The utility function for an individual is given as u (x; y)= xy. Suppose that his income is $ 100 and the price of Good Y is$ 10 per unit. However, Good X is priced somewhat different. It is priced as follows: The first 6 units cost $ 10 per unit andany additional units cost $ 5 per unit.a) Draw this individual's budget constraint.b) What consumption bundle will this individual choose?

This individual's budget constraint: The utility function for an individual is given as u(x:y)= xy…

Answered: The utility function for an individual…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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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.
Problem 3 (10 points; 5 points for each part): Richard has a total utility function of: TU = 10q₁q₁²+24q2q2² +9192, where q₁ and q2 are goods. Richard is currently consuming at q₁ = 4 and q₂ = 6, which is also his utility maximizing consumption level. (Richard's optimal point is an interior solution). (a) How much additional utility would Richard receive if he were to increase his consumption of q2 from 6 to 7? (5 points). (b) How much q2 is Richard willing to pay (in terms of q2) in order to consume the 5th unit of q₁? (5 points).
suppose the utility function of Vivian is U=602/3Y1/3. The unit priice of Good X is $10 while the unit price of Good Y is $30. Vivian has a budget of $1,800 to be spent on Good X and Good Y. Find the optimal consumption bundle of vivian show your calculations.
Kim spends all her weekly income of R200 on two goods, X and Y. The prices of the two goods are R5 per unit for X and R2 per unit for Y. She has a utility function expressed as: U(X, Y) = 5XY Express the budget equation mathematically. Determine the utility-maximising bundle of X and Y. Calculate the total utility that will be generated per unit of time for this individual.
Question 3. Suppose that Janice only cares about tea (T) and coffee (C). Her utility function is U = 2T + 4C. The price of T is $1.50, and the price of C is $2.50. Janice has a budget of $15 for tea or coffee during the week. (a) Write down the consumers maximization problem. (b) What are the consumption quantities of T and C that will maximize Janice's utility?
For the utility function U = (Qx0.5+Qy0.5)² and the budget 122 = 8Qx + 8Qy find the CHANGE in optimal consumption of X if the price of X increases by a factor of 1.7. Please enter your response as a positive number with 1 decimal and 5/4 rounding (e.g. 1.15 = 1.2, 1.14 = 1.1).
Find the optimal bundle using the following utility functions and budget constraints. 1. U(x,y)=lnx+yand2x+y=10 2. U(x,y)=3x+2yand3x+2y=24 3. U(a,z)=3a+2zand3a+6z=24 4. U(a,z)=a2z2 and4a+2z=485. U(x,z)=a2z3 and3a+2z=36
You consume music (M) and concert tickets (C). Your utility function is U(M, C) = M1/4C3/4. The marginal utility for concert tickets, MUC is MUC =3/4C-1/2M1/4 and the marginal utility for music, MUM is MUm = 1/4C3/4M-3/4 (a) Calculate MRSMC using only the given marginal utilities. (b) Solve for the utility of bundle A where M = 16 and C = 16. Solve for your utility at bundle B where M = 128 and C = 8. Are the utilities the same? (c) Calculate MRSMC at bundle A and at bundle B. Are they the same? (d) Are your indifference curves convex? Draw the ICs. Make sure to label the quantities of the consumption bundles, the axis, and the MRS at those bundles.
part C D
True/ False Marginal utility decline with the increase in the unit of consumption of a good.
Given a Utility function: U(x,y) = 3xy. Suppose the Price of x is 2, and the price of y is 4. Furthermore, suppose I = $16. How much of x and y do you consume?

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