Revist the example from question 3a. Recreate this graph, and add the following 2 things to your graph: 1) a compensated budget constraint and 2) a third indifference curve that captures the optimal choice on that compensated budget constraint curve. Label 3 points: 1) the original optimal choice, 2) the optimal choice after the price change, and 3) the optimal choice on the compensated budget constraint. Use this new graph to answer the following questions. (a) Graphically, what is the substitution effect? (b) Graphically, what is the income effect?
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- The relationship between the marginal utility that George gets from eating a bag of cookies and the number of bags he eats per month is as follows: Bags of Cookies 1 2 3 4 S 6 Marginal Utility 20 16 12 8 4 0 George receives 2 units of utility from the last dollar spent on each of the other goods he consumes. If cookies cost $4 per bag, how many bags of cookies will he consume per month if he maximizes utility? Add your answer Integer, decimal, or E notation allowed Question 10 If the utility function for the consumer is: U= min{10 x1, 50 x2} P₁= 4, P₂-6 and 1-2,000 What is the optimal amount of x₁? 10 Points4. If we have the utility function, U(x)=(x−7)^2, and we know that there is an indifference set around x = 4 and an upper contour set of x = 6. How to graphically represent this function? I'm confused about how to draw the upper contour set on the graph? I know the concept that upper contour is the area over the convex line, but don't know how to put it on the graph. Could you draw a simple graph to help me identify the upper contour?Demonstrate how a consumer’s equilibrium changes if the price of a product changesaccording to marginal utility theory. Include in your answer a discussion of the derivation of the demand curve according to marginal utility theory. Please provide a detailed answer with a graph if possible.
- 5. Janice consumes two goods, X and Y. Janice has a utility function given by the expression: U=4X05Y05 and current prices of X and Y are $25 and $50, respectively. Janice currently has an income of 750 unit per time period. a. Write an expression for Janice's budget constraint. b. Calculate the marginal rate of substitution of X for Y. (horizontal line X, vertical line Y). c. Calculate the values of X and Y that will maximize utility. d. Graph your answers (budget line, indifference curve)2. Suppose John's utility function is UX,Y) = 4VXY , where X is consumption of beer and Y is consumption of pizza. For this utility function, ( Calculus Kahuna say: MUx = 2VY/X and MUy = 2\X/Y ) a) What happens to the marginal rate of substitution between X and Y as consumption of X increases?Typed answer.
- Harry consumes 2 goods, X and Y and he spends N$60 per month. The price of good X is N$4 and the price of good Y is N$10. Harry's utility function is U(X, Y) = XY. (i) What is Harry's marginal rate of substitution? (5) (ii) What is the expression for Harry's budget constraint? (3) (iii) What is the slope of Harry's budget constraint? (2) (iv)Find the values of good X and Y maximizes Harry's utility. Show all your work. (6) (v) Illustrate Harry's utility maximizing combination on a clearly labelled graph. (4) (vi) Suppose the price of good X increased to N$6. Illustrate Harry's income and substitution effects on a well labelled graph. Show your work. (10) (vii) Suppose Genie is consuming two goods, coffee and beer. She spends all her income on a combination of coffee and beer where MUcoffee/Peoffee is 5 and MUbeer/Pbeer is 3. Explain why this combination is not maximizing her satisfaction. What should she do to maximize her utility? (5)6.Suppose that Dale consumes only coffee and cheese, both of which have diminishing marginal utility. For each of the following cases, determine whether Dale should 1Consume more coffee and less cheese, or2Consume less coffee and more cheese: 1.The marginal rate of substitution of cheese for coffee is 3 (i.e., the marginal utility of cheese is three times the marginal utility of coffee), while the price ratio is 2 (i.e., cheese costs twice as much as coffee). 2.The marginal rate of substitution of cheese for coffee is 1 (i.e., the marginal utility of cheese is equal to the marginal utility of coffee) while the price ratio is 2 (i.e., cheese costs twice as much as coffee). 3.The marginal rate of substitution is initially equal to the price ratio, but the price of coffee increases. 4.The marginal rate of substitution is initially equal to the price ratio, but the price of cheese decreases. 5.The marginal rate of substitution is initially equal to the price ratio, but Dale enters exam…
- 2. Suppose that the utility function U(c, s) = c +2s3 describes Molly's preferences over two goods: Carrots (c) and Spinach (s). For the following, think of Carrots as the good graphed on the horizontal axis. a. Derive an expression for her marginal utility for Carrots (U) and her marginal utility for Spinach (US) b. What is Molly's marginal rate of substitution (MRS)? Give a brief (2 sentences maximum) intuitive description of what MRS represents: if Molly has 8 units of spinach, holding her utility constant, how many units of Spinach would she be willing to give up in order to get one more unit of Carrots? Find the equation for and graph Molly's indifference curve for a utility level of 40. Be sure to specify at least 3 bundles of goods on the indifference curve. d. Which assumption about preferences means that Molly's indifference curve should slope down? Briefly support your answer. Give another utility function that represents Molly's preferences just as well as the one given…QUESTION ONE The only source of income available to Doreen, a level 200 student of UEW is her monthly stipend (M) from her parents. She neither saves nor borrows. Assuming she spends all her income on only two goods food (F) and Clothes (C), with Pr and Pc being the prices of the two goods respectively and having a utility function of the form: U = 6F°C i. Write an expression for Doreen's budget constraint. ii. Assuming good Fis on the vertical axis, produce a sketch of her budget constraint and determine the slope. iii. Find Doreen's monthly equilibrium demand functions for both goods. iv. With Pr and Pcgiven as ¢12 and ¢15 respectively and income of ¢300, calculate the equilibrium quantities of both goods. v. Compute the price elasticity of demand for both goods and interpret your results. vi. If income and prices of the two goods increase by 50%, calculate the equilibrium quantities of Food and Clothing.a,b,c