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3. Market Demand Suppose Joyce consumes two goods, z, and a2 with prices p, and p2. She has income M. Joyce's demand function is given by: I(PI, P2, M) = p2M - Pi a) Draw a sketch of the Engel curve for this demand function (For a sketch I am looking for ) b) Are goods a and 2 complements or substitutes? c) If there are 20 consumers in the market, and they all have identical demand function, what is the market demand function? d) What is the price elasticity of demand at p, = 3 if py = 5 and M = 10? e) Is r, an ordinary good or a Giffen good?demand equations X* = = and Y = [-@1 a) Derive the indirect utility function. Simplify as much as possible. (Hint: during the simplication, you'll come across a mess that looks like a" (1 - a) . As ugly as that is, it's just a number. So you might find it easier to call it A, and then use A in parts b and c.) b) Derive the expenditure function. That is, given prices Px and Py, find the equation showing how much the consumer must spend to achieve desired utility U. c) Calculate the compensated demand functions for X and Y. d) Use the compensated demand functions to calculate the substitution effects for both X and Y. That is, calculate op, ARE and oksQuestion 1. Consider the following information: the British pound is currently trading at $1.60 US and the Euro is trading at $1.28 US. Someone quotes a Euro price for the British Pound at f1 = ( 1.23. Carefully describe a series of trades you could make to earn big money. How much do you make per unit of currency initially traded? Question 2. Sven, our international banker friend in Sweden and all around cool dude, observes that $10,000 U.S. T-bills that mature in one year are selling at discount at $8333.33 and 2000 SKr Swedish Government bills that mature in 1 year are selling at discount at 1777.78 SKr. Currently, the dollar is trading at 6.50 SKr. If uncovered interest parity holds, where does the market believe the dollar will trade at 1 year from now? Show your work. Question 3. Sven notes one day that the premium on a 150,000 Euro June Call Option with strike price of $1.21 is $.02 per Euro. In addition, there's a bank in Germany offering a June Forward contract for $1.24 per Euro, and a bank in NY is willing to make him a loan (in dollars) for 25%. Show how Sven can make a killing with very little effort. What's the minimum he'll earn for each 150,000 Call Option contract he purchases? How and when will he make more than this minimum amount? Explain.Assume that the following equations summarize the structure of an economy. C=C, +0.8(Y -T); C. =700-15r; 7 = 200 +0.2Y; (M / P) = 0.1Y -10r; M' / P =440; I = 600-25r; G =1,000, NX = 100-0.04Y. Answer the following questions: (a) What is the equation of the IS curve? (b) What is the equation of the LM curve? (c) What is the equilibrium real output? (d) What is the equilibrium interest rate? (e) What is the level of saving at equilibrium? (f) What is the level of planned investment at equilibrium? (g) Determine whether leakages equal injections at equilibrium. (h) Assume that > = 4 and Y = 5000. Is there an excess demand for money or an excess supply of money? How much? Is there unplanned inventory change? If so, what is its value