Homework Answers
Answer option D)
price elasticity is negative for both goods .
Cross price elasticity is zero for both goods
Both Income consumption curve & price consumption curve slopes upwards
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5. Assume an individual has preferences represented by the utility function U(x, y) = x1/2y1/3 Which...
A consumer has preferences represented by the utility function u(x, y) -xlyi. (This means that a....
A consumer has preferences represented by the utility function u(x, y) -xlyi. (This means that a. What is the marginal rate of substitution? b. Suppose that the price of good x is 2, and the price of good y is 1. The consumer's income is 20. What is the optimal quantity of x and y the consumer will choose? c. Suppose the price of good x decreases to 1. The price of good y and the consumer's income are unchanged....
3. Suppose an individual has perfect-complements preferences that can be represented by the utility function U(x,y)=...
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.
Suppose a consumer's preferences can be represented by the utility function: U(X,Y)=X3/5Y1/4 a. Derive the function...
Suppose a consumer's preferences can be represented by the utility function: U(X,Y)=X3/5Y1/4 a. Derive the function for the marginal rate of substitution holding utility constant: U X Y b. Derive the demand curves for the two goods, X and Y. c. Confirm that both demand curves slope downward. d. Calculate the price elasticity for each of the goods. e. Calculate the income elasticity for each of the goods.
Question 2 Question 2 (15 pts) A consumer has preferences represented by the utility function u(x,y)...
Question 2
Question 2 (15 pts) A consumer has preferences represented by the utility function u(x,y) -xlyi. (This means that a. What is the marginal rate of substitution? b. Suppose that the price of good x is 2, and the price of good y is 1. The consumer's income wWhat is the optimal quantity is 20. What is the optimal quantity of x and y the consumer will choose? c. Suppose the price of good x decreases to 1. The...
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.
1 pts Question 2 A consumer has preferences represented by the utility function: u(x1, x2)= x...
1 pts Question 2 A consumer has preferences represented by the utility function: u(x1, x2)= x x Market prices are pi = 3 and P2 = 4. The consumer has an income m 30. Find an expression for the consumer's Engel curve for good 1. x1(m). ооо D Question 3 1 pts
Suppose the preferences of an individual are represented by a quasilinear utility function: U (x, y)...
Suppose the preferences of an individual are represented by a quasilinear utility function: U (x, y) = ln(x) + y (a)Suppose px =1, py =5 and I = 20. The price of x increases to 2 (px = 2). Calculate the changes in the demand for x. What can you say about the substitution and income effects for small changes in the price of x? What happens to the demand for y? Is y a gross substitute? (b)Now suppose px...
Question 2 (15 pts) A consumer has preferences represented by the utility function ufa,y)ty. (This means...
Question 2 (15 pts) A consumer has preferences represented by the utility function ufa,y)ty. (This means that Muy and Muy ly 1) a. What is the marginal rate of substitution? b. Suppose that the price of good x is 2, and the price of good y is 1. The consumer's income is 20. What is the optimal quantity of x and y the consumer will choose? c. Suppose the price of good x decreases to 1. The price of good...
Assume that an individual’s preferences is represented by the following utility function: ?(?, ?) = (?^1/3)*(y^2/3)...
Assume that an individual’s preferences is represented by the following utility function: ?(?, ?) = (?^1/3)*(y^2/3) a. What could you tell about the type of x and y? (“good” , “bad” or a “neuter”) b. Derive the equation for his/her indifference curve for utility level of 100? c. Derive marginal utility of x and marginal utility of y as a function of x,y. d. Does goods x and y exhibit diminishing marginal utility, constant marginal utility, or increasing marginal utility?...
3. Suppose that Bob’s preferences can be represented by the utility function u(x, y) = 32x^0.5...
3. Suppose that Bob’s preferences can be represented by the utility function u(x, y) = 32x^0.5 + y. The MUx = 16x^-0.5 and MUy = 1. (a) Determine Bob’s demand functions for x and y. (b)If the price of x is $8, and Bob’s income is $1000, how many x would Bob consume? How much income would be devoted to spending on y? (c) Suppose that the price of x doubles to $16. Calculate the income and substitution effects. (d)Is...
A consumer has preferences represented by the utility function u(x, y) -xlyi. (This means that a. What is the marginal rate of substitution? b. Suppose that the price of good x is 2, and the price of good y is 1. The consumer's income is 20. What is the optimal quantity of x and y the consumer will choose? c. Suppose the price of good x decreases to 1. The price of good y and the consumer's income are unchanged....
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.
Question 2
Question 2 (15 pts) A consumer has preferences represented by the utility function u(x,y) -xlyi. (This means that a. What is the marginal rate of substitution? b. Suppose that the price of good x is 2, and the price of good y is 1. The consumer's income wWhat is the optimal quantity is 20. What is the optimal quantity of x and y the consumer will choose? c. Suppose the price of good x decreases to 1. 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.
1 pts Question 2 A consumer has preferences represented by the utility function: u(x1, x2)= x x Market prices are pi = 3 and P2 = 4. The consumer has an income m 30. Find an expression for the consumer's Engel curve for good 1. x1(m). ооо D Question 3 1 pts
Question 2 (15 pts) A consumer has preferences represented by the utility function ufa,y)ty. (This means that Muy and Muy ly 1) a. What is the marginal rate of substitution? b. Suppose that the price of good x is 2, and the price of good y is 1. The consumer's income is 20. What is the optimal quantity of x and y the consumer will choose? c. Suppose the price of good x decreases to 1. The price of good...
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