Utility maximization with more than two goods Suppose that there four goods Q, R, X and Y , available in arbitrary non-negative quantities (so the the consumption set is R 4 +). A typical consumption bundle is therefore a vector (q, r, x, y), where q ≥ 0 is the quantity of good Q, r ≥ 0 is the quantity of good R, x ≥ 0 is the quantity of good X, and y ≥ 0 is the quantity of good Y . The consumer has a total wealth of w = 12, and the each of the goods has a strictly positive price. In particular, let pQ = 1 be the price of good Q, pR = 1 be the price of good R, pX = 2 be the price of good X, and pY = 2 be the price of good Y . In the following three questions, you are asked to study the utility maximization problem for the consumer for three different utility functions. Your final solution for each part should indicate the quantity of goods Q, R, X, and Y that the consumer will purchase at the given prices and wealth when the consumer’s preferences can be represented by the respective utility function (i.e., utility function u1 for part 1, u2 for part 2, or u3 for part 3). Please carefully show the reasoning behind all of your answers.
(a) Suppose that the consumer’s preferences over consumption bundles can be represented by the following utility function: u1(q, r, x, y) = min{qr, xy}. Formulate and solve the consumer’s utility maximization problem.
(b) Instead, now suppose that the consumer’s preferences over consumption bundles can be represented by the following utility function: u2(q, r, x, y) = qr + xy. Formulate and solve the consumer’s utility maximization problem.
Utility maximization with more than two goods Suppose that there four goods Q, R, X and Y , avail...
Suppose that there two goods X and Y, available in arbitrary non- negative quantities (so the the consumption set is R2). The consumer has preferences over consumption bundles that are strongly monotone, strictly convex, and represented by the following (differentiable) utility function: u(x, y)-y+2aVT, where z is the quantity of good X, and y is the quantity of good Y, and a 20 is a utility parameter The consumer has strictly positive wealth w > 0. The price of good...
Suppose that there two goods, X and Y , available in arbitrary nonnegative quantities (so the the consumption set is R 2 +). The consumer has preferences over consumption bundles that are monotone, strictly convex, and represented by the following (differentiable) utility function: u(x, y) = α √ x + (1 − α) √ y, where x is the quantity of good X, y is the quantity of good Y , and α ≥ 0 is a utility parameter. The...
what is the utility maximization for u1(q, r, x, y) = min{qr, xy} where w=12, py=2, Price of q=1 price of x=2 and price of r =1
what is and MRS for this utility maximization u1(q, r, x, y) = min{qr, xy} where w=12, py=2, Price of q=1 price of x=2 and price of r =1
Sally consumes two goods, X and Y. Her preferences over consumption bundles are repre- sented by the utility function r, y)- .5,2 where denotes the quantity of good X and y denotes the quantity of good Y. The current market price for X is px 10 while the market price for Y is Pr = $5. Sally's current income is $500. (a) Write the expression for Sally's budget constraint. (1 point) (b) Find the optimal consumption bundle that Sally will...
Utility Maximization with Substitutes Carol needs to decide how to spend her wealth on fish and chicken. For Carol, 1 lb of fish is equivalent to 2 lb of chicken. Her preferences can be represented by the utility function u(x, y) = 2x +y where x is the quantity of fish (in lbs) and y is the quantity of chicken (in lbs). The consumption set is R 2 +. (a) Draw two typical indifference curves for Carol, one corresponding to...
Utility Maximization with Non-Monotone Preferences Suppose there are two goods, coffee (C) and tea (T). The consumption set is R 2 +, so both goods can be consumed in arbitrary non-negative quantities. Abdul owns 2000 grams of coffee but does not own any tea. He has no other wealth. The price of coffee is pC = 2 (in Dhs per gram) and the price of tea is pT > 0 (in Dhs per gram). Abdul can sell coffee to earn...
A consumer has preferences represented by the utility function u(x, y) -xlyi. (This means that a. What is the marginal rate of substitution? b. Suppose that the price of good x is 2, and the price of good y is 1. The consumer's income is 20. What is the optimal quantity of x and y the consumer will choose? c. Suppose the price of good x decreases to 1. The price of good y and the consumer's income are unchanged....
Suppose James derives utility from two goods {x,y}, characterised by the following utility function: $u(x, y) = 2sqrt{x} + y$: his wealth is w = 10 let py = 1: (a) What is his optimal basket if px = 0.50? What is her utility? (b) What is his optimal basket and utility if px = 0.20? (c) Find the substitution effect and the income effect associated with the price change. (d) What is the change in consumer surplus? Suppose Linda...
Question 2 Question 2 (15 pts) A consumer has preferences represented by the utility function u(x,y) -xlyi. (This means that a. What is the marginal rate of substitution? b. Suppose that the price of good x is 2, and the price of good y is 1. The consumer's income wWhat is the optimal quantity is 20. What is the optimal quantity of x and y the consumer will choose? c. Suppose the price of good x decreases to 1. The...