Consider an individual making choices over two goods, x and y with initial prices px=5 and py= 2, with income I= 100:
a) If the individual's preferences can be represented by the utility function u = 4x+ 2y; find the income, substitution and total effects of a decrease in the price of x to px= 3.
b) If the individual's preferences can be represented by the utility function u = min(4x,2y); find the income, substitution and total effects of a decrease in the price of x to px= 3.
c) If the individual’s preferences can be represented by the utility function u= 4xy, and the income, substitution and total effects of a decrease in the price of x to px= 4.
Consider an individual making choices over two goods, x and y with initial prices px=5 and...
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...
(b) You consume two goods, good x and good y. These goods sell at prices px = 1 and py = 1, respectively. Your preferences are represented by the following utility function: U(x; y) = x + ln(y): You have an income of m = 100. How many units of x and y will you buy and what will is your utility? If px increases from $1 to $2; figure out the compensating variation (CV) associated with price change. (c)...
An individual has preferences over housing, x (measured in square metres), and other goods, y, represented by utility function u(x,y) = x4y. Her disposable income is $75000, and the price of housing is $1000/m2, while that of other goods is py = $1. a) [5 marks] Find this consumer’s optimal bundle and utility level, given initial prices and income.
Consider preferences over x and y given U(x,y) = min(x,2y) and suppose that income is 60. Let the initial prices be px=1 and py=2. 1. What is the initial optimal consumption? 2. Suppose px increases to px=2. Find the total change in the consumption of x and y. 3. Decompose the total effect into its substitution effect and its income effect. Please do each step of every question for a complete understanding of the reasoning behind the steps.
3. Suppose an individual has perfect-complements preferences that can be represented by the utility function U(x,y)= min[3x,2y]. Furthermore, suppose that she faces a standard linear budget constraint, with income denoted by m and prices denoted by px and p,, respectively. a) Derive the demand functions for x and y. b) How does demand for the two goods depend on the prices, p, and p, ? Explain.
2. Jane's utility function defined over two goods and y is U (x, y) = !/2y\/? Her income is M and the prices of the two goods are p, and Py. (e) Determine the substitution and income effects for good when ini- tially M = $12. Pa = $2, Py = $1, and then the price of good rises to $3. (f) Show the effects from the previous part graphically. (g) How many dollars is Jane willing to accept as...
An individual has preferences over housing, x (measured in square metres), and other goods, y, represented by utility function u(x,y) = x4y. Her disposable income is $75000, and the price of housing is $1000/m2, while that of other goods is py = $1. b) [5 marks] The government decides to subsidize housing at a rate of 20%. Find the resulting optimal bundle and utility level.
Suppose an individual’s utility function for two goods X and Y is givenby U(X,Y) = X^(3/4)Y^(1/4) Denote the price of good X by Px, price of good Y by Py and the income of the consumer by I. a) (2 points) Write down the budget constraint for the individual. b) (4 points) Derive the marginal utilities of X and Y. c) (3 points) Derive the expression for the marginal rate of substitution of X for Y. Write down the tangency...
2. Consider a utility function that represents preferences: u(x,y)= min{80x,40y} Find the optimal values of x and y as a function of the prices px and py with an income level m. (5)
u(x,y)= x+3y,INCOME=12;px =1,py =2;p′x =1,p′y =4 initial prices px,py and final prices p′x,p′y. For THE problem, you are to find: (a) the optimal choice at the initial prices (b) the optimal choice at the final prices (c) the change = optimal choice at final prices - optimal choice at initial prices (d) the income effect and the substitution effect