A consumer must maximize utility, U-f(x.y), subject to the constraint that she spends all her inc...
A consumer must maximize utility, U-for.y), subject to the constraint that she spends all her income, M on purchasing two goods x, y. The unit prices of the goods, p, and py respectively, are market determined and hence exogenous (3 marks) (3 marks) rKS rice marks) (i e1 (2 marks) 0.8,0.2 (d) Let the utility function be U -5x ф Solve the maximization problem in this case (that is obtain x*, y*, 8y0.z and unit prices pr - p- 1...
U(X,Y,Z) = 10x67.73 Write the Lagrangean Function and the first-order conditions for utility maximization of this function. Now solve this equation for the X, Y, and Z as a function of the prices. Px, PY, and Pz and income, I.
Suppose that a consumer’s utility function is U(x,y)=xy+10y. the marginal utilities for this utility function are MUx=y and MUy=x+10. The price of x is Px and the price of y is Py, with both prices positive. The consumer has income I. (this problem shows that an optimal consumption choice need not be interior, and may be at a corner point.) Assume first that we are at an interior optimum. Show that the demand schedule for x can be written as...
Question 1. (Consumption-Saving Problem): Suppose that a consumer lives for two periods. The utility function of the consumer is given by with u> 0 where c and c2 are consumption in period 1 and period 2 respectively. Sup- pose that consumer has income y in the first period, but has no income in the second period. Consumer has to save in the first period in order to consume in the second period. Let s be the savings in the first...
Question 1. (Consumption-Saving Problem): Suppose that a consumer lives for two periods. The utility function of the consumer is given by with u> 0 where c and c2 are consumption in period 1 and period 2 respectively. Sup- pose that consumer has income y in the first period, but has no income in the second period. Consumer has to save in the first period in order to consume in the second period. Let s be the savings in the first...
X-EC2010-1 1. An individual consumer with Cobb-Douglas preferences over two products, x and y, maximises utility, U(X.y) = x10y10, subject to the constraint that all income, M, is spent on x and/or y. Products x and y are priced at Px and Py, respectively. (a) Set up the appropriate lagrangian for this maximisation problem, find the appropriate first-order conditions for this lagrangian and solve for x and y in terms of px, Py and M. (40 marks) (6) For product...
f. (BONUS Solve the utility maximization problem in general (xỈ + subject to the budget constraint, pM + pr,-I max 2 x1,x2 Again, the marginal utility of good i is MU,-X1ới +均一; the marginal utility of good 2 is MU,-X2(xf + xj)--. Find the quantities of good i and good 2, x1 and X2, in terms of prices, p, and p2, and income I.
Suppose that a household has a utility function and intertemporal budget constraint as follows: U(C1,C,) - (cº:" + Bc2:5)1-y U(C1,C2) = - 1- ITBC: C1 + = yı + 1+1 a) Determine the marginal rate of substitution for this utility function and derive the Euler equation faced by this consumer (define the Lagrangian and then obtain first order conditions as we did it in the lecture). Explain the intuition of the Euler equation. b) Find a solution for optimal consumption...
The utility function is given by U(x, y) = xy2 . (a) Write out the demand functions for goods x and y in terms of I, px, and py. (b) What is the maximum utility the consumer can achieve as a function of I, px, and py? (c) What is the minimum the consumer needs to spend to achieve a level of utility U as a function of px, and py? (d) The initial income is $576, initial prices are...
The utility function is given by U(x, y) = xy2 . (a) Write out the demand functions for goods x and y in terms of I, px, and py. (2) (b) What is the maximum utility the consumer can achieve as a function of I, px, and py? (2) c) What is the minimum the consumer needs to spend to achieve a level of utility U as a function of px, and py? (2) (d) The initial income is $576,...