Question Two Given a utility function: U = u(X,Y) =of two products.x²+x²=3where X and Y are the unitsa) 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.

(a) How to Graph the Utility Function Manually The utility function is U=3x2+y2. This function…

Answered: Question Two Given a utility function:…

Economics:

10th Edition

ISBN:9781285859460

Author:BOYES, William

Publisher:BOYES, William

Chapter21: Demand: Consumer Choic

Section: Chapter Questions

Problem 1E

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1. Consider the following utility functions: (a) u(x1, x2)=x1x2, I (b) u(x1, x2)=xx, (c) u(x1, x2) = ln x1 + ln x2, and (d) u(x1, x2)=√√x1x2, where x is the amount of good 1 and x2 is the amount of good 2. (1) (2) (3) (4) For each of the utility functions, find the marginal utility (MU₁) with respect to good 1. (5 points) For each of the utility functions, find the marginal utility (MU2) with respect to good 2. (5 points) For each of the utility functions, consider the following indifference curve: k = u(x1, x2) for some constant k. Find the marginal rate of substitution (MRS) of good 1 for good 2 at a point (x1, x2) on the indifference curve. (5 points) Show that each of the utility functions has a diminishing MRS. (5 points)
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?
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Graphical and Intuitive Optimization Consider a consumer who must allocate their available income between the consumption of two goods, Beer and Pizza. Their preferences over Beer and Pizza adhere to the usual assumptions we have made about preferences. The indifference curve map below reflects their preferences and the budget constraint reflects current income and prices. In the simplest terms possible, define or explain the term "Marginal Utility of Beer" (MUB). In the simplest terms possible, define or explain the term "Marginal Rate of Substitution of beer for pizza" (MRSBP). In the simplest terms possible, intuitively explain the meaning of MUB/PB, where PB represents the price of one unit of Beer.
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?
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) = 2
1. 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?
Question3 a) Suppose a household is faced with the choice between consuming gasoline (G) and all other goods (OG). Today the household consumes 800 liter of gasoline a year.Suppose then that a gasoline price increase is perfectly compensated by a wage increase. If the family followed the utility maximization model, how would this affect their consumption of gasoline? Explain by using a figure. b) Explain by using an example why an MRS (Marginal Rate of Substitution) between two goods must equal the ratio of the price of the goods for the consumer to achieve maximum satisfaction?
SLOPE OF A LINE 1. Compute the slope between points B and D. 2. Interpret/Explain descriptively the slope of the line as shown on the graph. What is the nature of the relationship between the two goods in terms of purchases? 3. What is the price per unit of the food? What is the price per unit of the clothing? Help me with this one, please. Thank you.
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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)
Imagine you have a movie streaming platform that offers new movies at the time of release. Your market research has revealed the following about your typical consumers’ satisfaction from watching movies: Number of movies (per month) Total Utility or Satisfaction 0 0 1 25 2 47 3 66 4 82 5 94 6 105 The maximum number of movies the consumer watches in a month is 6. (a) Construct a third column for this table to derive “Marginal Utility” corresponding to the number of movies watched. Explain in words what this concept means and why it is important to derive the marginal utilities in pricing.

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