) = 2xy2 . The price of x is Px, theprice of y is Py, and the consumer’s income is I. (x and y do not have to be integers.)a) Derive the equation of the consumer’s demand curve for x.b) With y on the vertical axis and x on the horizontal axis, draw a price-consumptioncurve when the price of x changes.c) Suppose the consumer has income I = 150 and faces prices Px = 5 and Py = 10.What is the optimal basket? Calculate the income and substitution effects (withrespect to x) when Px increases to 8.
Answered Same Day Dec 22, 2021

Solution

David answered on Dec 22 2021
124 Votes
A consumer’s utility function is U(x, y) = 2xy^2 . The price of x is Px, theprice of y is Py, and
the consumer’s income is I. (x and y do not have to be integers.
a) Derive the equation of the consumer’s demand curve for x.
Answer:
Budget constraint: PxX+PyY = I
At optimum point, MUx/MUy = Px/Py i.e.
2y^2/4xy = (Px/Py) or
y/2x = Px/Py or
y = 2x*(Px/Py)
Substitute this in budget constraint:
PxX+Py*[2x*(Px/Py)] = I...
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