Written Comprehensive Exam in Economics, 1998

Instructions:

This part of the written comprehensive exam in Economics is divided into two parts, macro and micro, which are given equal weight in your final Economics comprehensive grade.

Answer each part in a separate bluebook. Be sure to put your identification number on each bluebook. In addition, put "Micro" on the cover of the bluebook containing the micro part and "Macro" on the other bluebook.

Your answers should include appropriate verbal, graphical, and mathematical reasoning. Please number each answer in your bluebook and write coherently and legibly.

Remember, the Macro and Micro sections are equally weighted, so you should allocate your time efficiently. Do NOT spend too much time on one part of the exam or on one question. If you can't get it, MOVE ON!

Use the 30 minute reading period to read the entire exam carefully, underlining important information. You may write notes on the exam but we will only evaluate answers in the blue book.

You have until 12:00 PM to complete the exam. Good luck.

Instructions:Be sure to label your answer to the sections of the exam; e.g., "Part I: Section A". Label the axes and curves on your graphs.

Part I: Computation of the General Equilibrium Assuming Stable Asset and Product Demands

Instructions:If you are unable to numerically derive and solve the problem, be sure to verbally explain the logical relationships and graphically derive the relationships.

Section A: Constant Price Case

Based on the following behavioral assumptions and assuming the price level is constant (the aggregate supply curve, S(P), is horizontal at P (price level) =2), calculate the following (that is derive the equations for each curve based on the following relationships and solve for the interest rate and output) :
a. The IS curve
b. The LM curve
c. The General Equilibrium Interest Rate
d. The General Equilibrium Output Level

C =600 + .8XD; (consumption expenditures on goods)
I = 2000 - 280r; (investment expenditures on goods)
G = 350; (government expenditures on goods)
NX = -150; (net exports of goods)
XD = X - T; ( disposable income; assume transfer payments (R) are zero and that taxes are proportional to income; the income tax rate is .1.)
T = .1X; (Total taxes)
M = 1800; (supply of nominal money balances)
L = 200 + .1X - 5r; (demand for real money balances.

where X = total output; r = interest rate; and P = price level (P=2).

Section B: Varying Price Case

First sketch the results from Section A. Use a stacked pair of graphs with a figure of IS/LM curves vertically above a second figure with aggregate demand, D(P), and aggregate supply, S(P), below the IS/LM figure.

Now briefly explain and graphically illustrate how the general equilibrium result would differ from the results in Section A if the economy were characterized by shortrun stickiness of wages and errors in forecasting the price level. Assume that the natural rate of output is 7500 and that the expected inflation rate is zero. Part II: Analysis of Macroequilibrium under Unstable Demands and Constant Prices

In this part assume that the price level is constant.

Section A. Analysis of the Implications of Unstable Financial Asset Demands

Economists in the Federal Reserve system have argued that in the early 1990s the demand for key financial assets, especially the demand for money, was unstable. They argued that, given the level of interest rates and income, the quantity of money demand was different from that forecasted on the basis of historical data. Explain and illustrate general equilibrium consequences for interest rates and output of an unstable demand for money balances assuming the Fed keeps the supply of nominal balances constant. Include two figures: (1) demand and supply for money balances and (2) IS/LM curves. Assume for simplicity that a third of the time the demand for money balances is unusually high; a third of the time the demand for money balances is unusually low; and a third of the time the demand for money balances is midway between the other two cases.

Section B. Analysis of the Implications of Unstable Demand for Investment Goods

Some economists claim that investment demand is unstable. Investment is the process of adding to the capital stock, e.g. additions to plant and equipment. Explain and illustrate the consequences for general equilibrium interest rates and output of an unstable investment demand assuming the Fed keeps the supply of nominal balances constant. Include two figures: (1) investment demand ( I vs interest rate), and (2) IS/LM curves. Assume for simplicity that a third of the time the investment demand is unusually high; a third of the time the investment demand is unusually low; and a third of the time the investment demand is midway between the other two cases.

Section C. Analysis of the Optimal Monetary Target

Analysts have advocated two basic strategies for the Fed to follow in attempting to steer the economy on a smooth path. One is that the Fed target the money supply and permit interest rates to vary as private demands vary. The second is to select an interest rate target and vary the nominal money supply as needed to achieve the interest rate target.

Policy #1: The Fed keeps the supply of money balances constant at a level such that when both the demand for money and investment demand are at their intermediate levels, output is at the natural rate of X* and the interest rate is r*. This is the exercise you performed in Section A; you can reproduce that graph here.

Policy #2: The Fed targets the interest rate and varies the money supply such that the interest rate is always at r*.

(Please see the next page for the question itself.)
Compare and contrast the effects of these two alternative Fed policies on the range of output under circumstances in which the demand for money is unstable: one third of the time unusually high, on third of the time at an intermediate level (the level predicted by the Fed) and one third of the time unusually low money demand. You may assume product market demands are stable. Use IS/LM curves to illustrate your answer. Show the two policies on the same figure in order to compare results.

Under which policy does output vary more?

Part III

In a few sentences, explain how the analysis in Section C of Part II would differ if an aggregate supply that is positively related to the price level were included.

Instructions:

There are 8 questions with clearly labelled point values. The question itself is bolded and italicized.

Answer each question in your Micro Essay blue book. Carefully number each answer in your blue book.

The questions are designed to be answered with a graph and a few sentences of explanation. Do not spend too much time on any particular question!

The exam seems long, but that is because we have many graphs, a great deal of explanatory text, and we have given you numerous hints. Work your way through each question patiently and systematically .

Introduction:

The Micro Essay part of the 1998 Economics Comprehensive Exam will test your knowledge of microeconomic theory by asking a series of questions about saving decisions made by individuals. We will be analyzing the effects of Social Security and the implications of newly passed legislation called the Roth IRA.

A Microeconomic Analysis of Saving:

Before we examine Social Security and the Roth IRA, we must ask the more fundamental question of why individuals save at all!

The question is:

The answer, obviously, is because saving increases satisfaction by shifting consumption from the present to the future. Saving, and its flip-side, borrowing, is nothing more than a re-allocation of income. Because the basic question is how to optimally allocate a scarce resource (income) across various alternatives (time periods), we can apply the principles of optimization and comparative statics that are embodied in the Economic Approach.
As you know, optimization problems have three parts:

1) Goal (or objective function)
2) Endogenous (or choice) variables
3) Exogenous (or given) variables

In a model of saving behavior, the goal is to maximize satisfaction from the consumption of goods and services during one's lifetime. The choice variables are the amounts of consumption in each time period. Each individual can choose how much to consume in each period. If you choose to consume less than you earn early in life, you are a saver and you will be able to consume more than you earn later in your life. The exogenous variables in this model will include: your income in each period, the interest rate, and your preferences for present and future consumption.

Instead of a complicated many period model, let's analyze saving with a simplified two period model. Suppose an individual chooses how much of a composite good, C, to consume in each of two time periods, called Working and Retired. We denote the amount of consumption in each period by CWorking and CRetired. The individual gets satisfaction (or utility) from consumption in each period which can be represented by an indifference map. The individual has an initial endowment of income in each period with which to purchase the composite good (assumed, for simplicity, to have a constant price=$1/unit in both periods). The individual's incomes in periods Working and Retired are denoted by MWorking and MRetired. Finally, the consumer can borrow or save money at some interest rate, r. (This is another simplifying assumption since the borrowing interest rate is typically higher than the interest rate for saving.)

Having set up the problem by examining the goal, endogenous, and exogenous variables, we can now turn to finding the initial solution. Since the individual's choices are constrained by the amount of income available, we are faced with a constrained optimization problem. These problems are solved by considering the constraint, the goal, and then combing the two parts to find the solution.

The Constraint:
The budget constraint for the individual is that total consumption cannot exceed total income. At first blush, we might write:
CWorking + CRetired # MWorking + MRetired

Assuming income is completely exhausted (so we can get rid of the "less than" part of the inequality) and rewriting the budget constraint, we get:
CRetired = MWorking - CWorking + MRetired

If MWorking - CWorking is positive, then the individual saved some income for consumption during the Retired period.

A complicating factor is that leftover or saved income in the Working period cannot be simply added to MRetired because the saved income and Retired income come in different time periods. If you save some income in the Working period (MWorking - CWorking > 0), then you'll have the amount you saved PLUS THE INTEREST EARNED ON YOUR SAVINGS in the Retired period.

Thus, taking into account the time the income is generated, the correct equation for the budget constraint becomes:

CRetired = (MWorking - CWorking) + r(MWorking - CWorking) + MRetired

Reorganizing terms a bit, we get:

CRetired = MRetired + (1 + r)(MWorking - CWorking)

The equation above says that the Consumption in the Retired period will equal the income in the Retired period (MRetired) plus the value of the savings in the Retired period ( (1 + r)(MWorking - CWorking)).

A graph of the budget constraint looks like this:

The Constraint

The person above has reallocated some of income earned in working period toward the retired period by saving (MWorking - CWorking > 0). Notice that the length of the Amount Saved distance is LESS THAN the height of the distance CRetired - MRetired Ð that's because there's interest earned on savings. Interest (earned or paid) makes the slope of the budget constraint equal to minus (1+r).

Goal:
The important point about borrowing (i.e., consuming more than your income in the Working period) and saving (i.e., consuming less than your income in the Working period) is that these moves are done in order to increase satisfaction. The individual has given tastes and preferences which establish an indifference map that looks like this:

The Goal

Finding the Initial Solution
By superimposing the constraint and the goal, the optimal solution is revealed. The figure below shows a situation in which the individual is a saver:

A Saver's Initial Optimal Solution

QUESTION 1: A Borrower instead of a Saver

(10 PTS)Draw a graph of an individual who is a BORROWER. Indicate the amount borrowed.
Carefully label all axes, curves, and points.

QUESTION 2: Mathematics

(15 PTS) The problem below has been set up for you. Find the optimal levels of Consumption in the Working and Retired periods (C*Working and C*Retired) and the optimal amount of saving (Saving*).

YOU SHOULD FIND THAT THE INDIVIDUAL IN THE PROBLEM ABOVE WILL SAVE $10,000, WHICH MEANS THE OTHER ANSWERS ARE NICE, ROUND NUMBERS ALSO!

YOU GET CREDIT FOR YOUR WORK, NOT THE ANSWER ITSELF! SHOW YOUR WORK SO YOU CAN EARN PARTIAL CREDIT.

 

DO NOT SPEND TO MUCH TIME ON THIS QUESTION. IF YOU CAN'T GET IT, MOVE ON!

 

But an important public policy issue arises if you have reason to believe that this amount of saving is not enough. In fact, Social Security was designed to fix the problem of too little saving. While working, individuals are required to pay taxes to support payments to retired workers. In essence, Social Security is a forced saving scheme.

QUESTION 3: SOCIAL SECURITY

(10 PTS)The graph below shows the individual of Question 2 being forced to save $20,000 for retirement (and we assume for simplicity that the savings will earn 10% and that you cannot borrow against your Social Security payments).

Social Security as a means to increase Saving

Many economists dislike the Social Security system as a means of increasing savings for retirement. Using the graph above, what is the argument against Social Security?

 

Another way to increase savings is to make saving during the working period more attractive. In 1997, tax legislation was passed that introduced the Roth Individual Retirement Account. In essence, the Roth IRA allows individuals who save (with after-tax dollars) to never pay tax on the income generated by their savings. Thus, $1000 saved today may grow to $8000 in 20 years and all of the money would go to the individual, tax free.

For our purposes, in terms of the optimization problem, the Roth IRA legislation is an exogenous increase in the effective interest rate earned by savers. It is an attempt by Congress to encourage, but not require (like Social Security), more saving. The big question, of course, is "By how much, if any, will saving increase when the interest rate for saving is increased?"

QUESTION 4: COMPARATIVE STATICSÐTHE RESPONSIVENESS OF SAVINGS TO CHANGES IN THE INTEREST RATE

If the interest rate changes, the budget constraint will rotate around the initial endowment -- the budget constraint WILL NOT pivot around the y-intercept as in the "conventional" model.

(20 PTS)Given this bit of information, show how the optimal amount of saving changes as the interest rate on savings increases.

Optimal saving may increase, decrease, or stay the same depending on how you draw the indifference curves. You may show any one of these three cases.

QUESTION 5: ELASTICITYÐTHE RESPONSIVENESS OF SAVINGS TO CHANGES IN THE INTEREST RATE

(5 PTS) 5A) In answering question 4, what elasticity are you exploring?
(HINT: We want an answer in the familiar "blank elasticity of blank" form.)

(5 PTS) 5B) Given the particular way you drew your graph in answering question 4, what is the sign and approximate magnitude of the elasticity?

(HINT: For magnitude, we want a number that roughly corresponds to the picture you have drawn for question 4. No calculation is needed.)

While working on this problem, you have seen that optimal saving depends upon the interest rate. It also depends on the initial endowment of income (MWorking and MRetired) and the individual's tastes and preferences for present and future consumption. Suppose an econometrician ran a regression to determine the responsiveness of saving to interest rates. Assume (for the sake of argument) that all of the requirements of the Classical Linear Model were satisfied. In particular, let's assume that tastes and preferences are not correlated with the included independent variables in the regression. The econometrician estimated the following model:

Suppose that higher income workers, in general, have access to higher interest rates on savings. The regression results look like this:

QUESTION 6: INTERPRET THE COEFFICIENT ESTIMATE

(15 PTS) What does the 5,802 coefficient on the interest rate variable mean? In other words, how is this number used or interpreted?

QUESTION 7: UNDERSTANDING MULTIPLE REGRESSION

(10 PTS) If we're interested in estimating the effect of the interest rate on savings behavior, why would we include MWorking and MRetired in the regression? Why not just estimate savings as a function of the interest rate alone?
A FEW SENTENCES OF EXPLANATION ARE REQUIRED HERE.

QUESTION 8: PUBLIC POLICY DECISION

(10 PTS) Assume the model and coefficients are correct. Assume that President Clinton has said that we want to "substantially increase savings" (from the $10,210 average). Assume the CEA has calculated that the Roth IRA will increase the effective interest rate on savings by 0.02 (2 percentage points). Rep. Dick Gephardt says, "My people tell me the Roth IRA is foolproof. The coefficient on the interest rate is highly statistically significant and therefore we will see a LARGE increase in savings." Is this correct? Why or why not?