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Economics 314 Spring 2009 Project #6 Assignment Due: 10am, Wednesday, April 1 Partner assignments Gavin Bell Alex Ragus Juan Brito Rodriguez Ethan Knudson Andrew Dubay Nina Showell Laura Florescu Robert Kahn Erik Swanson Trey Sands Cori Savaiano Derek Rutter We shall construct macro models from the following equations: DE: ()0 YrEYT rG=α +α − −α + KC: YE= LM: ()01 2emp Y r−=β+β −β +π MP: 0 YrYπ=γ +γ +γ π CAS: YY= KAS: orpp=π=π The Greek letters α, β, and γ with various subscripts are positive coefficients, with 1Yα<. G, T, and πe are exogenous. Y is the full-employment level of output and is exogenous. p and π are the pre-determined levels of prices and inflation in a fixed-price model and are exogenous. The constant terms are “shift parameters” that reflect the effects of all other (exogenous) factors. For example, an increase in desired spending due to more optimistic expectations about the future (or anything else other than disposable income, the real interest rate, or government spending) would cause an in-crease in α0. Note on solving models: One of the most difficult things for young, budding macroeconomists to learn is how to recognize when they have (and have not) solved a model. Solving a model means express-ing the values of the endogenous variables (some or all) as functions only of the exogenous variables. If there is still an endogenous variable on the right-hand side of the equation, you have not solved it yet; you are still looking at a partial effect holding other endogenous responses fixed, not the com-plete effect. For example, if you were asked to calculate the effect of G on Y, you could not simply substitute the DE equation into the KC equations above and say that ∂Y/∂G = 1. This is because other endogenous variables (r and Y itself) appear on the right-hand side of DE. To calculate the ef-fects of G on Y, you would need to solve the Y out of the right-hand side and use one or more other2 equation(s) to eliminate r. Once you get an expression for Y that involves only exogenous variables, you have what is called a reduced-form equation. This equation is a solution for Y. If it is linear, then the effects of exogenous variables on Y are just the expressions by which those variables are multip-lied in the linear equation. If an exogenous variable does not appear in the reduced-form equation for Y, then that exogenous variable does not affect Y. The mathematical analysis gives you a formula for the effect of one variable on another. The ma-thematics is important to establish whether we can determine with certainty (based on our assump-tions) whether an effect is positive or negative. Even more important is understanding the economic intuition of the results. Whose behavior changes and why? What are the connections that link the change in the exogenous variable to the ultimate change in the endogenous variable? Which parame-ters of the model are crucial in that chain? These are the kinds of considerations that should be dis-cussed in your explanations of intuition on these problems. 1. The basic IS/LM model The basic IS/LM model consists of equations DE, KC, and LM with m assumed to be the exogen-ous monetary-policy instrument. (a) Combining the IS/LM model with the static form of the KAS curve, solve the model for Y and r as functions of G, T, m, πe, p, and the parameters of the model. (b) Use the results of part (a) to evaluate whether each of the following is true of false, using both mathematical analysis and also explaining the intuition of the result: (i) An increase in αY would increase the impact of G on Y. (ii) An increase in m affects Y and r. (iii) An increase in the interest-sensitivity of money demand would increase monetary poli-cy’s impact on Y and r. (iv) A decrease in the overall level of the demand for money, such as might result from hav-ing more convenient ATMs and online banking, would affect Y and r. If the central bank wanted to neutralize this effect, it should lower m. (v) An increase in the expected rate of inflation would raise the nominal interest rate by an equal amount, leaving the real interest rate unchanged (the Fisher hypothesis). (c) Now combine the IS/LM model with the classical CAS curve, solving the model for r, and p as functions of G, T, m, πe, Y , and the parameters of the model. (d) Use the results of part (c) to evaluate each of the following, explaining the intuition of the result: (i) An increase in m lowers r and raises Y and p. (ii) An increase in G has similar effects (i.e., the same sign) on r, Y, and p as in the model of part (a). (iii) An increase in G “crowds out” (lowers) private spending by an equal amount. (iv) An increase in expected inflation raises the price level. (v) An increase in the expected rate of inflation would raise the nominal interest rate by an equal amount, leaving the real interest rate unchanged (the Fisher hypothesis).3 2. The IS/MP model The IS/MP model consists of equations DE, KC, and MP. If we want to know what happens to m, we add the LM equation and consider m an endogenous variable. Otherwise m does not enter into the model. (a) Solve the IS/MP model together with the inflation form of the KAS curve with r and Y as the endogenous variables. (b) Use the results from part (a) to examine each of the following, explaining the intuition of the re-sult: (i) How would a change in the monetary-policy rule to become more expansionary (a de-crease in γ0) affect r and Y? Compare these effects to those of an increase in m in the IS/LM model. (ii) If the aggregate-demand curve is to slope downward, then an increase in π should lower the equilibrium Y. Is this true in this model? Discuss the mechanism through which this happens and compare it to the IS/LM model. (c) Now solve the IS/MP model with the classical CAS curve treating r and π as endogenous. (d) Use the results from part (c) to answer the following, explaining the intuition of each result: (i) How would a positive productivity shock (an increase inY ) affect r and π? How does the effect on r compare with the effect predicted in the real-business-cycle model? (ii) Suppose that the monetary authority sets the real interest rate based solely on the level of real output (γπ = 0). What is the slope of the aggregate-demand curve? Is there a unique equilibrium value of π? Explain. What will happen if the central bank’s target value of Y


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