Find and expression for the marginal rate of substitution

Reference no: EM13163007

Consider the utility function U(x, y) = -8/x, -8/y. Find and expression for the marginal rate of substitution (MRS_x,y) at any point (x, y). Suppose x = 3 and y = 2, what is the MRS_x,y?

What about at (x, y) = (1,4)? Now consider another utility function W(x, y) = -(2/x)³ - (2/y)³ Does it represent the same preferences as the first one? Explain fully.

. The show that the following utility function is homothetic: U(x, y, z) = x^αy^βz^γ . Is it also homogeneous and if so what is the degree? Are all homothetic functions homogeneous? Show this or give a counterexample.

. Jon's favourite sports are golf and tennis, and his preferences are given by U(G, T) = G^1/3T^4/3. If the yearly prices for playing a half hour a week of each sport are PG and PT, and he has a budget of B, what are his demands for each sport as functions of prices and his budget?

. Remember Jon from question 4. Suppose that at the club where he plays, he pays P_G = 400 and P_T = 160, and suppose that Jon's budget is B = 1600, what is his utility? Now suppose he can buy a premium membership to the golf-tennis club for $500, and then he pays only half price for both sports. Will he be better off with the premium membership pass? Find the range of values for the cost of the membership pass where he will be worse off, and the range where he will be better off.

Reference no: EM13163007

Questions Cloud

Determine the final pressure of the system of two tanks : The temperature remains unchanged. Determine the final pressure of the system of two tanks.

Describe the long run average cost curve : A company wishes to introduce a new flavour of tea in the market. Discuss how the company can forecast demand for the new flavour of tea.

Calculate the quantity of energy required to melt : The enthalpy change for melting ice at 0°C and constant atmospheric pressure is 6.01 kJ/mol. Calculate the quantity of energy required to melt a moderately large iceberg with a mass of 1.39 million metric tons. (A metric ton is 1000 kg.)

Use le chatelier principle : Use Le Chatelier's principle to explain the color change which you observed after the addition of distilled water to the equilibrium mixture above.

Find and expression for the marginal rate of substitution : Find and expression for the marginal rate of substitution (MRS x,y ) at any point (x, y). Suppose x = 3 and y = 2, what is the MRS x,y ?

The solubility of oxygen gas in water : The solubility of oxygen gas in water at 25°C and 1.0 atm pressure is 0.041 g/L. What is the solubility of oxygen in water at 8.4 atm pressure?

The class linked bag did not have the data member itemcount : the class LinkedBag did not have the data member itemCount. Revise the method getCurrentSize so that it counts the number of nodes in the linked chain

Calculate the mass in grams of iodine : Calculate the mass in grams of iodine (I2) that will react completely with 29.1 g of aluminum (Al) to form aluminum iodide (AlI3).

What is the freezing point of a solution : The freezing point of ethanol (C2H5OH) is -114.6 degrees C and the molal freezing point depression constant for ethanol is 2.00 degrees C kg mol-1. What is the freezing point (in C) of a solution prepared by dissolving 57 g of glycerin (C3H8O3) in..

User Account

All Pages