Question

2. Jane's utility function defined over two goods and y is U (x, y) = !/2y\/? Her income is M and the prices of the two goods are p, and Py. (e) Determine the substitution and income effects for good when ini- tially M = $12. Pa = $2, Py = $1, and then the price of good rises to $3. (f) Show the effects from the previous part graphically. (g) How many dollars is Jane willing to accept as a compensation for this price increase?

Answer 1

Amy Budget line u(ny) = n/2 y Y2 Budget line 12=anty At equm, MRS = P happens MRSM Me ama to P " at egun e por on ya Px a on y py aut line I put this y in budget line Prnt PyyaM we will Pynt Py. Ph a = M. on 2pna = M A. n = and yoy 2X2 when, M=12 Pxz2 and Py = 1, then, I No 12 = 3 and to = 214 26 when, Pr' = 3 then, 2² 12 22 and ya 12 = 6 Total effect (2-3) = -1 compensated income is extra income paid to consumes so that he/she could pmchane the old bundle at new price. 2x3 3x3 + 6X1 = 15 kabul compensated income - (15-12) 2&3 income

substitution substitution effect X effect = M/ 2011 - 22 22.5 ni-20 = 2.5-2 = -0.5 22-29 = 3-215 - = -0.5 and income effect Ilo IC2 LILO -ILI T 2 253 & Compensated income M-M. = 3x3 + 186 - 12 - 15-12 -$3