Question

ECON11: Problem Set 6 Due on November 14 before 9:30 in class Put name (Last, First), Student ID, and TA Section letter on submissions 10.7 1. Judy's Marshallian demand for oranges is anges is 2 n + 3)0.4, where pa is the price of apples, P. is the price of oranges, and I is Judy's income. Suppose I = 100, Pa = 2, and p. = 1. (a) Find and interpret the income elasticity for the demand for oranges. Are oranges an inferior or normal good? (b) Find the own price elasticity of demand for oranges. Discuss how the price elas- ticity varies with Po. (c) Find the cross price elasticity for oranges. Are oranges and apples gross substitutes or gross complements? 2. Suppose the preferences of an individual are represented by a quasilinear utility func- tion: U(x,y) = ln(x) + 3y (a) Initially, Pr=1, Py=6 and 1=102. Then, the price of increases to 2 (p,=2). Calculate the changes in the demand for x. Please also calculate the substitution and income effects of the change in pa on r. (Hint: since the change in price is not small, you cannot use the Slutsky equation. You need to have numbers instead of functions as the answer.) (b) Please also calculate the substitution and income effects of the change in P, on y. (c) Instead of doubling to 2. suppose p, is only increased by a small amount. Use the Slutsky equation to find the substitution and income effects of the change in the price of 2 on z. Compare your result to (a). Explain why there's no income effect of the change in pon x. Show your result on an indifference curve. (d) Use the Slutsky equation to find the substitution and income effect of the change in P, on y. Compare your result to (b).

Answer 1

A) Income elasticity shows how the quantity responds to changes in income.

Here income elasticity is 0.7 which means that demand is inelastic to changes in income i.e. demand doesn't respond much to a given change in income.

I Po Pa 2 ou nastialy a In omu (2P)alo4) 0,1 I po Cpatao.y) 0.7

Since income elasticity is positive , therefore ,the quantity demanded will increase for an increase in income( less than proportionate increase in income) and hence the good is a normal good.

B) own price elasticity shows how the demand responds to changes in its own price.

Here, own price elasticity comes out to be (-1) which means that for a unit increase in price, the quantity demanded will decrease by one unit.

pt elastrieuty dao aun 8о 2 (at4 al Po 7 (Pa +.4 Po) (Po) (--2 Po -I

C) cross price elasticity of oranges will show how the quantity of oranges responds to changes in price of apples.

Here the cross price elasticity is = (-0.4pa(pa+3)^-1), which is negative. This means that for an increase in price of apples, the demand of oranges decreases which means that apples are gross complements to oranges.

O. chers phice elastiuty do I(a) Pa dPa 2 Po Eo.) (Pat 3) Pa (a+3)-0.4 Par3)1.4 Pa. (04) (Pa) a 13)