Question Two Given a utility function: U = u(X,Y) = of two products. x²+x² = 3 where X and Y are the units a) Demonstrate how to graph the utility function manually. b) Suppose a study tool is used to slice the graph in Part a) vertically and horizontally, respectively. Which shapes of curves do you expect to see on the sliced surfaces, respectively? Draw and explain your answer.
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- 1. For each of the three utility functions below, find the substitution effect, the income effect, and the total effect that result when prices change from p = (2,1) to p' = (2,4). Assume the consumer has income I = 20. (a) Before doing any calculation, make an educated guess about the relative magnitude of the three substitution effects and the three income effects to be found below. (b) u(x1, x2) = x1 + x2. (c) u(x1, x2) = x1x2. (d) u(x1,x2) = min {x1,x2). (e) Rank the substitution effects and the income effects found above by their magnitude. To what extent do they conform to your guess?From the hypothetical data in table 1, provide the following requirements. Table 1. Total Utility & Marginal Utility for Chocolate Bars Quantity (Chocolate Bars) Total Utility Marginal Utility 0 0 1 7 2 11 3 13 4 14 5 14 6 13 Solve the marginal utility column. Show the graphical solution. What does your graph implies?For the following utility function, graphically depict the following set on a number line:
- 1 Marginal utility and marginal rate of substitution Suppose an individual who derives utility u(x, y) from consuming a units of good X and y units of good Y. For each of the following utility functions, derive the marginal utility of good X, the marginal utility of good Y, and the marginal rate of substitution between X and Y. (A) u(x, y) = x+by¹/3 (B) u(x, y) = (xy) (C) u(x, y) = ax + xy + by² (D) u(x, y) = n(ax + y) 1 (E) u(x, y) = (x² + √y²) = 21. Calculate the marginal rate of substitution for the following utility functions: (a) u(x1, x2) = ax₁ + bx2 (b) u(x1, x2) = 2√√x₁ + x₂ (c) u(x1, x2) = ln(x₁) + x2 (d) u(x1, x2) = x1x2 (e) u(x1, x2) = xx h (f) u(x₁, x₂) = x + x² 2. Marie Curie has a utility function U(x, y) = max{x, 2y}. Note that the max{} function es- sentially says that the value of the function takes the highest of the values in the set (the set is denoted as the things inside the curly braces). (a) Draw a graph, plotting the indifference curve along which U(x, y) = 10. (b) Are Marie's preferences convex?Help me
- 1. Prove if the indirect utility function is quasiconvex The indirect utility function: V(p,w) = w[P1^(p/p-1) + P2^(p/p-1)]^((1-p)/p)The owner of Grand Central Bookstore is looking into the sales of its Health & Fitness magazine section. She finds that her equilibrium is at 800 magazines per month sold at an average price of $4.75 per magazine. When the price of these Health & Fitness magazines rose to $5.00 each, the quantity sold fell to 725 magazines per month, while the quantity supplied to her increased to 900 a month. From the scenario described, answer the questions below. Draw an appropriate graph for Grand Central’s Bookstore’s to illustrate this change in the Health & Fitness magazines market position when the price rises to $5.00. Calculate the price elasticity of demand for the Health & Fitness magazines between prices $4.75 and $5.00. Is it elastic or inelastic? How do you know? Calculate the price elasticity of supply for the Health & Fitness magazines between prices $4.75 and $5.00. Is it elastic or inelastic? How do you know based on your answer? The owner also noticed that…With diminishing marginal utility, how do consumers decide how much to consume? Students are expected to give a detailed answer to this question. You must include an explanation about what diminishing marginal utility means in your answer. Concepts such as "budget constraint", "more is better", "utility". "marginal utility", and "marginal utility per dollar spent" must be used in your answer. No graph or calculation is required in this question.
- Kate’s utility function includes coffee (c) and sugar (s). She only consumes coffee and sugar together, and she only consumes in the ratio of one unit (cup) of coffee with two units (spoons) of sugar. Her utility function is What is her marginal utility of sugar if she has 4 cups of coffee and 6 spoons of sugar? Remember that unit are infinitely divisible (you can have parts of units). (a) 0 (b) 1 (c) ½ (d) 2PART D Eonly typed solution