Ch 4, q7. Suppose Humphrey and Matilda live together. Humphrey currently smokes 20packs of cigarettes per month; Matilda hates the smoke. They currently have no agreementrestricting smoking. Their only joint expense is monthly rent, which they split 50:50. Drawan Edgeworth box with two goods: smoke and rental payments. Make up some reasonableindifference curves. Show the initial endowment. What Pareto efficient points might resultfrom bargaining to restrict smoke? How does the graph show what price per pack Matildamight pay to buy down Humphreys smoking (i.e., show the relative prices on your figure)?How would your answer change if the status quo is that the two have an agreement for nosmoking and Humphrey would like to smoke as much as 20 packs per month? He must seekMatildas permission to do so. (Hint: For Matilda, redefine Humphreys smoking as smokereduction.)

Step 1:We need to draw an edgeworth box showing the changes in utility of both Humphrey and Matilda…

Answered: Ch 4, q7. Suppose Humphrey and Matilda…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Peter has an endowment of 3 units of good x and 5 units of good y. He can buy and sell x at a price of 100 and y at the price of 200. He receives an income of $700 as alimony from a former spouse. a) Draw Peter’s budget line for x and y. Show his initial endowment of x and y on your diagram. b) Calculate the amount of x that he could afford if he bought only x and the amount of y he could afford if he bought only y. c) Write an equation for Peter’s budget.
Two individuals, Fred and Helen, are in an economy with no production, and each have the utility function U = 10XY. Prices of both X and Y are set at $1. Initial endowments for Fred are 10 units of X and 6 units of Y. Helen has 8 units of X and 12 units of Y. Find the general equilibrium prices and allocation, then show that the G.E. allocation is Pareto efficient.
Graph make graph
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Damian and Kira trade in antique cars. They typically buy either 1 or 2 cars at any given time, since they are difficult to find and expensive. The price per car P(Q) where Qis the total number of cars traded at a given time, is determined by the demand equation: K P(Q) 1 where K is a positive constant. If a € {1, 2} is Damian's choice and b = {1,2} is Kira's choice, (so Q = (a + b)) it costs Damian 2a to find and prepare a cars for market, and it costs Kira 3b to get b cars ready for market. Damian has better connections and access the cars before Kira, and so Damian chooses his value of a first. Kira then chooses his value of b, knowing Damian's choice. Their choices are determined by maximising their individual profits, ie the difference between how much they can sell their cars for, minus the total costs to prepare them for sale. (i) Express this game as an extensive form game tree, making sure to fully label all the nodes and links, and especially writing down their payoffs. (ii)…
4. Aaron and Burris have the following utility functions over two goods, x and y. Aaron’s utility function: UA(xA, yA) = min{xA/3, yA} Burris’s utility function: UB(xB, yB) = 9xB + 3yB Aaron’s endowment is eA = (2, 4). Burris’ endowment is eB = (10, 8). In an Edgeworth Box diagram, show which allocations are in the core. Solve for the set of Pareto optimal allocations (i.e. the contract curve) in the Edgeworth Box. Illustrate the contract curve in an Edgeworth Box diagram. Let good y be the numeraire (i.e. set py = 1 and let px = p). Solve for the Walrasian competitive equilibrium allocation and price ratio.
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True or false: keeping his maximum willingness to pay for a yacht in mind, Tim will buy the yacht because it will be worth more to him than its market price of $350,000
5.18 In a two-good, two-consumer economy, utility functions are u¹ (x₁, x₂) = x₁(x₂)², u² (x₁, x₂) = (x₁)²x₂. Total endowments are (10, 20). (a) A social planner wants to allocate goods to maximise consumer 1's utility while holding con- sumer 2's utility at u² = 8000/27. Find the assignment of goods to consumers that solves the planner's problem and show that the solution is Pareto efficient. (b) Suppose, instead, that the planner just divides the endowments so that e¹ = (10, 0) and e² = (0, 20) and then lets the consumers transact through perfectly competitive markets. Find the Walrasian equilibrium and show that the WEAs are the same as the solution in part (a).
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6. Sarah and Clare have identical utility functions U = 5 In(x)+y: Sarah starts out with 16 units of x and 5 units of y and Claire starts out with 4 units of x and 15 units of y. a. Draw the Edgeworth box, label the endowment point and sketch some "normal" indifference curves through the endowment point. Shade the region where trades are possible. b. Find Sarah and Claire's Marshallian demands as a function of the price of x, price of y and their endowments. c. Find the market clearing price and how much x and y the two consumer after trading. d. Who is happier after trading?

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