1. Utility is given by the function U(X,Y) (X+ 5)0.6y0.3. The price of X is P, and the price of Y is P. Income is I. a. Solve for the optimal values of X and Y in terms of P, Py, and I. Show your work. b. Are goods X and Y complements or substitutes? Explain. c. Are corner solutions possible? If yes, explain when it (or they) can happen. Show your work.

ENGR.ECONOMIC ANALYSIS
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Chapter1: Making Economics Decisions
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1. Utility is given by the function U(X,Y) (X+ 5)0.Y0.3.
The price of X is P, and the price of Y is Py. Income is I.
a. Solve for the optimal values of X and Y in terms of
Py, Py, and I. Show your work.
b. Are goods X and Y complements or substitutes?
Explain.
c. Are corner solutions possible? If yes, explain when it
(or they) can happen. Show your work.
d. Draw the Engel curve for good X. Label the slope
and both axes.
e. Suppose I = $100, P, = $1, and P, = $1. Then P,
rises to $2. Using the utility function above,
calculate the sizes of the substitution effect, income
effect, and total effect with respect to good X only.
Anyone short of Einstein will need a calculator of
%3D
some sort.
Transcribed Image Text:1. Utility is given by the function U(X,Y) (X+ 5)0.Y0.3. The price of X is P, and the price of Y is Py. Income is I. a. Solve for the optimal values of X and Y in terms of Py, Py, and I. Show your work. b. Are goods X and Y complements or substitutes? Explain. c. Are corner solutions possible? If yes, explain when it (or they) can happen. Show your work. d. Draw the Engel curve for good X. Label the slope and both axes. e. Suppose I = $100, P, = $1, and P, = $1. Then P, rises to $2. Using the utility function above, calculate the sizes of the substitution effect, income effect, and total effect with respect to good X only. Anyone short of Einstein will need a calculator of %3D some sort.
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