answertohomework5spring2005 - Economics 302 Prof. Kelly...

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Economics 302 Prof. Kelly Problem Set 5 Due: Wednesday, April 27 ANSWER KEY Exercise 1 Comparing Classical and Keynesian-Sticky Price Models Consider the market for wheat. In Econ 101, you analyze this market by …nding the equilibrium price and quantity as the point where the supply curve intersects the demand curve. If we throw out the graph and handed our functions for supply and demand to a mathematician, she would see two equations (an equation that gave the quantity supplied as a function of price and an equation that gave the quantity demanded as a function of price) and two unknowns (price and quantity) [to be technical, there is a third equation in the system: that quantity demanded equals quantity supplied equals quantity]. This system of equations produces an equilibrium because we have the same number of equations as unknowns. Now, consider the whole economy. We have 3 unknowns: output, the real interest rate, and the price level. Since we have 3 unknowns, to solve for these 3 unknowns, we better have 3 equations to describe what is going on. a) Before reading the rest of the question, can you think which 3 equations we are going to use (Hint: what equations/relations connect r, Y, and P)? Try and explain why you are selecting these 3 equations. Don’t worry about getting this wrong or right, just think. The rest of this question proceeds through a series of steps, building the necessary equations one-by-one Step 1 Loanable Funds Market: The marginal propensity to consume is mpc. Full-employment output (the output of the economy when workers and capital are employed at their normal levels and intensities) is ¹ Y = F ( ¹ K; ¹ L ) . Government spending is G and the tax level is T . The investment function is : I = : 1 r b) De…ne and derive the IS curve in this closed economy (it will have many, many letters hanging around). The IS curve is the combination of Y and r that are equilibria in the Loanable Funds Market when T; G; and mpc are held constant. Y = C + I + G Y = mpc ( Y ¡ T ) + : 1 r + G : 1 r = (1 ¡ mpc ) Y + mpcT ¡ G r ( Y ) = : 1 (1 ¡ mpc ) Y + mpcT ¡ G 1
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Step 2 Money Market: The nominal money supply is M, the price level is P, and the demand for real money balances is: L ( Y;r ) = Y
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This note was uploaded on 08/08/2008 for the course ECON 302 taught by Professor Gold during the Spring '07 term at Wisconsin.

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answertohomework5spring2005 - Economics 302 Prof. Kelly...

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