Question

2. (30 pts) Carol likes milk (201) and cookies (2). She always takes one cup of cookies with two cups of milk. Let Pı be the price of milk (per cup), P2 be the price of cookies (per cup), and m be her weekly income. (a) Draw some of her indifference curves and find her ordinary demand functions for milk and cookies. (b) Derive her price offer curves and her income offer curve. (c) Suppose that Pı = P2 = $2 per cup and m = $24. Consider a price drop in milk to Pi = $1 per cup. Calculate her optimal consumption bundle and her level of utility before and after the price change. (d) Calculate the substitution effect and the income effect of the price change in Carol's demand of milk. Use a graph to show the two effects. CAR

Answer 1

X line Q) a) u (X1, X2) = Min (2X1, X2) Q) a) UCXI, X 2) = Min (2X2, XI), 80 that Eqm 2X2=X1 X2 = 1 gc are L Right angled shape, Kink along x = 2x2 from B.C. - Pix, TP2X2= m . put XI = 2x2 2X2P 1 + P2 X2=m 1 X 2 = [X, * = 2m QP,+P2 QP+P2 b.) Ang Price after curve 10c: x2=X1/2 x2=X1/2

A) IC

2X2 = XT

(0) 477 PI = P2=2, m= 24 , P = 1, Initial Bundle, x= 2x24 = 48 = 8, X2 = 8/2=4. 4+2 New Bundle, X = 2x24 = 4 X2 = (48) 2+2 4 Initial u= Min (2x4,8)=8 New u= min (QX6,12)=12 d.) as Preferences are perfect complements, two Goods are consumed au fixed prop", 80 only Income effect exist, p substitution effect is absent, Bioz two Goods can't be Substituted for each other thus TE=IE= XI-XI * = 12-8=4. Income effect = 4 Ang

Graph

_20 -1-5- IC2 -10 X2 -57B61 BC2 X1 20 5 10 12 8 IE = TE 15