Assume that Kelly is a life cycle consumer and receives incomes of 20, 30, 45 and 0 in her four period life. What is Kelly's marginal propensity to consume out of her new wealth (AC/AW) in the following situations: [Hint: Let AC be the the change in consumption compared to what she would have done before the inheritance changed her wealth AW]. 19. In period 2 following an unexpected inheritance of 10: (a) 0.25; (b) 0.33; (c) 0.75; (d) 1.0; 20. In period 3 following an expected lump sum payment from her trust fund of 15: (a) 0.33; (b) 0.75; (c) 0.45; (d) 0.50; 21. What is her desired optimal consumption in period 3 with the anticipated trust fund gift of 15: (a) 20; (b) 30; (c) 27.50; (d) 22.50; 22. In what period of her working life (Y > 0) would her marginal propensity to consume out of an unexpected inheritance of 10 be the highest: (a) 1; (b) 2; (c) 3; (d) 4;

4. P4: Functions of two or more independent variables a. An individual's utility function has the Cobb-Douglas form: U=X0.5y2 where U is an index of her utility and X and Y are the weekly quantities of the two goods consumed. Find the marginal utilities of the two goods. Does the consumer ever experience satiation with respect to either good? b. How does the marginal utility of each good vary as consumption of it increases with consumption of the other good held constant? What is the economic significance of the signs of these partial derivatives? c. By differentiation, show that the indifference curve is negatively sloped and convex in the KL plane. Give an economic interpretation to the slope and curvature of the indifference curve. Sketch the graph of the indifference curve. 5. P5: Lagrange Multiplier Method a. Consider the following utility function: U=X¹Y4, x, y> 0. Let Px = 2 and Py = 3 and M = 100. Find the utility-maximizing consumption bundle. b. Find the marginal utilities of…

P3

Can you please solve 8 e knowing that the awnser to 8 d is found written below. Please also see attached question     Awnser to 8d: U = (X1)^(1/2)*(X2)^(1/3) We have budget constraint as, m = P1*X1+P2*X2 Let's set up the Lagrange maximizing function as below. L = U(X1, X2) - λλ(P1X1+P2X2-m) L = (X1)^(1/2)*(X2)^(1/3)- λλ(P1X1+P2X2-m) Finding first order condition, dL/dX1 = (0.5)*(X2)^(1/3)/(X1)^(1/2)-λλP1 dL/dX2 = (1/3)*(X1)^(1/2)/(X2)^(2/3)-λλP2 Equating these equations to zero to get, (0.5)*(X2)^(1/3)/(X1)^(1/2)-λλP1 = 0 (1/3)*(X1)^(1/2)/(X2)^(2/3)-λλP2 = 0 (0.5)*(X2)^(1/3)/(X1)^(1/2)/P1 = (1/3)*(X1)^(1/2)/(X2)^(2/3)/P2 (3/2)*(X2/X1) = P1/P2 X1 = (1.5P2*X2)/P1 dL/dλλ = P1X1+P2X2-m=0 P1X1+P2X2 = m P1*(1.5P2*X2)/P1+P2X2=m 2.5*P2X2=m X2 = 0.4*m/P2 X1 = 0.6*m/P1 Hence, Marshallian demand function for good q and good 2 respectively are X1 = 0.4*m/P1 X2 = 0.6*m/P2