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Problem 1. The preferences of an average smoker between cigarettes (X) and other goods (Y) can...
Sally consumes two goods, X and Y. Her preferences over consumption bundles are repre- sented by the utility function r...
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...
1. U = XY where MRS = Y/X; I = 1500, Px = Py = 15,...
1. U = XY where MRS = Y/X; I = 1500, Px = Py = 15, A. Derive optimal consumption bundle. B. If Px increases to be $30, derive the new optimal consumption bundle C. Using the results from A and B, derive the individual demand for good X assuming the demand is linear. 2. Assuming the market has two consumers for a very special GPU and their individual demands are given below Consumer A: P = 450 – 4...
Consider preferences over x and y given U(x,y) = min(x,2y) and suppose that income is 60....
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.
4. Andy's utility is represented by the function U(X,Y) - XY. His marginal utility of X...
4. Andy's utility is represented by the function U(X,Y) - XY. His marginal utility of X is MUx = Y. His marginal utility of Y is MUY = . He has income $12. When the prices are Px - 1 and Py -1, Andy's optimal consumption bundle is X* -6 and Y' = 6. When the prices are Px = 1 and P, = 4, Andy's optimal consumption bundle is X** = 6 and Y* 1.5. Suppose the price of...
An individual has preferences over housing, x (measured in square metres), and other goods, y, represented...
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.
An individual has preferences over housing, x (measured in square metres), and other goods, y, represented...
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.
1. Clara's utility function is U(X,Y)= (x + 2)(Y +1). a) Write an equation for Clara's...
1. Clara's utility function is U(X,Y)= (x + 2)(Y +1). a) Write an equation for Clara's indifference curve that goes through the point(X,Y)-(2,8). b) Suppose that the price of each good is one and that Clara has an income of 11. Write an equation that describes her budget constraint. c) Find an equation the describes Clara's MRS for any given commodity bundle (X,Y). d) Use the equations in parts b) and e) to solve for Clara's optimal bundle Hint use...
D X-EC2010-1 M. 1. An individual consumer with Cobb-Douglas preferences over two products, x and y,...
D X-EC2010-1 M. 1. An individual consumer with Cobb-Douglas preferences over two products, x and y, maximises utility, U(x,y) = x1910, 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) (b)...
Question 2 (20 points) A consumer purchases two goods x ano y. The consumer's income is...
Question 2 (20 points) A consumer purchases two goods x ano y. The consumer's income is 1. Hi S income is 1. His utility is given by is * and y. Px is the price of x. Py is the price of a) Calculate consumer's optim U(x,y) = xy s optimal choice of x and y under his budget.hu uncompensated demand) b) Derive the indirect utility function. c) Are these two goods normal goods? Why d) Derive the expenditure function....
X-EC2010-1 1. An individual consumer with Cobb-Douglas preferences over two products, x and y, maximises utility,...
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...
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...
4. Andy's utility is represented by the function U(X,Y) - XY. His marginal utility of X is MUx = Y. His marginal utility of Y is MUY = . He has income $12. When the prices are Px - 1 and Py -1, Andy's optimal consumption bundle is X* -6 and Y' = 6. When the prices are Px = 1 and P, = 4, Andy's optimal consumption bundle is X** = 6 and Y* 1.5. Suppose the price of...
1. Clara's utility function is U(X,Y)= (x + 2)(Y +1). a) Write an equation for Clara's indifference curve that goes through the point(X,Y)-(2,8). b) Suppose that the price of each good is one and that Clara has an income of 11. Write an equation that describes her budget constraint. c) Find an equation the describes Clara's MRS for any given commodity bundle (X,Y). d) Use the equations in parts b) and e) to solve for Clara's optimal bundle Hint use...
D X-EC2010-1 M. 1. An individual consumer with Cobb-Douglas preferences over two products, x and y, maximises utility, U(x,y) = x1910, 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) (b)...
Question 2 (20 points) A consumer purchases two goods x ano y. The consumer's income is 1. Hi S income is 1. His utility is given by is * and y. Px is the price of x. Py is the price of a) Calculate consumer's optim U(x,y) = xy s optimal choice of x and y under his budget.hu uncompensated demand) b) Derive the indirect utility function. c) Are these two goods normal goods? Why d) Derive the expenditure function....
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...
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