Given the utility function U = 10X1.5Y0.5 a. Suppose prices of goods PX = 10, PY = 5, and income I = 400, solve for the optimal levels of X, Y, and U using the Lagrange Multiplier Method and graphically illustrate the resulting substitution, income, and net effects if the price of good Y is doubled, cet. par.
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Given the utility function U = 10X1.5Y0.5
a. Suppose prices of goods PX = 10, PY = 5, and income I = 400, solve for the optimal levels of X, Y, and U using the Lagrange Multiplier Method and graphically illustrate the resulting substitution, income, and net effects if the
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- Ruby has the following utility function: U(X, Y) = X^3/4 , Y^1/4, where X is her consumption of food items, with a price of $10, and Y is her consumption of clothing items, with a price of $30. She plans to spend $360 on food and clothing over the next week. Using the Lagrange multiplier technique, determine the number of food and clothing items that will maximize Ruby's utility.Given the utility function U = 10X1.5Y0.5, a. show and discuss if the individual is experience diminishing marginal utility. b. calculate the MRSXY and interpret your computed value. Would you say that this individual prefers more balanced bundles over extremes? Support your claim. c. and suppose prices of goods PX = 10, PY = 5, and income I = 400, solve for the optimal levels of X, Y, and U using the Lagrange Multiplier Method and graphically illustrate the resulting substitution, income, and net effects if the price of good Y is doubled, cet. par.I need help with this question in my homework. Suppose a consumer’s utility function is given by U(X,Y) = MIN (5X, Y). Also, the consumer has $60 to spend, and the price of good X is P(x) = $5. Let good Y be a composite good (good Y is the “numeraire”) whose price is P(y) = $1. So, on the Y-axis, we are graphing the amount of money that the consumer has available to spend on all other goods for any given value of X. What is the Indirect Utility Function? What is the Expenditure Function?
- A consumer consumes two agricultural products: Red Meat, and Tomatoes according to the following utility function: U = RT That is, the total utility is the multiplication of the quantity consumed of the two products. Given that consumer's income is 210, price of R is 10, and the price of Tis 2, a)Write down the budget constraint (budget line equation) for this consumer. b)Determine the quantities that the consumer should consume of each of the two products c)Calculate the value of the lagrangian multiplier and derive the demand function for Red Meat and for tomatoes.An economy described in an edgeworth box consists of 2 goods, namely X and Y and two consumers, namely A and B. Initially A has goods X and Y equal to 12 and 2 respectively, with the utility function UA (XA, YA) = XAYA . Meanwhile, B initially has goods X and Y equal to 8 and 18, respectively, with the utility function UB (XB, YB) = XBYB. It is known that the price of item X is IDR 50,000 and the price of item Y is IDR 50,000. a. Draw the economy above, in an edgeworth box representing the endowment positions of individuals A and B complete with their respective utility curves. Don't forget to include all relevant symbols and numbers on the vertical and horizontal axes. b. Is initial ownership an efficient allocation? By evaluating the endowment and MRS of individuals A and B, will there be an exchange? c. Determine the competitive balance allocation! (hint: considering the ratio of the price of goods X and Y)Please answer in detail A corner solution exists when a consumer spends all of her or his income on all goods in a consumption bundle or the utility max True false
- Continue to consider Ronald from Q1. Suppose that Ronald’s preferences over movies and climbing are such that he likes them exactly equally: he is always willing to trade one movie for one climbing session and remain exactly as well of as he was before. One valid utility representation of Ronald’s preferences is u(x, y) = x + y. (a) On the same picture as before, plot indifference curves for the utility levels u = 5.8, 10, 14.2, 18.4. (b) Compute Ronald’s marginal utilities for each good. Using the marginal utility formulas you have just computed, prove that Ronald’s preferences are strongly monotone. (c) i. Label three distinct bundles (x, y) on the indifference curve corresponding to a utility of 5.8. ii. Hence, or otherwise, argue that his preferences are not strictly convex. (d) i. Explain why Ronald’s optimal consumption bundle must lie on the outer boundary of his budget set. ii. Identify Ronald’s optimal bundle by visual inspection. Briefly explain what you did. iii. Find…Question 1 Consider an economy with two goods t = 1, 2. Whenever an individual consumes x1 units of good 1 and x2 units of good 2, their utility is given by u(x1 ,x2 ) = lnx1 +δlnx2 , where δ is a parameter taking values 0 < δ < 1. (i) How does the parameter δ affect the marginal rate of substitution between goods 1and 2? Explain intuitively how does the relative preference for goods 1 and 2 change as the parameter δ increases.Assume that Bob's utility function over beer x and pizza y is U(x,y) = 4x+12y. Which of the following statements is false? a) If the price of pizza is 12 and the price of beer is 3, then we can't determine how much pizza relative to beer Bob purchases. b) If the price of pizza is 16 and the price of beer is 5, then Bob only purchases pizza. c) If the price of pizza is 15 and the price of beer is 5, the own price elasticity of the demand for pizza as well as beer is infinite. d) It the price of pizza is 15 and the price of beer is 4, Bob purchases only beer e) Pizza and beer are perfect substitutes.
- Miss Coco consumes cheese cake and curry puff. Her consumption yields the following total utility as shown in the given table. Miss Coco has RM52 to spend. Suppose that the prices of cheese cake and curry puff are RM8 and RM4, respectively. Quantity (units) Total Utility Cheese Cake Curry Puff 1 56 32 2 104 60 3 136 84 4 160 104 5 170 116 6 176 126 7 178 134 How many units of cheese cake and curry puff should Miss Coco buy to maximize her utility with the income of RM52?The preferences of a typical Californian can be represented by the following utility function: U (x1 , x2 ) = α ln(x1) + (1 − α) ln(x2) Here, x1 and x2 are the quantities of electricity and gasoline, respectively. The consumer faces prices given by p1 and p2 and has income m. Currently, the government has decided to impose a consumption restriction so that any person in the state is allowed to consume at most 50 units of electricity (x1 ≤ 50). Call this restriction a rationing constraint. (a) If α=0.25, m=100,and p1 =p2 =1, find the optimal consumption bundle of gasoline and electricity. Is the electricity rationing constraint binding (meaning does x1∗ = 50)? (b) Suppose that α = 0.75, but the other parameters are the same. What is the optimal consumption bundle? Is the rationing constraint on electricity consumption binding? (c) Now, assume that there is no rationing constraint. Assume m = 100 and p1 = p2 = 1, but α remains as a generic parameter. Solve for the optimal quantity…(In this question, differently from our lecture notes, income will be denoted by Y, not W). The following figure shows a two-good consumption space for an agent. The horizontal axis measures good x and the vertical axis measures good y. There are three budget lines shown in the figure. The first budget line has vertical intercept Y/py and horizontal intercept Y/px. The second budget line has vertical intercept Y/p’y<2, and horizontal intercept Y/px. The third budget line has vertical intercept Y/py, and horizontal intercept Y/p’x<3. There are two indifference curves. These are downward sloping thin curves that do not touch. One of this curves intersects the third budget line only at bundle (3,2). The other curve intersects the second budget line only at (4,0.6) and intersects the third budget line only at (1,2.5). Then Qy(p’x,p’y,Y), the demand of good y for prices p’x and p’y and income Y is less than 2? True. False.