Question

Show all work please.

1. U(x, y) x,ax,1-a) a. Solve for the marshallian demands for x, and x2, as functions of p1, p2, and m. (Hint: your solutions will be equations, not numbers). (4pts) b. For x, find the own-price elasticity and income elasticity. (4pts) c. Suppose a = d. What happens to these quantities when p1 doubles to $4? (4pts) e. What does this say about the price consumption curve (PCC)? (4pts) 100, p1 2, and p2=8, find the quantities of x, and x2. (2pts) 0.2, m

Answer 1

(a) UCXI,X2) = x,a xal-a ov - Mo, ax4-1 x, -а OX1 ao - mor= (1-2) X, 9 x2 t-a-1 = (1-2) X, 9 xz a MRS = - мо, MU2 ax,- 'х-4 (1-a) x, a za X X X la -a (3) C lia) (*) ) X. (x2) Bl: Pixit P2 X2. = m o At optimal choice MRS = Pi - Get *) = X2 put x 2 = (1-2) ( ) x x Equ-o. in P. XL+ P2X2 = PiXLT Psi-a m pi x =m a Pr . a Pixit (1-2) PIXI =m a

Pix lat la) zm 1 = m Pixn= am xi² am *2= line you lanmou) X2 = (-a)m P2 X = am 2x % own price elasticity of ad d o ExiPi = 0x1 P. X1 = -1 JE) = |-) = 1

income elasticity of demand Ex, m = em = 1 c) a=0.2, m=100, P1=2, P2 = 8 xi= am - x = A = (220 b) = lo (0.2) (150) Po x2 = (-a) m = (1-0-2) 100 = 0.8x160 = 10 d) Now P,'=u, P2=8, m=100 x1= = 0.2x100 = 5 X=am = 0.2 x 100 = 5 am P X 2 = (1 -a m = 0.9 X 100 = 10 P2