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4. Let the household utility function be given by U(x,y) = Vxy. a. Find the marginal...
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...
4. Let a person's utility function over consumption, X, and leisure, L, be given by U...
4. Let a person's utility function over consumption, X, and leisure, L, be given by U = XL2, SO MUx = L2 and MUL = 2xL.The individual may work up to 24 hours per day at wage rate, w = $10 per hour, and he has non-labor income of $50 per day. The price of x, px, is $5. (a) Find the utility-maximizing x and L. (b) Show that at the utility- maximizing quantities of x and L, the consumer's...
Problem 1 (10 marks) Answer the following questions regarding a Cobb-Douglas utility function U(X,Y)= X0.3 0.7...
Problem 1 (10 marks) Answer the following questions regarding a Cobb-Douglas utility function U(X,Y)= X0.3 0.7 (a) Does this utility function exhibit diminishing marginal utility in X? Show why or why not. (b) Does this utility function exhibit diminishing marginal rate of substitution? Mathematically show and verbally explain why it has (or doesn't have) such property. Problem 2 (10 marks) Consider the following utility function U(X,Y)= X14734 Suppose that prices and income are given as following Px= 1 Py =...
1.Suppose a consumer had a utility function given by: U= 9X + 2Y. If the price...
1.Suppose a consumer had a utility function given by: U= 9X + 2Y. If the price of Good X (Px) is $8 and the price of Good Y is $4then what is the utility maximizing quantity of Good X the consumer will purchase with a budget of $32? 2. Suppose an individual had a utility function given by: U=X^4Y^0.6 Calculate this individual's Marginal Rate of Substitution (MRSxy) when they have a bundle with 3 units of Good X and 1.8...
A consumer's utility is given by U (,y) = ry. Income is m and prices are given by pa and Py. (aFind the demand function...
A consumer's utility is given by U (,y) = ry. Income is m and prices are given by pa and Py. (aFind the demand functions for x and y. (b) What is demand for each good if px = 2 and pu= 1 and income is m = 30? (c) If price of x fell to pc = 1, what is the consumer's new bundle? (d) How much of the response in the consumption of x is due to the...
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?
Suppose that a consumer’s utility function is U(x,y)=xy＋10y. the marginal utilities for this utility function are...
Suppose that a consumer’s utility function is U(x,y)=xy＋10y. the marginal utilities for this utility function are MUx=y and MUy=x＋10. The price of x is Px and the price of y is Py, with both prices positive. The consumer has income I. (this problem shows that an optimal consumption choice need not be interior, and may be at a corner point.) Assume first that we are at an interior optimum. Show that the demand schedule for x can be written as...
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...
The utility function is given by U(x, y) = xy2 . (a) Write out the demand...
The utility function is given by U(x, y) = xy2 . (a) Write out the demand functions for goods x and y in terms of I, px, and py. (b) What is the maximum utility the consumer can achieve as a function of I, px, and py? (c) What is the minimum the consumer needs to spend to achieve a level of utility U as a function of px, and py? (d) The initial income is $576, initial prices are...
The utility function is given by U(x, y) = xy2 . (a) Write out the demand...
The utility function is given by U(x, y) = xy2 . (a) Write out the demand functions for goods x and y in terms of I, px, and py. (2) (b) What is the maximum utility the consumer can achieve as a function of I, px, and py? (2) c) What is the minimum the consumer needs to spend to achieve a level of utility U as a function of px, and py? (2) (d) The initial income is $576,...
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...
4. Let a person's utility function over consumption, X, and leisure, L, be given by U = XL2, SO MUx = L2 and MUL = 2xL.The individual may work up to 24 hours per day at wage rate, w = $10 per hour, and he has non-labor income of $50 per day. The price of x, px, is $5. (a) Find the utility-maximizing x and L. (b) Show that at the utility- maximizing quantities of x and L, the consumer's...
Problem 1 (10 marks) Answer the following questions regarding a Cobb-Douglas utility function U(X,Y)= X0.3 0.7 (a) Does this utility function exhibit diminishing marginal utility in X? Show why or why not. (b) Does this utility function exhibit diminishing marginal rate of substitution? Mathematically show and verbally explain why it has (or doesn't have) such property. Problem 2 (10 marks) Consider the following utility function U(X,Y)= X14734 Suppose that prices and income are given as following Px= 1 Py =...
A consumer's utility is given by U (,y) = ry. Income is m and prices are given by pa and Py. (aFind the demand functions for x and y. (b) What is demand for each good if px = 2 and pu= 1 and income is m = 30? (c) If price of x fell to pc = 1, what is the consumer's new bundle? (d) How much of the response in the consumption of x is due to the...
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?
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