For this part, solve for the utility maximization and cost minimization problems. Additionally, indicate each important step in solving for the utility maximization of the consumer and the cost minimization of the producer. a. Suppose that a consumer is faced with a utility maximization problem given as: U(a, b) = a0.²b0.8 s.t. I = P,a +Pzb The consumer has an income of Php 25,000 and that pa = 350 and på = 200. Solve for the consumer's Marshallian Demands and how the amount of utility the consumer has.

For this part, solve for the utility maximization and cost minimization problems. Additionally, indicate each important step in solving for the utility maximization of the consumer and the cost minimization of the producer. a. Suppose that a consumer is faced with a utility maximization problem given as: U(a, b) = a0.²b0.8 s.t. I = P,a +Pzb The consumer has an income of Php 25,000 and that pa = 350 and på = 200. Solve for the consumer's Marshallian Demands and how the amount of utility the consumer has.

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter2: Mathematics For Microeconomics

Section: Chapter Questions

Problem 2.7P

See similar textbooks

Similar questions

Irene spends all of her income M on soda and chips. The price of soda is 2 per unit. Irene’s utility function is U (s, c) = 5 ln(1 + s) + ln(1 + c).Hint: throughout the question, you can assume M ≥ 50 and pc ≤ 8 (these assumptions just rule out the possibility of corner solutions, but do not affect the way we solve the problem). (a) Derive Irene’s demand function for chips (as a function of her income and the price of chips). (b) Are chips an inferior good for Irene? Is the magnitude of the (total) effect of a decrease in price of chips greater or smaller than the corresponding substitution effect. (c) Obtain Irene’s inverse demand function for chips when her income is M = 50. Show that this function is decreasing and convex. is irenes engel curve upward or downward sloping? explain
Irene spends all of her income M on soda and chips. The price of soda is 2 per unit. Irene’s utility function is U (s, c) = 5 ln(1 + s) + ln(1 + c).Hint: throughout the question, you can assume M 》= 50 and pc 《 = 8 (these assumptions just rule out the possibility of corner solutions, but do not affect the way we solve the problem). (a) Derive Irene’s demand function for chips (as a function of her income and the price of chips). (b) Are chips an inferior good for Irene? Is the magnitude of the (total) effect of a decrease in price of chips greater or smaller than the corresponding substitution effect? (c) Obtain Irene’s inverse demand function for chips when her income is M = 50. Show that this function is decreasing and convex. (d) Is Irene’s Engel curve upward sloping or downward sloping? Explain in detail.
True/False/Uncertain: 1. In taking an exam, Atack, a rational student, allocates his time to the various questions so as to equalize hismarginal point utility per minute on all questions. 2. The marginal utility of food to Zecher depends only on the amount of food (and not on the amount ofhousing) and the marginal utility declines as more food is consumed; likewise for housing. Therefore,both food and housing are normal goods. (Hint: Express the optimality condition for Zecher’s [UMP], MUF/MUH = PF/PH. Notice that PF/PH is fixed. If all of an increase in income is spent on F, can the equality be maintained?)
Brit-Brick is a company that produces bricks and cement in the UK. Their largest consumer is ConstrUK, a UK construction company. The manager of Brit-Brick has asked the research department to find out how sensitive ConstrUK’s demand for bricks is. The research department has estimated that ConstrUK’s preferences over bricks (x) and cement (y) can be described by the utility function U(x,y) = x2/10y1-2/10 The price for one bag of cement is equal to £1. It is estimated that ConstrUK’s budget is £10,000. Find the price-consumption curve for bricks and the corresponding demand curve.
An agent has income m that can be spent on frequent flier miles f or on other goods – a “composite good” g. Their respective prices are: pf = 10 per mile and pg = 1 per unit. The flier miles have a stepwise price schedule. After the first 25 miles the price is reduced by 20% and after 50 miles the price is further reduced by another 50%.1. Put g on the vertical axis and f on the horizontal axis. Assume m = 200, and draw the budget constraint with all the intercepts and appropriate slopes. 2. On a separate graph, repeat part (1) for m = 300. 3. On a separate graph, repeat part (1) for m = 600.
Brit-Brick is a company that produces bricks and cement in the UK. Their largest consumer is ConstrUK, a UK construction company. The manager of Brit-Brick has asked the research department to find out how sensitive ConstrUK’s demand for bricks is. The research department has estimated that ConstrUK’s preferences over bricks (x) and cement (y) can be described by the utility function U(x,y)=x^(7/10)y^(1-7/10) The price for one bag of cement is equal to £1. It is estimated that ConstrUK’s budget is £10,000. Find the price-consumption curve for bricks and the corresponding demand curve.
Let the utility function be given byu(x1, x2) = √x1 +√x2.Let m be the income of the consumer, p1 and p2 the prices of good 1 and good 2, respectively.(a) Write down the budget constraint and illustrate the set of feasible bundles usinga figure.(b) Suppose that m = 24, p1 = 2 and p2 = 4 . Find the optimal bundle for theconsumer. In other words, find the combination of x1 and x2 that maximizes the consumer’sutility when the prices are p1 = 2 and p2 = 4, and her income is m = 24.(c) Determine the Marshallian demand function.(d) Determine the expenditure function.
Brit-Brick is a company that produces bricks and cement in the UK. Their largest consumer is ConstrUK, a UK construction company. The manager of Brit-Brick has asked the research department to find out how sensitive ConstrUK’s demand for bricks is. The research department has estimated that ConstrUK’s preferences over bricks (x) and cement (y) can be described by the utility function U(x,y) = x4/5y1/5 where x and y are measured in bags. The price for one bag of cement is equal to £1. It is estimated that ConstrUK’s budget is £10,000. Find the price-consumption curve for bricks and the corresponding demand curve. Note: The writing is clear and abbreviations are not allowed.
Indifference curve assumption where consumers aim to maximise utility given income andprices of products is called ________________________assumption.A. Ordinal util.B. Non-satiety.C. Rationality.B. Transitivity2. Economic profit =A. Total Revenue – Explicit costs.B. Total Revenue – Total costs.C. Total Revenue – Implicit Cost.D. Total Revenue – Opportunity cost.3. _____________________is a firm that owns, controls and manages assets in many countries.A. Sole trader.B. Partnership.C. Multinational firm.D. Monopoly.4. Which one of the following is remuneration for capital?A. Wages.B. Interest.C. Profit.D. Rent 5. ____________________is market structure with one single seller.A. Monopolistic competition.B. Monopoly.C. Perfect competition.D. Oligopoly.6. Complete the following table to answer question 6: Quantity of oranges Total utility Marginal utility 0 0 1 10 2 25 3 31 4 35 5 37 6 33 At which level of…
How does a consumer maximizes their utility given that they experience a budget constraint? Explain with graphical illustrations. Note:- Please avoid using ChatGPT and refrain from providing handwritten solutions; otherwise, I will definitely give a downvote. Also, be mindful of plagiarism. Answer completely and accurate answer. Rest assured, you will receive an upvote if the answer is accurate.
Which among the following is not true?Select one:a. None of the answers are correctb. When marginal utility declines, a higher price is needed to induce the consumer tobuy more of a particular productc. When marginal utility declines, a lower price is needed to induce the consumer tobuy more of a particular productd. All the answers are correcte. Utility maximizing rule and the demand curve are logically consistent
For a > 0, consider a consumer whose utility function amounts to u(x1, x2) = − exp(−ax1x2). Can you take first order conditions to solve the utility maximization problem? Explain your argument. Next solve the utility maximization problem, and derive Marshallian demands and the indirect utility function. Given your calculations, state and use the duality theorem to find the expenditure function and Hicksian demand Note:- Do not provide handwritten solution. Maintain accuracy and quality in your answer. Take care of plagiarism. Answer completely. You will get up vote for sure.