Bob's utility function is u(x,y)=xy where x is her consumption of good 1 and y is her consumption of good 2. Denote Bob's income by m, and denote the prices of good 1 and 2 by p1 and p2 respectively.
let m=120, p1=20, p2=5, graph Bobs budget line.
Bob's utility function is u(x,y)=xy where x is her consumption of good 1 and y is...
Alice’s utility function is ?(?, ?) = √?√? where ? is her consumption of good 1 and ? is her consumption of good 2. Denote Alice’s income by ?, and denote the prices of good 1 and 2 by ?1 and ?2 respectively. 1. What is the formula for Alice's marginal rate of substitution? 2. Write down the two equations necessary to solve for Alice's optimal values of x and y.
Problem 1: Alice’s utility function is ?(?, ?) = √?√? where ? is her consumption of good 1 and ? is her consumption of good 2. Denote Alice’s income by ?, and denote the prices of good 1 and 2 by ?? and ?? respectively. A) Derive the formula for Alice’s marginal rate of substitution. B) Write down the two equations necessary to solve for Alice’s optimal values of ? and ?. C) Using the equations from part B, solve...
5. Melissa’s utility function for the bundle (x,y) is U(x,y)=xy. Price of good x is p1=1, price of good 2 is p2=2 and income m=10. If the price of good 1 goes up to p1=2, but the rest remain the same. Derive: Total effect? Substitution effect? Income effect?
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...
Anna spends all her income on wine (good 1) and cheese (good 2). Her utility function is u(x1; x2) = x1x2. Her income is m = $200. The prices for the two goods are p1 = $20 and p2 = $10 respectively. Find Annaís optimal consumption bundle. Show the complete calculations, and illustrate your answer graphically (draw the indi§erence curve and the budget constraint). How would your answer change to part (a) if Annaís utility function were given by v(x1;...
Problem 1 (10pts) Jim's utility function is U (x, y) = xy. Jerry's utility function is U (x,y) = 1,000xy +2,000. Tammy's utility function is U2, y) = xy(1 - xy). Bob's utility function is U(x,y) = -1/(10+ 2xy). Mark's utility function is U (2,y) = x(y + 1,000). Pat's utility function is U (2,y) = 0.5cy - 10,000. Billy's utility function is U (x,y) = x/y. Francis' utility function is U (x,y) = -ry. a. Who has the same...
Question 1: Colin's utility function for goods X and Y is represented by U(XY) = X0.5Y0.5 . Assume his income is $1000 and the prices of X and Y are $50 and S100, respectively. a. Write an expression for Colin's budget constraint. b. Calculate the optimal quantities of X and Y that Colin should choose, given his budget constraint. Graph your answer. Suppose that government subsidy program lowers the price of Y from $100 per unit to $ 50 per...
(1 point) Suppose that you have two consumption choices: good X, and good Y. An indifference curve is the set of consumption choices with a CONSTANT utility. For example if consuming 10X and 6Y gives me the same utility as consuming 11X and 5Y, then these are both points on the same indifference curve. An indifference map is the set of all indifference curves with EVERY given utility. Consider the indifference map given by: U = XY, where U is...
Sally consumes two goods, X and Y. Her utility function is given by the expression U = 2 · XY ^2 . The current market price for X is $10, while the market price for Y is $12. Sally’s current income is $900. a. Sketch a set of two indifference curves for Sally in her consumption of X and Y. b. Write the expression for Sally’s budget constraint. Graph the budget constraint and determine its slope. c. Determine the X,Y...
h. U(1, 2 For the utility function above, find the consumer's optimal consumption bundle when prices of goods 1 and 2 are pl and p2, and the consumer has an income m. 1. 2. For the utility function above, find the consumer's optimal consumption bundle when prices of goods 1 and 2 are pl and p2, and the consumer has an endowment (el, e2) of the two goods. For each of your answers in question 2, write down the consumer...