QUIZ #1 (Suggested Solution): Fall 1997 (10/15/97)

Answer any 6 of 8 questions (30 points)
[Note: each question worths five points. If you answered more than six questions, we graded only the first six in the order that you answered them.]

Question 1. FALSE.
It is the sum of final sales, or equivalently of value-added. Adding "ALL business sales" would involve double-counting (intermediate inputs, and used goods). Remember that GDP is the value of FINAL goods and services produced in the economy during a given year.

Question 2. TRUE
This question was about OKUN's law, which shows that when GDP growth is high, unemployment falls and when GDP growth is low or negative, unemployment rises (Blanchard, pp. 27-28)
It does not necessary imply that the unemployment level is low, when GDP is high or when GDP growth is higher than average. Okun's law shows that there is a EMPIRICAL relationship between CHANGES in GDP and CHANGES in unemployment.

Question 3. FALSE
First of all, fluctuations in investment are as important as fluctuations in consumption. Second, only part of the fluctuation in consumption is due to changes in confidence - part is due to changes in wealth or current income. Even though, consumption represents close to 70% of GDP, it is much smoother than investment, which is much more volatile. (See Blanchard Ch 8. Volatility of Consumption and Investment pp.159-161)

Question 4. FALSE
This was about the "Paradox of thrift". When the savings rate, (1-c1), goes up, the marginal propensity to consume, c1, goes down. This means that, consumption goes down and so do output and income, therefore, investment and private savings end up being lower (this is just looking at the goods market). Some of you, recognized that in the general IS-LM model, a lower c1, implies that the IS shifts down (the slope also changes), this results in a lower equilibrium output and interest rates. The resulting effect on investment would be then ambiguous. The fact that investment is equal to private plus public savings (I=S+(T-G)) does not imply that an increase in the savings RATE (not level of savings, private or public) will translate into a higher level of investment.

Question 5. FALSE
This question was about CREATING money, not controlling the money supply! The central Bank creates the monetary base only, which consists of currency and reserves, H = CU + R. The actual money supply, M, includes checkable deposits and currency. The former are created in the commercial banking system. The minimal reserve requirement induces an upper bound for the creation of deposits. In the simple model presented in the book M = ( 1+c ) / ( c + theta) * H.

Note: When foreigners change foreign against domestic currency, H might be extended against the central Bank's will, but the currency is still created by the Central Bank.

Question 6. FALSE
Reducing the Budget Deficit means either raising T or lowering G. Both are contractionary and lead to lower demand and therefore lower equilibrium output. The Is curve shifts left. There is no way you can decrease T-G without a contraction effect.
However, a.) The contraction could be offset by a monetary expansion, shifting the LM curve to the right and resulting in higher output and lower interest rates. or
b.) The deficit reduction could increase consumers' confidence or could make them revise their expectations of future interest rates downwards, increasing Permanent Income and the PDV of investments and hence, shifting the IS back to the right.
So, Budget Deficit reduction does not necessarily lead to a contraction of output.

Question 7. TRUE
Investments depends on the real interest rate, the demand for money on the nominal interest rate, i= r + expected inflation. So, for every y, the real interest rate r at which i gives Money Market equilibrium is decreased 1-1 by the increase in expected inflation. So, the LM curve in ( r,Y) space is shifted down by the same amount. So, we obtain a new equilibrium with higher output and lower real interest rates. I = I ( r, Y), where r enters with a negative and Y with a positive derivative, so I goes up.

Note: No Dynamics Story was necessary here.

Question 8. FALSE
By the Permanent Income Hypothesis, the perfectly rational consumer should choose his consumption in period t only as a function of the PDV at time t of his total wealth. So, changes in current income would have only a small impact on current consumption.
However, there are several instances where current consumption should be by far more significant. Those that come to mind first are

Note: The fact that you might plan different levels of consumption at different stages of your life does not contradict the PIH.

PART B: TWO SHORT QUESTIONS (15 points each)

Question 1

(a). The package consists of a fiscal contraction and a monetary expansion. As a result, IS shifts down left and LM shifts down to the right. Final effect is that interest rate goes down, and output is in principle ambiguous. The most correct answer is that output will stay more or less constant or decrease, because the fed remains vigilant to inflation, but we accepted as correct the other options as long as your answer is consistent..

(b). Effect on investment: interest rate decreases means investment goes up. Regarding output, if said output constant then nothing else happens. if it goes down, investment goes down to so final effect is ambiguous.
Consumption goes down because T increase. If output constant nothing else happens. If output decreases C decreases too.
Unemployment varies negatively with output. If output constant U constant too.

(c). Short interest rates fall today and in the future, thus long term interest rates fall too. Therefore the prices of bonds go up (Price = $Z / (1+i)
Stock prices can decline if Y suffers a substantial decline, this is so because Y affects the size of dividends. Otherwise the price of the stock will rise due to a lower discount factor for future dividends (i.e. due to a lower i).

(d). This policy will reduce expected interest rates, therefore long term interest rates are reduced (remember the yield curve), thus prices of bonds today increase.
It is probably that the stock price will increase today, due to the lower future interest rates. But it could be the case that the increase in future taxes decreases future income, causing lower future dividends. Thus, the effect today is uncertain.
One point here, the policy is expected tomorrow, so tomorrow there won't be any change in prices (given no additional news in the future). But the announcement of the policy is today and it was not expected, that is reason why today we do have a change in the prices of bonds and stocks.

Question 2
[Note: Each part worths five points]

(a). The CPI is the price of purchasing a fixed basket of goods. It takes a group of goods that represents the consumption of the average urban dweller (done by surveys, not randomly neither theoretically) and get the price for that basket each year and compare it to the prices of that same basket in a base year.

(b). Basically there are 4 biases:

  1. Quality bias: Goods get better (this includes bigger apartments, better cars, better computers, etc.) and this will increase their price. However that doesn't mean that the cost of living is increasing. Nevertheless , CPI would take this as an increase in the cost of living. Moreover, things can get better, but prices don't change at all. Therefore the "true" price is decreasing, but CPI would imply that cost of living is not changing.
  2. Substitution bias: CPI won't take into account that people may substitute between goods if the price of one good increases relative to others. In this case CPI don't take into account this change in the basket. Therefore, it will imply that the cost of living has increased. However, in reality the cost of living is not going to increase proportional to the price change or increase at all, because people consume cheaper things. This substitution bias includes the fact that when import prices increase, people shift to national products
  3. Discount Stores bias: CPI does not consider the fact that people are increasingly going to Discount Stores. Since CPI is based mainly on retail stores, CPI won't consider the decrease in the cost of living that represents getting goods from Discount Stores.
  4. New goods bias: CPI does not take into account that there are new goods around. Usually the price of these new goods decreases after introduced, implying that the cost of living is decreasing, but CPI won't account this because the goods are not in their basket. An example is cellular phones: when they were introduced they cost around US$ 300 and now they come for free when you get a line. This price decrease is not in the CPI.
Note: the question was asking reasons for believing that the CPI OVERSTATES the true rate of inflation. So, there maybe some facts that make the CPI misstates the true rate of inflation but not necessarily overstates it. Examples: change of preferences, etc. Also, the question was not asking to compare CPI with the GDP deflator.

(c). This question was about prices (CPI), not consumption, income or standard of living.

The main idea was to check how the different biases on the CPI affect both groups. Some possible answers:

Yuppies are more affected by the quality bias, meaning that their true CPI is lower than the actual CPI. This would imply that the true inflation rate for them is lower than the true CPI for the welfare people.

Welfare people are more likely to do bargain hunting and shopping at discount stores, meaning that their true CPI is lower than the actual CPI. This would imply that the true inflation rate for them is lower than the true CPI for the yuppies. But as some people argue, only well-off people can pay fees or have cars to go to this stores, so the answer can be the other way around.

Some people argue that since yuppies don't care about the price they paid, merchants can increase the price of the goods yuppies consume freely, while if they increase it to the poor people they will go an substitute goods. This question gives a good answer about the price LEVEL of the goods for the yuppies (i.e. Designer's jeans vs. Outlet jeans). Therefore, you have to give a good answer to explain why the GROWTH has been higher.

Finally, you can't use the behavior of prices in the last years as an evidence for your argument without considering the biases present there. For example, you can't say that the increase in the price of the goods that the yuppies implies that their true CPI has been increasing, because we already know that the quality bias is present there.

[Note: each question worths five points]

1. The IS relation represents the goods market equilibrium, which states that in equilibrium, supply (production, output, Y) must be equal to demand (Z).

From the given model, we can write the IS relation as follows:

Y = Z = C + I + G = c0 + c1*(Y-T) + d0 + d1*Y + d2*i + G.
Thus, we can rewrite the relation as a function of Y.
Y = [1/(1-c1-d1)] * [c0 - c1*T + d0 - d2*i + G]
or, as a function of i,
i = [(c0+d0+G-c1*T)/d2] * [(c1+d1-1)/d2]*Y
Therefore, the slope for IS curve is (c1+d1-1)/d2, which has negative value as expected.

2. The LM relation represents the financial market equilibrium, which states that in equilibrium, money supply(Ms) is equal to money demand(Md).

From the given equation, the LM relation is

Md = Ms = M = k*Y - h*i
To find the slope for the LM curve, write in term of i.
i = (k/h)*Y - (M/h).
Therefore, the slope for LM curve is k/h, which has positive value as expected.

[Note: in this question, we ask for the expression of LM relation, which represents the combination of Y and i, in which the financial market is in the equilibrium. Thus, it is inappropriate to substitute for Y into the LM relation, since it will simply give us a single point, and not entire LM relation.

3. To derive the overall expression of Y from the two relations above, simply substitute the expression of i (from LM relation) into IS relation.

Then, we get equilibrium Y = {1/[1-c1-d1+(d2*k/h)]} * [c0+d0+G-c1T+(d2*M/h)].

[Note: this equation expresses Y as a function of all exogenous variables in the model (i.e. G,M,T) along with relevant parameters. Since i is an endogenous variable, we need to substitute for it in the above equation.]

4. In this model, decrease in consumer confidence can be represented by an increase in either c0 (autonomous consumption), or c1 (marginal propensity to consume).

As a result of this decrease, consumption will decline, leading to lower demand, and thus output. Decline in demand and output will be reflected in the IS-LM model through the shift of IS curve to the left, while LM curve stays the same. This results in lower output level and lower interest rate than the initial level.

The composition of GDP will be affected as follows:

5. The responsiveness of money demand to interest rate is h in this model. Show in graph or in algebra that a high h leads to flat LM curve and a low h leads to steeper LM curve. A flat LM curve means that monetary policy will affect output less effectively than fiscal policy, therefore less "important". A steep LM curve means that fiscal policy is less effective than monetary policy in influencing output change.

6. The multipler in this is 1/(1-c1-d1+(d2*K/h)).

The multiplier is IS-only world is 1/(1-c1-d1), which we know is definitely greater than one given c1+d1 <1. The multiplier effect works here because a rise in Y leads to c1 increase in consumption and d1 increase in investment, while the increases in consumption and investment will further increases Y. We all know this well.

However, the multiplier in IS-LM world can be less than 1 because rising Y leads to rising i(which is because i=(k/h)Y-(M/h)), crowding out investment (as I is negatively related to i).

Updated 15-Oct-97 at 18:00 EDT by ythai@mit.edu