1. A person has utility function U = 4X0.570.5 for goods X and Z at prices Px = $8 and Pz = $32 and income Y = $3200. The marginal utilities of the X and Z are: MUX = 2X-0.5z0.5 and MUZ = 2x0.5Z-0.5 A. Graph the budget constraint (place Z on the horizontal axis, X on vertical axis.) Document the intercepts and slope of the constraint. B. Find the utility maximizing consumptions of X and Y given these prices and income. Explain your work and show on your graph. C. P₂ decreases to $16. Show graphically and find the new utility-maximizing amount of Z.

1. A person has utility function U = 4X0.570.5 for goods X and Z at prices Px = $8 and Pz = $32 and income Y = $3200. The marginal utilities of the X and Z are: MUX = 2X-0.5z0.5 and MUZ = 2x0.5Z-0.5 A. Graph the budget constraint (place Z on the horizontal axis, X on vertical axis.) Document the intercepts and slope of the constraint. B. Find the utility maximizing consumptions of X and Y given these prices and income. Explain your work and show on your graph. C. P₂ decreases to $16. Show graphically and find the new utility-maximizing amount of Z.

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Question

1. A person has utility function U = 4X0.570.5 for goods
X and Z at prices Px = $8 and Pz = $32 and income Y =
$3200. The marginal utilities of the X and Z are:
MUX = 2X-0.570.5 and MUz = 2X0.5z-0.5
A. Graph the budget constraint (place Z on
the horizontal axis, X on vertical axis.)
Document the intercepts and slope of the
constraint.
B. Find the utility maximizing consumptions
of X and Y given these prices and income.
Explain your work and show on your graph.
C. Pz decreases to $16. Show graphically and
find the new utility-maximizing amount of
Z.
D. Sketch out the person's demand curve for
Z.
E. Explain precisely how/why the price paid
for an additional unit of Z can represent its
marginal value to this consumer.

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