# Consider the utility function U=x^a+ay a=alpha I=Pxx+Pyy (a) What is the optimal combination of...

## Question:

Consider the utility function U=x^a+ay a=alpha I=Pxx+Pyy

(a) What is the optimal combination of x and y?

(b) Solve for the indirect utility function.

(c) Show that utility is increasing in I and decreasing in px and py.

## Utility function

Utility function measures the satisfaction received from a given bundle of goods. It is represented by U. It is represented using an Indifference Curve or IC. It is used to measure the amount of satisfaction a consumer receives on consuming a particular combination of the commodities.

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The utility function and the budget constraint are:

{eq}\begin{align*} U &= {x^a} + ay\\ I &= x{P_x} + y{P_y} \end{align*} {/eq}

(a)

The...