Question

Consumer Theory 13 Ordinary Goods 1. Let U(x, y) = x2/3743, MU2 = 173 MUY = 2 x 5 Pa = 6, Py = 3, and M = 30. 2. Let U(x, y) = x2/3y1/3, MUX 17, MUY Px = 6, Py = 3, and M - 30. 3. Let U(x, y) = 2x1/3y2/3, MU, = 2 21/a, Px = 6, Py = 3, and M = 30. 4. Let U(x, y) = 2x4 3y1/3, MUx = * * 78, PX6, Py = 3, and M-30. 5. Let U(x, y) = 3x1/2y1/2, MU< = x/2, MUY = /2Px = 6, Py = 3, and M = 30. 4:13 4 x 1 , MU, = a) What is the equilibrium levels of X, Y, and U? Denote this point as A. b) Suppose now, Px = 3. What is the new equilibrium levels of X, Y, and U? Denote this point as C. e) Determine point B, where the individual is hypothetically given more income to compensate for the change in price levels, but is consuming the same utility as point A. (Hint: use the optimal relationship with the new price level and substitute it into the utility of the initial equilibrium.) d) Clearly illustrate point A, B, and C on the graph and accurately label everything.

Answer 1

ANSIER: All the vitilidywe functions are Cobb Douglas Function So, I'll show you a, b, c & d part for Part 3. (3) Given: (,y)=Jz"Sy4+3, MUx=2 y 3 , MU,= 4 (2)", P=6, P423, M230 and Py = 3 First of all, we will solve for a Marshallian demand functions Of Xe'yo. At equilibrium we have, MRS = Px 3813 14 MUX = Px Muy - R *** Y-2BX Budget constraint: Pr X + PyYa M. PxX + Ry/2BX_)=M so, B 3 PX=M TREM Ya (X) = 2 * 1]

ca) Pe=8, P423,M=30 30 š! 2333 == 2x5% (b) PY= 3 Py = 3 M= 30 | tone 392 1 1 Y = 3301= 20 u'= 2(7")" (ya) . (e) Let the hypothetical income be m' and the prices sere Pr' = 3,' R =3, and at U= 20 (2)"} We know, 2 x 1'3y213 47 24 hours cames) U= 2 MP (4) 20 (2)% = 2M! (4) "3 M's 30 or m'= 15:14) 3 (1) 3 t's 15(4%) vs Z(15)(u)* x= 1 | [ys 19 ws) 313)

Goddy a M=30,8=3) M: 1514313, 2-3) 7 All the doumwand Subung in one Budget lines (M=30, 8225) U=2013) 's 2 3 y 5 6 7 8 9 10 Goody