Your utility function over the goods X and Z takes the following form: You want to...
Question 5 4 pts Your utility function over the goods X and Z takes the following form: You want to maximize your utility subject to your budget constraint. Assume that the price of X is $3 per unit and the price of Z is $6 per unit, and that the total income you have to spend on X and Z is $720 The consumption bundle that will maximize your utility subject to your budget constraint is X- 240 and Z-0...
D Question 6 4 pts As in question 5, your utility function over the goods X and Z takes the following form: You want to maximize your utility subject to your budget constraint. Assume again that the price of X is $3 per unit and the price of Z is $6 per unit, but that owing to a new government welfare program, the total income you have to spend on X and Z is $900 instead of $720. The consumption...
As in the previous two questions, your utility function over the goods X and Z takes the following Suppose now that the government wants to discourage consumption of X. It places a tax on X such that the price consumers now face is $4 per unit instead of $3 per unit. Assume that the price of Z remains at $6 per unit and that your income is $900. The consumption bundle that will now maximize your utility subject to your...
Imagine you consume two goods, X and Y, and your utility function is U = XY. Your budget is $100, the price of Good X is $4, and the price of Good Y is $25. So, the optimal bundle for you to consume is (12.5, 2). Now the price of good X increases to $10. The compensated price bundle is (7.91, 3.16). What is the income effect on X?
1. (24 total points) Suppose a consumer’s utility function is given by U(X,Y) = X1/2*Y1/2. Also, the consumer has $72 to spend, and the price of Good X, PX = $4. Let Good Y be a composite good whose price is PY = $1. So on the Y-axis, we are graphing the amount of money that the consumer has available to spend on all other goods for any given value of X. a) (2 points) How much X and Y...
Given: U(xi,x):x7x1 a) Write the Lagrangian given that you want to maximize utility subject to the budget b) Write the first order conditions for this problem constraint. c) What are the optimal amounts of x, and x2 to consume?
Question 1: Colin's utility function for goods X and Y is represented by U(XY) = X0.5Y0.5 . Assume his income is $1000 and the prices of X and Y are $50 and S100, respectively. a. Write an expression for Colin's budget constraint. b. Calculate the optimal quantities of X and Y that Colin should choose, given his budget constraint. Graph your answer. Suppose that government subsidy program lowers the price of Y from $100 per unit to $ 50 per...
suppose you are at a bundle, such that MRS>MRT, how should you change your consumption so as to maximize utility subject to your budget constraint?
An individual’s utility is expressed by the function u(x,y) = xy The person’s income is ten dollars (I = $10) The price of item x is $1. The price of item y is $1. Maximize this consumer’s utility subject to a budget constraint using the Lagrange Multiplier method. At what point does the marginal rate of substitution equal the price ratio?
4. An individual has preferences over two goods (x and y) that are represented by function U = min{x,y}. The individual has income $60, the price of x is $4 and the price of good y is $2. (a) What kind of goods are these to the individual? (i.e. what "special case” is this?) (b) What is this individual's budget constraint? (c) What is this individual's optimal bundle of x and y? [HINT: You can't take the derivative of this...