The utility function for goods X and Y is U=6(X^2)(Y^3) [6 times X-squared times Y-cubed], the price of X is 2, the price of Y is 4, and your income is $100. What is the optimal consumption of Y?
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The utility function for goods X and Y is U=6(X^2)(Y^3) [6 times X-squared times Y-cubed], the...
Ahn’s utility function for goods X (pizzas) and Y (cola) is represented as U(X, Y) = 2ln(X)+ln(Y). The prices of X and Y are $1 and $1, respectively. Ahn’s income is $12. 1) Calculate Ahn’s optimal consumption bundle (X*, Y*). (X*, Y*)= . 2) Suppose there is an increase in the price of X. Illustrate the net effect, income effect, and substitution effect on Ahn’s optimal consumption choice.
Consider a consumer whose utility function is given by U(x, y) = x^1/3 y^2/3, where x and y represent quantities of consumption of two consumer goods. (a) If the consumer’s income is $100 and the prices of x and y are both $1, how should the consumer maximize her utility? What is her maximum level of utility? (b) If the price of y rose to $2, what would be the resulting income and substitution effects? Illustrate your answer.
Ex. 1: Imagine there are two goods, X and Y. The utility function is: U = XY. The price of X is $2 and the price of Y is $4. The budget is $20. What is the optimal quantity of X and Y to consume? Ex. 2: Imagine there are two goods: books and coffees. Your utility function is U = BC, where B is the number of books you consume and C is the number of coffees you consume....
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...
Imagine you consume two goods, X and Y, and your utility function is U = XY. Your budget is $100, the price of Good X is $4, and the price of Good Y is $25. So, the optimal bundle for you to consume is (12.5, 2). Now the price of good X increases to $10. The compensated price bundle is (7.91, 3.16). What is the income effect on X?
Consider the following utility function of 2 goods, x and y: U(x,y)=min{x+2y, y+3x} ; x,y ≥0. a) Carefully draw the indifference curve when utility level is 10. Explain your answer. b) If income is $100 and price of good x and y is $10 and $20 respectively, then find out the consumption bundle that maximizes utility.
) A consumer's utility function is given by: U(x,y) = 10xy Currently, the prices of goods x and y are $3 and $5, respectively, and the consumer's income is $150 . a. Find the MRS for this consumer for any given bundle (x,y) . b. Find the optimal consumption bundle for this consumer. c. Suppose the price of good x doubles. How much income is required so that the Econ 201 Beomsoo Kim Spring 2018 consumer is able to purchase...
4. Assume that the utility function of a given agent is given by: U(X,Y) = log X + Blog Y. And that this agent faces the following vector of prices: (10, 8) and that his income is 100. What should be the optimal consumption of X and Y for this specific agent? (assume perfect divisibility of goods)
Suppose James derives utility from two goods {x,y},
characterised by the following utility function: $u(x, y) =
2sqrt{x} + y$: his wealth is w = 10 let py = 1:
(a) What is his optimal basket if px = 0.50? What is her
utility?
(b) What is his optimal basket and utility if px = 0.20?
(c) Find the substitution effect and the income
effect associated with the price change.
(d) What is the change in consumer
surplus?
Suppose Linda...
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...