Assume that a person's utility over two goods is given by: U(x,y) = x^(alpha)y^(1 - alpha). The...


Assume that a person's utility over two goods is given by:

{eq}U(x,y) = x^{\alpha}y^{1 - \alpha} {/eq}.

The price of Good X is {eq}p_{x} {/eq} and the price of Good Y is {eq}p_{y} {/eq}. The total income of the individual is given by M.

A) Write down the budget constraint of this person.

B) Determine the demand functions for x and y.

C) Is Good X a normal or inferior good? Is Good Y a normal or inferior good?

D) Calculate the own-price elasticities of demand for x and y.

E) Calculate the cross-price elasticities of demand for both goods.

Price elasticity vs cross price elasticity of demand:

Price Elasticity of Demand (PED) is characterized as the responsiveness of quantity demanded to a change in price. The demand for an item can be inelastic or elastic, contingent upon the rate change of demand with respect to change in its own price.

On the other hand, the cross elasticity of demand estimates the responsiveness in the quantity demanded of one commodity when the price for another product changes. Based on the sign of cross elasticity of demand, the related good can be classified as substitute or complement or neither.

Answer and Explanation: 1

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Utility function of the two goods is:

{eq}U(x,y) = x^{\alpha}y^{1 - \alpha} {/eq}.

Price of Good X = {eq}p_{x} {/eq}, price of Good Y =...

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Demand in Economics: Definition & Concept


Chapter 7 / Lesson 11

Learn about the demand curve and how the law of demand works with examples. See the demand definition, diagrams, and explanations.

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