
3. Suppose an individual has perfect-complements preferences that can be represented by the 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...
5. A consumer faces a standard linear budget constraint and has preferences that can be represented by the following utility function: U(x,y)= x + 2 In y. a) Suppose that we have an interior solution. Derive the demand functions for x and y. Denote the price of x by p,, the price of y by p,, and income by m. b) Is it necessarily the case that the optimal consumption is interior the way we assumed in part a)? If...
Suppose a consumer’s preferences are represented by the utility function U(X,Y) = X2*Y. Therefore, MUx = 2XY • MUy = X2 Also, suppose the consumer has $32 to spend (M = $32), PY = 1, and that they spend all of their money on goods X and Y. Also, assume the consumer maximizes their utility subject to their budget constraint. Complete the following table: Px Quantity Demanded of X $1 $2 $3
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.
5. Assume an individual has preferences represented by the utility function U(x, y) = x1/2y1/3 Which of the following statements is necessarily TRUE? Assume prices and income are positive. a. The price consumption curve as the price of x changes) slopes downward. b. The income consumption curve slopes downward. c. Cross-price elasticity of demand for good x with respect to the price of y is negative. d. Price elasticity of demand for good y is negative. (See Besanko 5.6 and...
Suppose a consumer views two goods, X and Y, as perfect complements. Her utility function is given by U = MIN [2X, Y]. Sketch the graph of the consumers indifference curve that goes through the bundle X = 7 and Y = 8. Put the amount of Y on the vertical axis, and the amount of X on the horizontal axis. Which of the three assumptions that we made about consumer preferences is violated in this case?
3 Clara consumes two goods x and y. Suppose her utility function is given as U(x,y)=min{3x,4y} The prices of the two goods are Px for good x and Py for good y. If her monthly income is $M, Derive her uncompensated demand function for good x Derive her uncompensated demand function for good y Derive the cross-price effects and show that the two goods are complementary goods.
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...
2. (24 points) Suppose a consumer has preferences represented by the utility function U(X,Y)- X2Y Suppose Py, and the consumer has $300 to spend. Draw the Price-Consumption Curve for this consumer for income values Px-1, Px 2, and Px- 5. Your graph should accurately draw the budget constraints for each income level and specifically label the bundles that the consumer chooses for each income level. Also, for each bundle that the consumer chooses, draw the indifference curve that goes through...
Clara consumes two goods x and y. Suppose her utility function is given as U(x,y)=min{3x,4y} The prices of the two goods are Px for good x and Py for good y. If her monthly income is $M, Derive her uncompensated demand function for good x Derive her uncompensated demand function for good y Derive the cross-price effects and show that the two goods are complementary goods.