Suppose we have two people in the market: A, B.Their utility functions are UAmin{x1, x₂},UB = min{x₁,2}. Solve their optimal choices andthen find market demand.=

The complement goods are used in fixed proportion. The indifference curve is L shaped.

Answered: Suppose we have two people in the…

Suppose we have two people in the market: A, B. Their utility functions are UA min{x1, x₂}, UB = min{x₁, 22²2}. Solve their optimal choices and then find market demand. =

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Smith and Jones are stranded on a desert island. Each has in her possession some slices of ham (H) and cheese (C). Smith prefers to consume ham and cheese in the fixed proportion of 2 slices of cheese to each slice of ham. Her utility function is given by Us = min(10H, 5C). Jones, on the other hand, regards ham and cheese as substitutes – she is always willing to trade 3 slices of ham for 4 slices of cheese, and her utility function is given by UJ = 4H + 3C. Total endowments are 100 slices of ham and 200 slices of cheese. a. Draw the Edgeworth Box diagram for all possible exchanges in this situation. What is the contract curve for this exchange economy? b. Suppose Smith’s initial endowment is 40 slices of ham and 80 slices of cheese (Jones has the remaining ham and cheese as her initial endowment). What mutually beneficial trades are possible in this economy and what utility levels will Smith and Jones enjoy from such trades? c. Now imagine a new endowment in which Smith has 60 slices…
Two friends, Karol and Manuel, like to drink kombucha (x₁) and matcha (x₂). Both X₁ and X2 are expressed in ounces. The following utility function represents Karol's preferences: 1 1 2 2 u (x1, x2) = x1 x3 The following utility function represents Manuel's preferences: u (x₁, x2) = √√x1 + x2 Karol's income in dollars is denoted by mk, and Manuel's income is denoted by mm. Both face the same prices in the market, denoted by p₁ and p2, for kombucha and matcha, respectively. Both prices are expressed in dollars per ounce. Assume p₂=1 throughout the whole question. 1) Draw Karol's and Manuel's indifference curves in separate graphs and describe any important similarities or differences between the two.
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Suppose the function for the utility from good c is denoted as U(c)=2c2. Which of the following expressions indicates the marginal utility of c? 1/c2 1/square root of c All of the above are correct.
1.2 Ann and Bob each own 10 bottles of beer and, altogether, they own 20 bags of peanuts. There are no other people and no other goods in the economy, and no production of either good is possible. Using a to denote bottles of beer and y to denote bags of peanuts, Ann's and Bob's preferences are described by the following utility functions: UA (XA, YA) = TAYA and UB (XB, YB) = 2xB+ YB. In each of the following cases, determine the market equilibrium price ratio and allocation and depict the equilibrium in an Edgeworth box diagram. (a) Bob owns 20 bags of peanuts and Ann owns no peanuts. (b) Bob owns 15 bags of peanuts and Ann owns 5 bags. (c) Ann owns 20 bags of peanuts and Bob owns no peanuts.
Suppose that consumer has the following utility function: U(X,Y) - X1/2y1/4. Suppose also that P 2, P -3 and 1=144. What would be the optimal consumption of X and Y at the equilibrium. respectively? 36, 24 12,40 24,32 48.16
Consider the following utility function: U = 100x.50,0.50 A consumer faces prices of P, = $2 and Py =$1. Assuming that graphically good X is on the horizontal axis and good Y is on the vertical axis, suppose the consumer chooses to consume 6 units of good X an units of good Y. Then the marginal rate of substitution is equal to: MRS = 1.83. (Enter your response rounded to two decimal places. Do not forget to include the negative sign.) Use absolute values. The consumer should consume to maximize utility. more Y and less X the same amount of X and Y more X and less Y 15 tv MacBook Air 80 esc DII F1 F2 F3 F4 F5 F6 F7 F8 @ #3 % 2 7 8. Q W E Y tab s lock A S F G H J Z C V N M Onteel 8 : < CO T D
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Fang likes playing badminton with her friends. Her utility function for playing badminton every week is given by U(t) = 11t – 2t2, where t is measured in hours. They play on a badminton court, which they can rent per hour. Suppose the current price to play on the badminton court is £2.50 per hour. How many hours should Fang play if she wishes to maximise her utility? Explain what we mean by the principle of diminishing marginal utility. Does the principle apply in Fang’s case? Explain why. In a diagram with income in pound sterling on the horizontal axis and quantity on the vertical axis, show the relationship between Fang’s budget and the number of hours that would maximise her consumer surplus.
Consider a consumer whose preferences are given by the utility function U (x, y) = (x + 1)² (y + 1)where x and y are the quantities he consumes of goods x and y and the prices of good x and good y are p, and p, respectively and his income is m. Assume that p, is twice of p,. The demand function of good x (p,, m) is (а) т Зр, 2m (b) Зр, (c) 3p. 2m (d) 3p, (e) None of the above.
Part A . Consider an economy with the following features. • There are 100 identical consumers that derive utility from consuming three different goods: software, computers, and good m. • Each consumer decision utility function is given by U (c, 8) = 4c¹/48¹/4+m, where e denotes the amount of computers that she consumes, s denotes the amount of software that she consumes, and m denotes the amount of good m that she consumes. cand s must be non-negative, but m can take any real value. • Computers are produced by 20 identical competitive firms with a total cost function given by 10c². • Software is produced by 40 identical competitive firms with a total cost function given by 20s². . QUESTION 1: What are the equilibrium prices for software and comput- ers in equilibrium? Part B • Suppose that there is a positive technology shock in the software industry so that that the new cost function of the software firms becomes 10s². Let C and S denote, respectively, the aggregate level of…