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MIT. Final Exam in Graduate Macro I. Stanley Fischer, 1975

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Today another posting from the more recent history of economics for that professor who succeeded where others had failed before him, namely in first teaching me the economic intuition behind macroeconomic models, Stanley Fischer. While James Tobin had succeeded in convincing the undergraduate me of the utter importance of getting macroeconomic policy right, I was still much too immature to “receive wisdom” as a sophomore…but enough about me.

I thought of Stan Fisher this morning as I read his marvelous summary of his own 55 years of experience with macroeconomics.

I earlier posted Fischer’s reading list for his undergraduate course at the University of Chicago in 1973. Below is the exam from the first half-semester course in the required four quarter sequence in macroeconomics for the cohort that entered MIT in the Fall of 1974, the cohort that included Paul Krugman, Jeffrey Frankel, Francesco Giavazzi, Andrew Abel, Dick Startz, to name only a few, sandwiched between Olivier Blanchard’s and Ben Bernanke’s respective cohorts.

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Spring 1975

Final Exam 14.451

Stanley Fischer

Time available is two hours. Answer all questions. You have a choice on question 2.

  1. (50 points) it is sometimes asserted that the key to the effectiveness of monetary policy is the fixed nominal return on money. Suppose that means were devised of paying interest on money and that the nominal bond interest rate were fixed in an arbitrary level.
    1. Using any convenient variant of a three asset (money, bonds, capital) model, explain the determination of asset market equilibrium and then of the overall equilibrium of the economy, under the assumption of a fixed bond interest and a rate market-determined money interest rate. (Maintain this assumption here after.)
    2. Analyze the consequences of an open market purchase for the interest rate on money and other endogenous variables. What are the differences between your results and those in the more usual model in which the bond interest rate varies?
    3. Suppose a helicopter dropped bonds on the populace. What happens to the interest rate on money and other endogenous variables?
    4. What do you make of the assertion mentioned in the first sentence of this question in the light of your answers to (ii) and (iii) and/or in the light of any other relevant considerations?
    5. Extra credit (5 points max). Can you envision any type of institutional arrangements which make the premise of this question — fixed bond interest rate and market determined interest rate on money — empirically reasonable?

 

  1. Answer A or B (30 points each)

A.

  1. What theoretical reasons are there to assume the demand for money is a function of the interest rate?
  2. Why does it matter?
  3. Review relevant empirical evidence.
  4. Discuss any econometric difficulties of the empirical work.

 

B.

A household has the utility of wealth function

U(W) = W (b/2)W2.

Its initial wealth is W0.
It can hold in its portfolio a safe asset paying a safe rate of return of our rB in the risky asset paying rE+g, where rE is the expected return and sg2 is the variance of return.

    1. Derive demand functions as a function of rB, rE, sg2, and W0.
    2. Suppose that a tax on next period’s wealth is announced, at rate t, i.e. t% of wealth at the beginning of next period will be paid to the government. What effect does this have on the asset demands? Can you give an intuitive explanation?
    3. Suppose instead that positive returns on the risky assets are taxed at a rate t, but not negative returns. Thus if A2 is the holding of the risky asset, the tax is tA2(rE + g) if rE +g > 0 and zero otherwise. The return on the safe asset is not taxed. What effect does this have on asset demands?

 

  1. (20 points)
      1. Define free reserves.
      2. Define excess reserves.
      3. What effect would Federal Reserve System payment of interest on reserves held at FR banks have on the demand for reserves? (Use any appropriate model, and assumed the rate on reserves as fixed below the rate on short-term government securities and the discount rate.)
      4. What effect would these interest payments have on the money multiplier? (For simplicity, assume there is only one type of deposit in existence.)
      5. It is sometimes said that payment of interest on reserves would strengthen Fed control over the money stock. Can you justify or refute this view?

 

Source: Irwin Collier.

Image Source: MIT Museum.