Lucas likes lemon soda (X) and chips (Y).His utility function is given by: U (X, Y) = X0.2Y0.8 He earns $40 per week to spend on lemon soda (X) and chips (Y).The prices of lemon soda and chips are $2 and $4 respectively.Find out Lucas’s utility-maximizing bundle of lemon soda and chips (X*, Y*). Set up the utility-maximization problem and find out the price ratio of these two goods. Find out Lucas’s marginal utility of lemon soda (MUX) and marginal utility of chips (MUY). Calculate the MRSXY .Set up the optimal tangency condition and solve for Y in terms of X. Solve for Lucas’s optimal consumption bundle of lemon soda (X*) and chips (Y*).Draw the optimal consumption bundle on the budget constraint BC1 in Q1. Denote it as Bundle A. Make sure to indicate the optimal consumption of lemon soda (X*) and chips (Y*). Draw an indifference curve that is tangent to the budget constraint at Bundle A. Calculate the value of the MRSXY (the value not the formula) at the optimal consumption bundle and provide an economic interpretation.

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Answered: Lucas likes lemon soda (X) and chips…

Economics:

10th Edition

ISBN:9781285859460

Author:BOYES, William

Publisher:BOYES, William

Chapter21: Demand: Consumer Choic

Section: Chapter Questions

Problem 1E

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Lucas likes lemon soda (X) and chips (Y).

His utility function is given by: U (X, Y) = X^0.2Y^0.8
He earns $40 per week to spend on lemon soda (X) and chips (Y).
The prices of lemon soda and chips are $2 and $4 respectively.

Find out Lucas’s utility-maximizing bundle of lemon soda and chips (X*, Y*).

Set up the utility-maximization problem and find out the price ratio of these two goods.
Find out Lucas’s marginal utility of lemon soda (MU_X) and marginal utility of chips (MU_Y). Calculate the MRS_XY .
Set up the optimal tangency condition and solve for Y in terms of X.
Solve for Lucas’s optimal consumption bundle of lemon soda (X*) and chips (Y*).
Draw the optimal consumption bundle on the budget constraint BC₁ in Q1. Denote it as Bundle A. Make sure to indicate the optimal consumption of lemon soda (X*) and chips (Y*). Draw an indifference curve that is tangent to the budget constraint at Bundle A.
Calculate the value of the MRS_XY(the value not the formula) at the optimal consumption bundle and provide an economic interpretation.

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