An economy with no production technologies has two individuals.

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Intermediate MicroeconomicsFall 2015Homework 3 – Part AExercise 1:An economy with no production technologies has two individuals. There aretwo goods, good x and good y. Individual A owns 60 units of good x and 90units of good y. Individual B owns 40 units of good X and 10 of good Y . A’spreferences can be represented by the following utility function:UA (xA ; yA ) = smallestfxA ; yA g:B’ preferences can be represented by the following utility function:s2UB (xB ; yB ) = 2xB (yB ) :a. Draw an Edgeworth box where you can represent the amounts of both goodsthat each individual owns. Also show three indi¤erence curves for each of thetwo individuals.b. Find all Pareto e¢ cient allocations both analytically and graphically (youdon’ need calculus, just take a good look at the indi¤erence curves).tc. If prices are px = A + 1 and py = 2, where A is the last digit of your StudentID#, …nd what each individual would want to consume.d. Are prices in (c) General Equiblibrium prices? Explain why.Exercise 2:An economy with no production technologies has two individuals. There aretwo goods, good x and good y. Individual A owns 30 units of good 1 and 60units of good 2. Individual B owns 60 units of good 1 and 30 of good 2. A’spreferences can be represented by the following utility function:UA (xA ; yA ) = ln(xA ) + ln(yA ):B’ preferences can be represented by the following utility function:suB (xB ; yB ) = 2xB + 9yB :a. Draw an Edgeworth box where you can represent the amounts of both goodsthat each individual has. Also show three indi¤erence curves for each of the twoindividuals.1b. If prices are px = 1 and py = 1, …nd what each individual would want toconsume.c. If py = 1 and individual 2 can choose any price px desired, what would bethe optimal choice? Also …nd what each individual would end up consuming.d. Are prices in (b) or (c) General Equiblibrium prices?Exercise 3:For the Endowment Economy described in Exercise 1, assume that the initialendowments are:! A = 20(xwhereID#.= 1+pB22+ 1); ! A = 40; ! B = 30; ! B = 60yxy2;8B + 16, and B is the 2nd -to-last digit of your Studenta. Solve for the General Equilibrium relative price p .b. Determine the General Equilibrium allocation (xA ; yA ; xB ; yB )Exercise 4:For the Endowment Economy described in Exercise 2,a. Explain why any relative price p < 2=9 would lead to an excess supply ofgood Y:b. Explain why a relative price of p = 2=9 demand for good X by A is greaterthan aggregate supply.c. Solve for the General Equilibrium price p ; knowing –from parts (a) and(b)– that it must be the case that p > 2=9:d. Show your results from part (c) in an Edgeworth Box where the GeneralEquilibrium allocation is clearly marked along with all other e¢ cient allocations.2Intermediate Microeconomic TheoryFall 2015Student Name:___________________Student ID________Homework 3 – Part AFront PageSelected Answers:Exercise 1.c.The amount of good y that consumer B wants to consume is:yB = ___________Exercise 2.c.If consumer B is the monopolist, then the price of good x selected is:pm = ___________xExercise 3.The General Equilibrium relative price (p = px =py ) is:p = ___________Exercise 4.a.If the relative price is p = 1=15 then aggregate demand for good y is::YD = ___________Exercise 4.If the relative price is p = 2=9 then aggregate demand for good x is at the veryleast equal to:XD = ___________3

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