1. Updated slides have been posted.
2. Quiz 2 will cover all of Chapter 4, and Chapter 5 up to page 104 (i.e., short-selling, forward price for an asset with no income and forward price for an asset with a known income).
3. HW for next week includes 4.25, 5,23 and 5.24 (give it your best shot, anyway). We’ll go over it in class next week.
4. I will be having office hours next week before class. Which means I’ll be there at 5pm if you have any questions.

1. For the quiz tomorrow (Quiz 1), you are only responsible for Chapters 1 to 3. You are not responsible for Chapter 4. We have not covered it in class, yet. For future reference: You will rarely (if ever) be held responsible for something that I have not explicitly covered in class.
2. I will be going over how to trade on OptionsXpress in class tomorrow. If you haven’t figured it out yet, don’t worry. A week here or there will not affect your grade. I am more interested in your trading philosophy than whether you trade for 8 weeks or 7.
3. For tomorrow’s HW, you only need to do the Chapter 3 problems (see #1 above).

In class tomorrow, I will be doing a pre-quiz review, going over the Chapter 3 HW problems, and then we’ll have the quiz, and move on the Chapter 4. This is in addition to the pre-class question-answer session at 5pm, which is not compulsory. Show up if you can, and if you have questions.

A professor of global health at Sweden’s Karolinska Institute, his current work focuses on dispelling common myths about the so-called developing world, which (he points out) is no longer worlds away from the west.

…

Rosling’s presentations are grounded in solid statistics (often drawn from United Nations data), illustrated by the visualization software he developed. The animations transform development statistics into moving bubbles and flowing curves that make global trends clear, intuitive and even playful. During his legendary presentations, Rosling takes this one step farther, narrating the animations with a sportscaster’s flair.

Rosling developed the breakthrough software behind his visualizations through his nonprofit Gapminder, founded with his son and daughter-in-law. The free software — which can be loaded with any data — was purchased by Google in March 2007. (Rosling met the Google founders at TED.) [link]

Enjoy.

To that end, I’ve edited the necessary slides in Lecture #5. I’ve also written up a short handout and using an example of a European price increase, illustrated how we get to what is “foreign” and what is “home” when it comes to calculating the real exchange rate from the nominal exchange rate. Please see the ‘Handouts’ section on the right.

For the sake of the exam, I think it’s important for you to qualitatively understand what happens where, and which currency becomes more expensive and less expensive, rather than focusing specifically on what is “home” and what is “foreign.” Nevertheless, if this is something that’s in your head, nagging you, as it has been for me, then read my write-up.

I also dredged up a handout that’s written by an IMF economist (Luis A. V. Catão) about the basics of the real exchange rate and purchasing power parity (PPP). We’ll soon be talking about PPP, so it won’t hurt to take a look at what Catão has written up. He starts by questioning: How do we value a currency?

George Soros had the answer once—in 1992—when he successfully bet $1 billion against the pound sterling, in what turned out to be the beginning of a new era in large-scale currency speculation. Under assault by Soros and other speculators, who believed that the pound was overvalued, the British currency crashed, in turn forcing the United Kingdom’s dramatic exit from the European Exchange Rate Mechanism (ERM), the precursor to the common European currency, the euro, to which it never returned.

This is, of course, not the best way to value a currency, but certainly a great way to make a point (so long as you have $1b to make bets against currencies). So Catão introduces a RER index which he calls the real effective exchange rate or the REER, which is defined as follows:

The REER is an average of the bilateral RERs between the country and each of its trading partners, weighted by the respective trade shares of each partner. Being an average, a country’s REER may be in “equilibrium” (display no overall misalignment) when its currency is overvalued relative to that of one or more trading partners so long as it is undervalued relative to others.

This is one way to measure whether purchasing power parity exists, and if it doesn’t, the direction that the nominal rates will move to adjust towards it. It’s important to remember that, as long as markets are free, nominal rates will move towards purchasing power parity. This goes back to the example of Kenyan coffee that I had talked about in class. If coffee is cheaper in real terms in Kenya than it is in the US, ignoring transportation and other costs, people (or arbitrageurs) will buy coffee en masse from Kenya and sell it in the US, driving coffee prices up in Kenya, and down in the US, so that PPP will ultimately exist between Kenyan coffee and US coffee .

This also forces us to think about the real exchange rate not just as the nominal rate without inflation, but as a measure of PPP. More on this when we get to revisit exchange rates in our flexible-price model. At that point, we can also take a look at The Economist‘s Big Mac Index.

While this is all fun stuff, I don’t know about you, but I suddenly feel like having a burger and some coffee…

1. Potential output
2. Labor market equilibrium (using the marginal propensity of labor)
3. The consumption function (and the marginal propensity to consume)
4. The investment function (and the sensitivity of investment to interest rates)
5. Government spending (particularly, transfer payments)
6. Net exports (and their sensitivity to foreign GDP, domestic GDP and exchange rates)

There was one aspect of exchange rates that we yet had to cover: The relationship of exchange rates to interest rate differentials between domestic and foreign rates. To motivate the understanding of this relationship, consider the highly liquid and highly volatile foreign exchange market. You have speculators betting on all aspects of foreign exchange. They operate based on two conditions:

1. r^f > r: That is, the foreign (be it any country) real interest rate is greater than the one in the US. If this is the case, then bonds abroad pay a higher return than bonds at home. And that leads to these speculators taking their money out of the US and putting it into foreign currency-denominated bonds abroad. This, in turn, affects the exchange rate, because if they are taking their money out of the US and investing it abroad, they will be selling dollars to buy the foreign currency. And a selling of any commodity means a reduction in its price, so the price of dollars decreases, and the dollar depreciates (and the real exchange rate will rise).
2. r > r^f: That is, the US real interest rate is greater than the foreign (any country) rate. In this case, speculators will take their money out of bonds in other countries and sell those currencies to buy dollars, so that they can buy US, dollar-denominated bonds. Buying more dollars, means that the price of dollars increases, and so the dollar will appreciate (and the real exchange rate will fall).

The relationship between the real exchange rate and the differential of the foreign real interest rate and the domestic real interest rate, can be summed up by this equation: ε = ε₀ – ε_r[r - r^f]

Thus, an increase in the foreign rate will cause the exchange rate to increase which is a currency depreciation. And an increase in the domestic rate will cause the exchange rate to decrease which is a currency appreciation.

With this, we conclude our understanding of the building blocks of the flexible price model. Now let’s go on to Chapter 7, where we’ll see everything put together.

First off, there are two approaches to understanding how the economy gets into equilibrium:

1. Flow-of-output approach: This has to do with looking at the aggregate demand, which is the sum of the components of total spending, or C + I + G + NX. When the aggregate demand equals the aggregate supply, which is nothing but our output, Y, the economy is in equilibrium. Remember though, that output is at its potential output level, so Y = Y*.
2. Flow-of-funds approach: This has to do with looking at the market for loanable funds or the markets in which funds are borrowed and lent out. The funds that are lent out from lending institutions like banks, are put there by via savings from households, the government and foreign lenders. These funds are then borrowed by businesses to be invested into the economy, to increase production, and create profits. When the supply of funds that comes from savings, is equal to the demand for funds that comes from businesses wanting to invest, the economy is in equilibrium.

Flow-of-Output Approach
This approach has to do with aggregate demand: AD = C + I + G + NX.

The aggregate supply is nothing but the output or production, which is denoted by Y. But since we assume flexible-prices, the output is always at its potential output level and Y = Y*.

When the economy is in equilibrium, Y = Y* = AD = C + I + G + NX, or to put it simply: AD = Y*.

This is the flow-of-output approach and, as we will see shortly, it is the real interest rate, r that equilibrates aggregate demand with aggregate supply.

Flow-of-Funds Approach
Savings have three components:

1. Household savings, S^H (is positive when Y – T – C > 0)
2. Governmental savings, S^G (is positive when T – G > 0)
3. Foreign savings, S^F (is positive when IM – GX > 0, or when -NX > 0)

When the economy is in equilibrium, S^H + S^G + S^F = I, or investment.

In the market for loanable funds, the price of borrowing is the real interest rate r and that is what equilibrates savings with investment.

Common factor: Real Interest Rate
The common factor, r, can be seen more clearly if we do a little algebraic manipulation:

Assume that all markets are in equilibrium, so by the flow-of-output approach, we see that

Y* = C + I + G + NX

Now take everything on the left-hand side, but leave investment (I) on the right-hand side, to get:

Y* – C – G – NX = I

Now add and subtract taxes, T, on the left-hand-side:

Y* – T – C + T – G – NX = I

Now group the terms on the left-hand side:

(Y*-T-C) + (T-G) + (-NX) = I

But (Y*-T-C) is S^H, T-G is S^G and -NX is S^F. So when the markets are in equilibrium via the Flow-of-Output approach, they are also in equilibrium via the Flow-of-Funds approach. The important result from all of this is: The two approaches are equivalent.

This is where we stopped. We’ll pick up again in the next class.

Based on my crude analysis, and the information from the Economist that:

In America politicians and central bankers are focusing on policy stimulus. The Federal Reserve has cut short-term interest rates by 1.25 percentage points in recent weeks, to 3%. [link]

We can actually calculate the change in investment that would result from the decrease in real rates. Firstly, the rate the the Fed controls is not the lending rate. We can use the Prime Lending Rate instead. But is that related to the Fed Funds Rate? Take a look.

There is a clear correlation, and I am assuming that the prime rate = fed rate + 2.5%. In fact, the above figure also shows the relationship between investment (the green line) and the Fed Funds rate (the red line). Based on my crude analysis, my assumption that prime rate = fed rate + 2.5%, we can assume that if the fed decreases rates from 4.25% to 3%, the prime rate will go down from 6.75% to 5.5%. And given this information, we can conclude that investment will increase from $6,331.36b to $6,332.41b, a total increase of $1.05 billion.

Government Spending
We finally got to looking at government spending today. The key fact about government spending that we must take into account is that of transfer payments. These are the payments that are made by the government to the people – like social security, Medicare, etc. We view them as negative taxes. Other than this, we don’t look too deeply into how the government spends its money.

Finally, we look at the last component of GDP – that of net exports. Now, we know that net exports are gross exports minus imports. In mathematical terms, NX = GX – IM. We look at each of the components of net exports individually.

Gross Exports
We assume that gross exports are affected by two main factors: (1) the real exchange rate, and; (2) the level of income in the foreign country (or foreign GDP). To understand this better, let’s take a closer look at the relationship of both of these factors with gross exports. A cursory search on the Census Bureau’s website will reveal that the country that did the most trade with the US in 2007 was Canada ($44.23b) [1]. Looking at data on Canada, we first see how the real exchange rate affects net exports from the US.

For this graph, I took the values of gross exports and real exchange rate (1974-2004) from the BEA website, and added a trend-line to the data. The relationship is clearly positive. We call the slope of this line the factor by which exports are effected by exchange rates – it can be viewed as the marginal propensity to export based on the real exchange rate. For this graph, the value is $4,903m. That is, for each dollar increase in the real exchange rate, exports will increase by $4,903 million.

Next, we take a look at the relationship that the Canadian GDP per capita has on exports to Canada from the US.

As you might expect an increase in the real GDP per capita, will cause an increase in the gross exports to that country. The data here is once again from 1974-2004, and the slope of the trend-line is positive, indicating the positive relationship between these two. The marginal propensity to export based on the GDP per capita is $5,973 million. That is, for each dollar increase in the Canadian real GDP per capita, exports will increase by $5,973 million.

In sum, we add the two factors together, to get the following relationship between gross exports, the real exchange rate and foreign GDP.

Here, X_f is the marginal propensity to export based on the foreign GDP, and X_? is the marginal propensity to export based on the real exchange rate.

Imports
To examine this relationship, we start out by assuming that imports depend on the home (or domestic) GDP, and the real exchange rate. However, as the real exchange rate increases, the imports decrease, and vice versa. So, given enough time, imports will adjust to changes in the exchange rate, and we assume that the total dollar value of imports will remain constant. Thus, the real exchange rate does not affect imports. Finally, we just assume that imports are a constant proportion of the domestic GDP: IM = IM_y Y

To see this, we look at overall imports into the US, and the domestic GDP.

The slope of the trend-line is $119.2 billion. This means that for each billion dollar increase in real GDP, imports will increase by $119.2 billion. This stands to reason – as we get richer, we will buy more from abroad.

Net Exports
Now, if we put everything together, we can say something about net exports.

So, we know that NX = GX – IM.

And also that GX = X_f Y^f + X_ε ε

And also that IM = IM_y Y

Putting everything together, we get that NX = X_f Y^f + X_ε ε – IM_y Y

Thus, we can say that net exports depend on three things:

1. Foreign GDP
2. Domestic GDP
3. Real Exchange Rates

Although I did talk a little bit about exchange rates and the effects of foreign exchange trading on exchange rates, we will revisit that in the next class.

There are two ways in which economists categorize investments:

1. Net vs. gross
2. By use

For the Net vs. Gross categorization, we differentiate between net investment and gross investment. And, essentially, net investment = gross investment – depreciation. So this type of categorization is useful when we are examining the value of investment in new capital and not including the costs of that result from wear-and-tear.

When we categorize investment by use, we distinguish between the different places that investment money is going, in the macroeconomy. The NIPA categorizes broadly as: (1) Fixed investment (in durables); (2) Residential construction; (2) Non-residential construction and; (3) Changes in business inventories.

Getting into either of those categorizations in more detail would be more appropriate for an accounting course. We’ll stick to that superficial categorization. What we are really concerned with, is what causes changes in overall investment. That can be summed up broadly into two areas:

1. “Animal spirits”
2. Real interest rates

The “animal spirits” are the same sort of thing that affect the stock market: optimism results in more investment, pessimism in less. Future expectations of wealth lead to increased investment, and if you expect wealth to decrease, your investment will decrease.

Real interest rates affect investments differently, and the relationship is inverse – that is, a higher rate leads to lower investment, and a lower rate will spur investment. One way to remember this is to think of the interest rate as a rate that your bank offers for CDs. If the interest rate increases, you (as a manager of a firm) would prefer to invest in the bank than in an asset. Conversely, if the interest rate decreases, you (as the manager of a firm) would prefer to invest in an asset than in the bank. This is another thing that the stock market and investments have in common.

Present value (a new concept) is the value today, of a future revenue. This follows from the fact that we assume that inflation-adjusted money loses value over time. If you receive a $1 today, you should be ready to trade it in for $1.05 a year from now, provided the interest rate is 5%. In other words, the value of $1.05 a year from now, is equal to $1 today, if the interest rates are 5%.

So, for instance, if you are expecting a revenue of $105 from a piece of machinery one year down the line, and the interest rates are 5%, you should not pay more than $100 for it right now. Using the rules of compounding to calculate the revenues from something that come in for more than one year, we get the present value formula:

Over here, r is the real interest rate, and n is the number years into the future you expect your revenues. For instance, if you expect $130 five years later, how much should you be willing to pay right now, if the interest rate is 5%?

You should not pay more than $101.50 for this particular investment. Now, if the interest rates go up to 6%, and the market price of that particular item is $101.50, and you still expect $130 from that item in five years, then your investment decision would change because:

At a rate of 6%, since the Present Value of that investment is $97.14, and the market price is $101.50, this item is over-priced and you’ll be better off investing in a bank, rather than in that item, even though you are getting a revenue of $130 in five years. In fact, even if you have a $101.50, at the higher rate of 6%, if you invest it in a bank, you’ll end up with:

And since you’ll get a higher return from investing in the bank, it makes more sense to do that.

A little addendum: Most of the times, investments last forever – so there is no real “life” of an investment. In that case, we alter our formula a little, and the present value is given as:

If an investment is going to give us a steady revenue of $10,000 per year forever, and the interest rate is 10%, then we should not pay more than $10,000/10% = $10,000/.1 = $100,000 for that investment. If the rates increase, the present-value decreases, and if the rates decrease, the present-value increases.

The Bottomline is that in the macroeconomy, people invest less when the rates increase, and invest more when rates decrease.

To model the effect of interest rates on investment, we take a look at some historical values. Here is a graph of the level of investment versus the bank loan prime rate, from 1990 to 2007.

Although investment is volatile, we do have a downward trend showing us that as the lending rates increased, investment decreased. In fact they decreased by $83.50 billion, for each percentage point increase in the lending rates. This brings us to a more generalized version of the relationship between investment and the real rates: . Here, I₀ is the “baseline investment”or anything that affects investment, but is independent of the real rate, and I_r is the “investment response to changes in the real rate.”

So, for the figure above, I₀ = $6,337 billion, and I_r = $83.50 billion.

This is where we stopped. Next class, we’ll do a short review of this stuff, and move on to the other components of GDP. Hopefully, we’ll finish up with Chapter 6 by next time.

Using the fact that the first derivative (or slope) of the firm’s production function can be calculated using calculus, we know that the MPL is given by . The profit-maximizing condition for a firm in our economy is when MPL x P = W. If we plug in the formula of MPL that we have using calculus, into the profit-maximizing condition, then after a little manipulation, we get the labor demand function for the entire economy. That is, . And when L^d = L, the total labor supply for the economy, then the our macroeconomic model’s labor market is in equilibrium, which looks something like this:

Marginal Propensity to Consume
We next talked about the consumption (C) part of the real GDP, Y (recall that Y = C + I + G + NX). From the circular-flow diagram, we know that households spend all of their income on one of three things: (1) Consumption; (2) Savings and; (3) Taxes. The after-tax income is called the disposable income (Y^D) and we are mainly concerned with the effects on total consumption, C, for changes in the disposable income, Y^D. To look at that, we divide total consumption spending into two parts:

1. Baseline consumption (C₀)
2. Marginal propensity to consume (C_y)

The marginal propensity to consume (MPC) part of the consumption is what determines by how much total consumption will change for changes in disposable income. Everything else that affects consumption (optimism, pessimism, risk, etc.) is lumped into the baseline consumption part it. When we plot the per capital disposable income against the total per capital consumption expenditure, from 1959 to 2006 (both in terms of year 2000 dollars), we get the following graph.

The average slope for the plot is around .35, so we can say that the crude value of the MPC using inflation-adjusted, per capita data from 1959-2006, is .35, and the baseline consumption is $8,850.

Since consumption and disposable income have a linear relationship, we model consumption as: C = C₀ + C_yY^D, where Y^D is the disposable (or after-tax) income, and Y^D = (1-t)Y.

This is where we stopped. Next week, we will continue on with investment or I component of the real GDP, and talk about present value and how the real interest rate affects investment decisions.

1. “Predictably Irrational: The Hidden Forces That Shape Our Decisions” (Harper; $25.95), Dan Ariely
2. “Nudge: Improving Decisions About Health, Wealth, and Happiness” (Yale; $25), Richard H. Thaler and Cass R. Sunstein

We talked briefly about how, when visibly faced with a higher number, you will assign a higher price to an object and vice versa, without consciously being aware that they are doing so. Ariely’s experiment on students assigning prices after being told to write the last two digits of their SSN confirmed this. Students with the highest SSNs had three times as high prices than those with the lowest SSNs. This is disturbing to economists because in all of our models, prices are determined by supply and demand, and not by the presence or absence of large numbers in view.

We then went over the results of Tuesday’s class survey and, as you all overwhelmingly pointed out – I am going too fast. In response to that, I will do my best to go slower and implement as many of your various suggestions as I can.

As I said in class, your feedback is much appreciated.

On to Regular Business
We started out by reviewing the assumptions of the flexible-price model. The time horizon of the model is such that it allows all prices and wages to adjust, so that all markets are in equilibrium. We talked about the example of umbrella-sellers in Times Square in Manhattan. When it rains, the prices increase, and when it stops they go down again. This is a case of perfectly flexible prices  – they adjust to increases in demand instantaneously. This flexibility is the fundamental basis of this model: Everything is always in equilibrium. Later, we will look at when everything is not always in equilibrium.

We reviewed the concept of potential output and distinguished it from actual output (current real GDP). In our model however, because we have everything always in equilibrium, there is no unemployment (everyone who wants to work is always working) and so our actual output is always equal to potential output.

We calculate potential output by using a close cousin of our old friend Cobb-Douglas, but this time, labor (L) is held constant, along with efficiency (E) and the diminishing-returns-parameter (). The new function (and its graph) looks like this:

Now that we know how potential output is determined, we are concerned with how the labor market comes into equilibrium.

The Labor Market
The labor market depends on the businesses in the economy. Since we are in equilibrium, it so happens that the businesses hire all available workers. Each individual business however, will hire workers to maximize its own profits. And the rule it uses to maximize profits, is marginal revenues = marginal costs. That is, the revenue gained from producing one extra unit of output, should equal the costs of hiring one extra worker. Since we are looking at the labor market, we hold the amount of capital constant, and to simplify things we let the total amount of capital (K) = 1.

Each business has its own Cobb-Douglas III production function, and while we assume K = 1, and E are determined from firm to firm and L is determined by the profit-maximizing rule. At this point, we introduce a new concept – that of the marginal productivity of labor (or MPL). It is the additional output produced by adding one extra unit of labor (or one worker) to the firm. This has to do with profit-maximization, and the MPL x Price of product (or P) = marginal revenue. The marginal costs are the costs of hiring one additional laborer, which is the wage rate (W). The free markets decide W and P. So, the profit-maximizing rule in our case becomes: MPL x P = W.

We went over an example to calculate MPL – this is in my slides (and in your text, with less detail), and I will not repeat that here – do take a look at the slides for that example. We ran out of time finishing up the example, but a take-home exercise for you to do was to calculate the MPL and the revenues when the firm in our example goes from hiring 400 laborers, to 401.

We’ll go over this again in the next class.

We started out by talking about the concept of potential output – or that output level where the economy is at its full-employment potential. Basically, the output of the economy when it is using all of its resources. The potential output is calculated using a slight variation on the Cobb-Douglas production function, one where labor is held constant, along with efficiency and alpha. This production function relates the amount of capital with the total output.

We also talked about the marginal productivity of labor, which is the additional unit of output produced by an adding an additional unit of labor to your firm. A firm’s optimal output will be when the dollar value of the marginal productivity of labor is equal to the wage rate (or when marginal revenues equal marginal costs). Essentially, it’s when the last person you employ is producing enough to balance out his or her wage-rate. This is how firms calculate how many workers to employ. Since the labor market is always in equilibrium, and the output is at its potential-output-level, we assume that all firms in the economy are at their optimal hiring point and their corresponding optimal production levels, and (again) that everyone in the labor force is employed. That is, everyone who wants to work, is working.

Since markets are in equilibrium, nothing alters the output of the economy. If anything affects labor or prices, the markets adjust so that they are in equilibrium again. However, what does change are the components of output. The components of output, as you well know by now, are Y = C + I + G + NX, where C is consumption, I is investment, G is governmental expenditure and NX are net exports (gross exports minus imports).

Assuming away foreign markets for the time-being, we look at domestic spending, which is just consumption, investment and governmental spending.

Consumption
This is the amount of income households spend after they have paid their taxes, and saved their money. Assuming an average tax rate for all the economy’s residents (say, t), the total tax paid will be $T = tY. So disposable income (another new term) or Y^D is income after taxes, or Y – T = Y – tY = Y(1-t).

Since consumption is what households spend after they save and pay their taxes, we get that C = Y – T – S^H, but Y – T = Y^D, so C = Y^D – S^H.

Now what we are interested in really is by how much does consumption really change with changes in disposable income. For that, we divide consumption into two parts: baseline consumption and the marginal propensity to consume. The former is fixed and does not vary with changes in disposable income, but the latter is the change in consumption for every dollar change in disposable income. We also assume that there is a linear relationship between consumption spending and disposable income. In fact, we say that C = C₀ + C_y(Y^D), where C₀ is baseline consumption and C_y is the marginal propensity to consume.

One thing we should remember is that the usual factors that affect consumption (i.e., risk tolerance, wealth expectations, etc.) affect the baseline consumption, but not the marginal propensity to consume (MPC).

Investment
Investment can be divided either based on what its used to buy (residential, non-residential, inventories or durables), or based on the kind of capital it buys (new vs. repairing old or depreciation). The two things that investment depends on are the real interest rates and “animal spirits”. The latter represents confidence and “irrational exuberance” – the kinds of things that affect the stock market.

We are more interested in the real interest rate, and how the present value of a particular investment stream determines whether we will invest in something or not.

Although I talked a little bit about present value in today’s class, I will pick up from this point in the next class.