A consumer has an income of $400 and is deciding between two products: X and Y.Assume that the X product is the horizontal axis product. The price of X is $10 andthe price of Y is $2. Assume the consumer currently wants to consume 50 units ofproduct Y to maximize his utility.a) Write out the equation to this consumers budget line. What is the slope to thisbudget constraint?b) How much of X and Y will the consumer consume to maximize his utility subjectto his budget constraint.C) Now assume the price of X changes to $5 and price of Y and Income stays thesame. At the new price, the consumer wants to buy 60 units of product X tomaximize her utility given her budget How much X and Y will the consumerconsume to maximize utility. Sthe before and after the change of the budget constraint and indifference gra onthe same graph space. Show all necessary points. Label clearly.s. Drawd) Write out the expression of the utiity maximizing ruie here.?

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Answered: A consumer has an income of $400 and is…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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21. A consumer has a utility function defined over two goods X and Y. Let the quantity of Good X be x ≥ 0 and the quantity of Good Y be y ≥ 0. The utility function is given below: u(x, y) = xy + 2y. Assume that the consumer has income m and that prices are på and py. (a) Explain whether the preferences underlying this utility function satisfy completeness and transitivity. (b) Explain whether the preferences underlying this utility function satisfy monotonicity and convexity. (c) Find the consumer's Marshallian demands for Good X and Good Y at prices px > 0 and Py > 0. (d) Show that goods X and Y are normal goods and explain whether either good is a substitute for the other. (e) Assume that px 10, Py = 5 and m = 100. Suppose that px increases to px = 15, how much of the change in demand for Good X is via the substitution effect and how much is via the income effect? Note: You may assume an interior solution (i.e. x > 0 and y> 0). =
Consider a consumer whose utility function is (screenshot) Assume the consumer has income $120 and initially faces the prices px=$1 and py=$1. How much x and y would they buy? Draw the budget constraint and the demands.
sketch a person’s indifference map and budget line for two goods, X on the horizontal axis and Y on the vertical axis. Mark the optimum consumption point. Now illustrate the following (you might need to draw a separate diagram for each): (a) A rise in the price of good X (a normal good), but no change in the price of good Y. (b) A shift in the person’s tastes from good Y to good X. (c) A fall in the person’s income and a fall in the price of good Y, with the result that the consumption of Y remains constant (but that of X falls).
Consider the single-good utility function u(x) = 3x². du(x) a) Find the marginal utility of x, MUx = dx b) Plot the utility function and marginal utility function on two separate graphs. c) Does this utility function satisfy the law of diminishing marginal utility? Explain.
Suppose we are able to model the total utility function for the consumption of two goods, good x and good z. The utility function is structured as U(x, z) = 3x2 + z2 - 2xz. The consumer is faced with the prices of goods x and z. The price for each unit of good x and z is $1 each. The consumer has an income $1 (in thousands). How many units of each good should the consumer consume so as to maximize his/her utility?
A consumer has an income of $400 and is deciding between two products: X and Y. Assume that the X product is the horizontal axis product. The price of X is $10 and the price of Y is $2. Assume the consumer currently wants to consume 50 units of product Y to maximize his utility. a) Write out the equation to this consumers budget line. What is the slope to this budget constraint? b) How much of X and Y will the consumer consume to maximize his utility subject to his budget constraint. C) Now assume the price of X changes to $5 and price of Y and Income stays the same. At the new price, the consumer wants to buy 60 units of product X to maximize her utility given her budget. How much X and Y will the consumer consume to maximize utility. g in the before and after the change of the budget constraint and indifference graph on the same graph space. Show all necessary points. Label clearly. ead oubstitutiofs. Draw d) Write out the expression of the utiiity maximizing ruie here.?
Suppose you had a budget of $20.00 and the prices of a burger and a slice of pizza are $5.00 and $2.00 respectively. What would be your optimal consumption bundle?
Ellie spends £20 on Energy drink (E) and Juice (J). Her preferences for these goods can be described by the following utility function: U ( E,J) = 2E + J^2 ( J squared) - J (MUt = 2, MUj = 2J - 1) Suppose that one energy drink costs £1.60 while one carton of Ellie’s favourite Juice costs £4.00. a) Find Ellie’s optimal consumption bundle. Provide both algebraic and graphical solution. Explain your reasoning. b) Discuss how Ellie’s optimal consumption choice would change when her disposable budget changes. c) If the price of energy drinks increases to £2.00 per can, how should the price of Juice change so that Ellie can be as well off as before this change in prices? d) Discuss the implications of the price change from c) on Ellie’s optimal choice. In your discussion, include the analysis of the substitution and income effects as well as Ellie’s demand for Energy drink and/or Juice.
A consumer has a budget of £12 to split between two goods: good 1 has a price of 2, good 2 has a price of 3. Write the consumer’s budget constraint algebraically. Convert this budget constraint into the formula for the budget line. Show this line on a suitably labelled graph. The consumer’s budget increases to £24. Show the effect of this change graphically. A consumer dislikes good 1, and dislikes good 2. Show these preferences on a suitably labelled graph with an indifference curve. Label the graph: which areas would be preferred to those on the line?
Question 3: Samantha has $3,000 to spend on two goods: sandwiches and beer. The price of a sandwich is $6 and price of a beer is $5. a) Draw Samantha's budget line. Put beer on the horizontal axis. b) If Samantha's optimal consumption bundle contains 400 sandwiches, how many beer does her optimal consumption bundle contain? Show her optimal consumption in the graph above. c) Draw Samantha's indifference curve crossing her optimal consumption bundle.
Suppose Paul gets utility from consuming two goods, pizza (P) and soda (S). His utility function is given by U(P,S) = p0.550.5. Paul's income is $20, the price of pizza is $5 and the price of soda is $2. Find Paul's utility maximizing quantities of pizza and soda.
Consider Gary's utility function: U(X,Y) = 5 XY, where X and Y are two goods. If the individual consumed 10 units of X and received 250 units of utility, how many units of Y must the individual consume? 5 25 0 10

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