The nominal exchange rate, or, for short, the ex-change rate, E is the price of one unit of foreign currency in terms of domestic currency:
If the Swiss francs/Swedish kronor exchange rate is 0.125, this means that one Swedish krona costs 0.125 Swiss francs. This commonly used definition has a counter-intuitive implication which may cause confusion for students new to international economics: if Switzerland’s exchange rate goes up, the Swiss franc loses value – it depreciates. The Swiss need more francs to obtain a given number of Swedish kronor. A falling exchange rate means that the domestic currency is getting stronger – it appreciates.
Formally, we have
The rate of depreciation may be positive, in which case the currency depreciates, or it may be negative, in which case the currency actually appreciates.
The right-hand part of the equation draws on the insight provided in the appendix to Chapter 1 that the percentage change in a variable can be approx-imated by the change in the natural logarithm of this variable over time.
We speak of appreciation and depreciation only if the exchange rate is moved by market forces. If gov-ernments decide to move the franc up to 0.2 against the krona in a system of fixed exchange rates, the franc is devalued. In the opposite case it is revalued.
On its own, the nominal exchange rate does not provide any information about the actual buying power of a given amount of money in different countries. It can only do this in combination with information about individual prices or the general price level. If the Volvo S60 sells for 50,000 francs in Switzerland and for 300,000 kronor in Sweden, where is it cheaper? A measure of the relative price level in two countries is the real exchange rate:
In the above example, to purchase an S60 costs 50,000 francs in Switzerland, but only
francs in Sweden. This also fol-lows from substituting prices and the exchange rate into the above equation. The real exchange
rate of means
that the Swiss only pay 75% of what the S60 costs in their home market when they buy the car in Sweden.
In this case, or whenever the real exchange rate is below 1, the Swiss franc is said to be overvalued.
If the real exchange rate is higher than 1, and Swiss franc prices abroad exceed home prices, the franc is undervalued.
When the real exchange rate changes we speak of real depreciation and real appreciation.
The exchange rate that exactly equalizes the domestic and the international purchasing power of a currency is called absolute purchasing power parity. It is the nominal exchange rate which sets the real exchange rate to a value of 1:
In the present example the purchasing-power-parity exchange rate turns out to be 50,000/
300,000 ⫽ 1/6
Macroeconomists do not usually look at prices for individual goods but at economy-wide price in-dexes which constitute a representative basket of goods and services.
There is still a second, weaker version of pur-chasing power parity, called relative purpur-chasing power parity. It predicts that the real exchange rate remains constant, which requires the rate of depreciation, , to be determined by the difference between the rate of inflation at home, , and the rate of inflation abroad, World:
Relative purchasing power parity does not predict goods to cost the same abroad as at home, as ab-solute purchasing power parity does. What it pre-dicts is that any price difference that exists remains the same over time.
=Swiss inflation - Swedish inflation ePPP= p - pWorld
Relative purchasing power parity:
p Purchasing power parity: EPPP =
P PWorld 0.125 * 300,000>50,000 = 0.75 300,000 = 37,500
0.125 *
=
Swiss francs
Swedish kronor * Swedish price Swiss price
Exchangerate: E = Swiss francs Swedish kronor
BOX 3.3
The IS curve depicts the equilibrium income levels from Chapter 2 at differ-ent interest rates. While drawing the curve, autonomous expenditures and the real exchange rate are kept constant. Raising either of these moves IS up and raises equilibrium income at any given interest rate.
The slope of the IS curve depends on the marginal propensity to consume (and to import) (equation (3.9)). The larger c is, the smaller is the numerator in the fraction preceding Y, and the flatter is the line. So when an income increase is considered permanent, meaning that c is large, the IS curve looks comparatively flat. For an income increase that consumers classify as transitory, the IS curve looks rather steep. The reasoning behind this is that in the latter case an interest rate reduction does stimulate investment and income in the first round, but there will be few of the second- and third-round effects described by the multiplier, since consumers adjust their consumption by only a small amount.
To strengthen understanding of the IS curve we may look at it from a dif-ferent angle by referring back to the circular flow. Figure 3.13 shows this flow again and includes what we know by now about the factors that influence leakages and injections.
Taxes rise Multiplier effect
raises income further
Saving rises
Imports rise
Exports Investment
Government expenditure Initial
spending and income Higher spending raises income
If i goes down, I goes up
T = tY IM = m1Y – m2R
G
S = (1 – c)(Y – T)
I = I – bi- EX = x1YWorld + x2R
Figure 3.13 This shows how what we learned in this chapter fits into the circular flow diagram. If i falls, I goes up. I increases by the grey segment of the investment injection. This demand rise adds to income. Since this stimulates con-sumption, second-round effects set in. The fact that leakages also get larger (not shown in graph) ensures that income does not continue to rise forever. Eventually, the stream of income settles into a new width determined by the multi-plier. Note that changes of world income, the exchange rate or taxes affect the circular flow in a similar way.
Note. We may also draw on the Keynesian cross to derive the negatively sloped IScurve:
Y0
Y1
i0
i1
Δi
–bΔi
Income Income
IS curve I – bi1 + NX + G I – bi0 + NX + G
A A
B
B Interest
rate rises
Interest rateExpenditure
3.3 The IS-LM or the global-economy model 83
Now suppose the interest rate falls. This boosts investment injected into the flow. To maintain equilibrium, i.e. equality between aggregate expenditure and income, income must rise. So when i goes down, Y must go up to keep the circular flow (the goods market) in equilibrium. This is reflected in the nega-tive slope of the IS curve.
Next, suppose the exchange rate depreciates (rises), with i remaining un-changed. Then exports rise (do you remember why?) and imports fall, increas-ing injections and lowerincreas-ing leakages, respectively. To maintain equilibrium, income must rise. Thus a rise in R shifts the IS curve to the right (or up).
Similar arguments reveal how changes in G, T or world income affect the position of IS.
3.3 The IS-LM or the global-economy model
The loose end left over after the discussion of the goods market in section 3.2 is the exchange rate. The exchange rate is determined in yet another market, the foreign exchange market. We postpone the introduction of the foreign ex-change market until the next chapter. The reason for this is mainly didactic, but not entirely so.
Recall that our first macroeconomic model of the determination of aggregate income, the Keynesian cross discussed in Chapter 2, comprises only one mar-ket: the goods market. Eventually, however, we will arrive at a model com-posed of three markets on the demand side of the economy: the goods market, the money market and the foreign exchange market. Going from one market to three interacting markets will turn out to be a huge step, perhaps too big a step to be taken in one stride. For this reason we will pause here and assemble a macroeconomic model from the two markets we have come across so far, the goods market and the money market. Doing so yields two kinds of benefits:
■ It shows us how to handle two markets that operate simultaneously and interact with each other, and thus serves a methodological purpose.
■ It generates a model that, while it still has clear limitations, constitutes a substantial improvement over the Keynesian cross. Since the limitations concern international macroeconomic aspects, the model is best understood as a picture of the global economy, as if viewed from a satellite camera in outer space, or of a national economy that does not interact with the out-side world.
Regarding the second point we need to accept that as long as we leave the foreign exchange market out of the picture, and thus cannot explain what de-termines the exchange rate, we cannot properly understand what dede-termines exports and imports. This does not matter as long as we consider an economy with no foreign trade, which would obviously be the case for the world, or the global economy. So whatever we learn in the remaining pages of this chapter will have relevance for income determination on a global scale, on a scale that ignores what happens in individual, national economies. Our insights would also be applicable to isolationist countries that choose not to trade with the rest of the world. But not many such countries exist anymore. Our insights
also give us a first, while incomplete and, therefore, imprecise, glimpse of how income is determined in large countries that export only a rather small frac-tion of their output.
The goods market equilibrium condition for the global economy reduces to
since On substituting the
consump-tion funcconsump-tion (3.5) and the investment funcconsump-tion (3.6) we obtain a new, global IS curve:
Global-economy IS curve (3.10) Comparing this to the national-economy IS curve given in equation (3.9) shows the following:
■ The global-economy IS curve is much simpler. The reason is that there are fewer leaks and injections. So everything that determines imports and ex-ports, that is the exchange rate, foreign income, and the marginal propen-sity to import, drops out of the picture.
■ The global-economy IS curve has a negative slope, just as the national-economy IS curve. The reason for this negative slope is investment behaviour, which is the same in both the global-economy and the national-economy version of the curve.
■ The global-economy IS curve is flatter. This is a consequence of less income leaking out of the circular flow because there are no imports. Hence, the multiplier is larger. If a falling interest rate now raises investment by a given amount, this translates into a larger rise in equilibrium income than it does with the national-economy IS curve.