Ch 4, q7. Suppose Humphrey and Matilda live together. Humphrey currently smokes 20 packs of cigarettes per month; Matilda hates the smoke. They currently have no agreement restricting smoking. Their only joint expense is monthly rent, which they split 50:50. Draw an Edgeworth box with two goods: smoke and rental payments. Make up some reasonable indifference curves. Show the initial endowment. What Pareto efficient points might result from bargaining to restrict smoke? How does the graph show what price per pack Matilda might 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 no smoking and Humphrey would like to smoke as much as 20 packs per month? He must seek Matildas permission to do so. (Hint: For Matilda, redefine Humphreys smoking as smoke reduction.)

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…

4. Two individuals, Amir and Budi, consume two goods, clothes (X) and shoes (Y). The utility functions for the two individuals are given as: Utility function of Amir, UA = 15X0.25Y0.75Utility function of Budi, UB = 25X0.5Y0.5 The current price for clothes (Px) is Rp 100,000 and the current price for shoes (PY) is Rp 150,000 a. Determine marginal rate of substitution (MRSXY)between clothes (X) and shoes (Y) for Amir and Budi! Please explain. b. Amir is currently consuming 5 units of clothes (X) and 10 units of shoes (Y), whereas Budi is consuming 12 units of clothes (X) and 8 units of shoes (Y). At this current consumption, have Amir and Budi reached the efficient allocation of clothes and shoes? If they have, explain why. If they have not, calculate the optimal allocation and explain. c. Considering the relative price between of clothes and shoes, at the current consumption, have Amir and Budi reached exchange equilibrium? Please explain d. Use the Edgeworth Box to illustrate the…

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?

!

Two individuals, Sam and Barb, derive utility from the hours of leisure (L) they consume and from the amount of goods (G) they consume. In order to maximize utility, they need to allocate the 24 hours in the day between leisure hours and work hours. The price of a good is equal to $1.00 and the price of leisure is equal to the hourly wage. We observe the following information about the choices that the two individuals make: Q 16- 14- 12- Sam Barb Sam Barb Price of Price 10- L L of L (hours) (hours) G ($) G ($) G 8- 7 13 10 77 98 1 132 1 11 10 12 154 1 15 7 14 255 150 6- Graphically, illustrate Sam's leisure demand curve and Barb's leisure demand curve. 4- 1.) Using the line drawing tool, draw Sam's leisure demand curve. Label this line D' 2- 2) Using the line drawing tool, draw Barb's leisure demand curve. Label this line D' 0- 0 4 в 8 10 12 14 Leisure (hours) Carefully follow the instructions above, and only draw the required objects. Wage (S)

9. Consider an Edgeworth box economy with two consumers, whose utility func- tions and endowments are u'(x},x}) = (x}Xx})} (5,5) In the following, use the normalization p2 = 1. (a) Find the competitive equilibrium price. (b) State the first fundamental theorem of welfare and verify that it holds in this economy. (e) Consider the allocation ĩ = (x',) = (2,3), (8, 7). Show whether this allo- cation can supported as an equilibrium with transfers. (d) State the second fundamental theorem of welfare, and briefly discuss whether the result in part (c) conform with or violate this theorem. 3.