Suppose a consumer utility from goods X and Y are given by ?(?,?) = ? ?? ? and ? + ? = ?. The money income is M, and the prices of goods X and Y are ?? and ??, respectively. a) Draw a budget constraint (X on the horizontal axis, Y on the vertical axis). b) Find the optimal levels of X and Y that would maximize the consumer's utility. c) Is X normal good? Justify. d) Is Y normal good? Justify. e) What's the price elasticity of demand for good X? f) What's the income elasticity of demand for good Y? g) Now, suppose the price of good Y reduced by 20%. Draw a new budget constraint. h) Find the new optimal levels of X and Y that would maximize the consumer's utility. i) Now, assume the original prices of goods in part (a). But the money income increased by 50%. Find the new optimal levels of X and Y that would maximize the consumer's utility.

e l-V X e I'Ipese I-CE Files I0 Pratt; I S Supp: I6 230th I 0 [8)Wi In Given I 9 Maria; I 5 (unit In HW-2 I ) Home I 5 What: In Supp: I + V X C G) maznl Cu'Users/AsustownloadsfHW-Epdf E {y E; n o a) Find the price elasticity ofdemand. b] Is the demand elastic or inelastic? Justify. c) Find the cross-price elasticity of demand. (:1) Are goods X and Y substimtes or complements? Justify. e) Find the income elasticity of demand. 1) Is good Xnonnal or inferior? Justify. g) Is good Xluxury? Justify. Suppose a consumer utility from goodsX and Y are given by U (X . Y) = X \"l\"? and a: + B = 1. The money income is M, and the prices of goods X and Y are PK and Py. respectively. a) Draw a budget constraint (X on the horizontal axis, Y on the vertical axis). b) Find the optimal levels of X and Y that would maximize the consumer's utility. c) Is X normal good? Justify. d] Is Y normal good? Justify. e) What's the price elasticity of demand for good X? 0 What's the income elasticity of demand for good Y? g] Now, suppose the price of good Y reduced by 20%. Draw a new budget constraint. h) Find the new optimal levels of X and Y that would maximize the consumer's utility. i) Now, assume the original prices of goods in part (a). But the money income increased by 50%. Find the new optimal levels ofX and Y that would maximize the consumer's utility. ' 13C. Cloudy