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Problem 3. Suppose Jeny (from Seinfeld) has a utility function u(x) 2 Inln (a) Find the...
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...
3. Suppose the utility function for two goods, x and y, is: U = U(x,y) =...
3. Suppose the utility function for two goods, x and y, is: U = U(x,y) = xłyż. a. Graph the indifference curve for U = 10. b. If x = 5, what must y equal to be on the U = 10 indifference curve? What is the MRS at this point? c. Derive a general expression for the MRS for this utility function. Show how it can be interpreted as the ratio of the marginal utilities. d. Does this individual...
A consumer's preferences are given by the following utility function: u(x,y) = xy Assume Pold =...
A consumer's preferences are given by the following utility function: u(x,y) = xy Assume Pold = 1, Py = 1, and I = 8. a. Solve for the Marshallian demand functions of x and y (your answer should have numbers, not variables. You should round your answers to three decimal places): * old 4 y = 4 b. What is the utility associated with these demands, prices, and income? u = 16 c. Suppose the price of x rises to...
3. (14 points) A consumer's utility function is given by U(x,y) = x1/2y1/2 (1) Find the...
3. (14 points) A consumer's utility function is given by U(x,y) = x1/2y1/2 (1) Find the consumer's Marshallian demand functions. (2) Find the consumer's compensated demand functions. (3) Suppose the price of good y is Py = $1 per unit and the consumer's income is 1 = $20. Find the total effects on good x and good y when the price of good x increases from px - $1 per unit to p} = $2 per unit.
3) Consider the utility function U = 3FC. a. Carefully sketch the indifference curve for utility...
3) Consider the utility function U = 3FC. a. Carefully sketch the indifference curve for utility of 24. Label four market baskets on the indifference curve. (Hint: In Desmos, enter 24=3xy) b. Carefully sketch the indifference curve for utility of 48. Label four market baskets on the indifference curve. c. Which market basket gives highest utility: (0,10) or (2,8) or (5,5) or (9,2)? Rank the market baskets and identify them on your graph. 4) Consider the utility function U =...
Suppose an individual’s utility function for two goods X and Y is givenby U(X,Y) = X^(3/4)Y^(1/4)...
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...
4. Consider the utility function U(x, y) = x + ln y. (a) Find the marginal...
4. Consider the utility function U(x, y) = x + ln y. (a) Find the marginal rate of substitution, MRS of this function. Interpret the result (b) Find the equation of the indifference curve for this function (c) Compare the marginal utility of x and y. How do you interpret these functions? How might a consumer choose between x and y as she tries to increase utility by, for example, consuming more when their income increases?
how to find indirect utility function here? Jeanette has the following utility function: U-ain(x) + b*In(y), where...
how to find indirect utility function here?
Jeanette has the following utility function: U-ain(x) + b*In(y), where a+b=1 a) For a given amount of income I, and prices Px, Py, find Jeanette's Marshallian demand functions for X and Y and her indirect utility function. (6 points)
3. A consumer's utility function is: u x025y0.7s where x and y are two goods ()...
3. A consumer's utility function is: u x025y0.7s where x and y are two goods () Suppose total income is £10,000 and the prices of the two goods are £4 and £6 respectively. Use constrained optimisation to find the consumer's demand for both goods. Now replace the price of the second good with p. Find a formula for the consumer's demand for this good. Draw the demand curve and comment on its properties (ii) (ii) What is the own-price elasticity...
4. Consider the utility function U(x,y) -Iny (a) Find the marginal rate of substitution, MRS of...
4. Consider the utility function U(x,y) -Iny (a) Find the marginal rate of substitution, MRS of this function. Interpret the result (b) Find the equation of the indifference curve for this function (c) Compare the marginal utility of x and y. How do you interpret these functions? How might a consumer choose between z and y as she tries to increase utility by, for example, consuming more when their income increases?
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...
3. Suppose the utility function for two goods, x and y, is: U = U(x,y) = xłyż. a. Graph the indifference curve for U = 10. b. If x = 5, what must y equal to be on the U = 10 indifference curve? What is the MRS at this point? c. Derive a general expression for the MRS for this utility function. Show how it can be interpreted as the ratio of the marginal utilities. d. Does this individual...
A consumer's preferences are given by the following utility function: u(x,y) = xy Assume Pold = 1, Py = 1, and I = 8. a. Solve for the Marshallian demand functions of x and y (your answer should have numbers, not variables. You should round your answers to three decimal places): * old 4 y = 4 b. What is the utility associated with these demands, prices, and income? u = 16 c. Suppose the price of x rises to...
3. (14 points) A consumer's utility function is given by U(x,y) = x1/2y1/2 (1) Find the consumer's Marshallian demand functions. (2) Find the consumer's compensated demand functions. (3) Suppose the price of good y is Py = $1 per unit and the consumer's income is 1 = $20. Find the total effects on good x and good y when the price of good x increases from px - $1 per unit to p} = $2 per unit.
3) Consider the utility function U = 3FC. a. Carefully sketch the indifference curve for utility of 24. Label four market baskets on the indifference curve. (Hint: In Desmos, enter 24=3xy) b. Carefully sketch the indifference curve for utility of 48. Label four market baskets on the indifference curve. c. Which market basket gives highest utility: (0,10) or (2,8) or (5,5) or (9,2)? Rank the market baskets and identify them on your graph. 4) Consider the utility function U =...
4. Consider the utility function U(x, y) = x + ln y. (a) Find the marginal rate of substitution, MRS of this function. Interpret the result (b) Find the equation of the indifference curve for this function (c) Compare the marginal utility of x and y. How do you interpret these functions? How might a consumer choose between x and y as she tries to increase utility by, for example, consuming more when their income increases?
how to find indirect utility function here?
Jeanette has the following utility function: U-ain(x) + b*In(y), where a+b=1 a) For a given amount of income I, and prices Px, Py, find Jeanette's Marshallian demand functions for X and Y and her indirect utility function. (6 points)
3. A consumer's utility function is: u x025y0.7s where x and y are two goods () Suppose total income is £10,000 and the prices of the two goods are £4 and £6 respectively. Use constrained optimisation to find the consumer's demand for both goods. Now replace the price of the second good with p. Find a formula for the consumer's demand for this good. Draw the demand curve and comment on its properties (ii) (ii) What is the own-price elasticity...
4. Consider the utility function U(x,y) -Iny (a) Find the marginal rate of substitution, MRS of this function. Interpret the result (b) Find the equation of the indifference curve for this function (c) Compare the marginal utility of x and y. How do you interpret these functions? How might a consumer choose between z and y as she tries to increase utility by, for example, consuming more when their income increases?
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