Closed Economy Analysis

Why should we bother analyzing closed-economy issues, given the global environment in which economic activity takes place?

A cheeky answer to this question might be "because the first three-quarters of most courses in macroeconomics is based on closed-economy analysis and open economy analysis belongs in the second half of International Economics courses". This typical course-design reflects the fact that most macroeconomic problems were first studied (and, indeed, the traditional classical, Keynesian and Neo-Keynesian models were developed) under the assumption that the economy is closed to international trade and capital movements---it was easier to understand what is going on in a single economy than a whole bunch of interrelated economies. And indeed, when analyzing complex problems it is still sometimes useful to begin the thought process under an assumption that the economy is closed and then extend the analysis to encompass the interrelationships between that economy and the rest of the world.

The problem is that pure closed-economy models are no longer useful in analyzing real economic problems, if indeed they ever were. There are no closed economies in today's world.

The latter statement might seem extreme in the light of many less-developed countries that attempt to manipulate and restrict their imports and isolate their economies from the world capital market by imposing government controls on foreign exchange and capital market transactions. While one cannot rule out the possiblity that such restrictions are effective creating a "zero capital mobility " situation, in most cases the rich and informed can convert their domestic asset holdings into foreign-currency assets abroad by bribing the appropriate government officials. And well-placed people can also import what they choose from abroad. Since the average person in these economies may not be able to engage in desired transactions with foreigners, however, observed interest rates and prices will be badly distorted by the effects of these government controls. This creates many difficult obstacles to doing economic analysis. One of those obstacles is that closed-economy analysis will lead to incorrect conclusions because net capital inflows are in fact taking place.

Apart from the occasional economy that is truly "closed", a large economy like that of the U.S. can sometimes be usefully analyzed using closed-economy models. This is clearly the case in a fixed exchange rate regime where the U.S. is the key-currency country. It may also be the case under flexible exchange rate regimes where foreign countries manage their exchange rates by "mimicing" U.S. monetary policy.

Closed economy analysis is also useful in thinking about how a hypothetical "world monetary authority" should behave. And it is useful for studying the origins of current ideas about macroeconomics and the controversies that surrounded their development.

Despite these caveats, it makes little sense to analyze macroeconomic issues in the typical country under the assumption that its economy is closed to trade and, especially, to capital movements with respect to the rest of the world.

In the standard classical model that was in vogue prior to 1930, an increase in the stock of money did not lead to an increase in the level of employment because the demand for money was perfectly interest inelastic. True or False? Explain your answer.

Wrong, but the demand for money in the traditional classical system was indeed perfectly inelastic with respect to the interest rate. The traditional classical model assumed that k, the ratio of desired money holdings to income, was a constant. The demand function for money could then be written as

M/P = k Y

where M is the nominal money stock, P is the price level, and Y is real output. The quantity of money demanded is obviously independent of the rate of interest, which explains why fiscal policy was not of consequence in the crude classical model.

Monetary expansion did not lead to an increase in the level of employment in the traditional classical model because the model assumed that money wages are flexible in response to the forces of supply and demand, ensuring that everyone who wanted a job always had one. The short-run and long-run aggregate supply curves were both given by the vertical line AS.

In the standard classical model that was in vogue prior to 1930, the aggregate demand curve (AD) is a rectangular hyperbola with unit elasticity because the demand for money is perfectly interest inelastic in the traditional classical model. True or False? Explain your answer.

True! The demand for money in the traditional classical model is indeed perfectly inelastic with respect to the interest rate. This implies that the demand function for money,

M/P = kY,

where M is the nominal money stock, P is the price level, and Y is real output, can be rearranged to yield

P = M/kY,

the equation of the aggregate demand curve. This curve gives the combinations of P and Y for which there is no excess demand or supply of money and, hence, no excess aggregate supply or demand for goods. Note from the equation that, given the values of M and k, a rise in Y is associated with a proportional fall in P ---i.e., the curve has unit elasticity.

The LM curve is vertical in the simple traditional classical model. True or False? Explain your answer.

True! The LM curve gives the combinations of the interest rate and income for which the demand for money equals the supply. When the quantity of money demanded is not dependent on the interest rate, as is clear from the simple traditional classical demand for money function

M/P = k Y,

any interest rate can be associated with each level of income along the LM curve. The LM curve is thus vertical.

Suppose that a union organizes the whole economy and raises the level of money wages by 20 percent. There will be an increase in aggregate demand and prices when the economy is closed because workers will have more income to spend and will buy more goods. True or False? Explain your answer.

False! To the extent that a rise in the money wage rate increases the aggregate earnings of labor, it does so at the expense of the aggregate earnings of capital. Aggregate spending would thus increase on this score only if workers have a greater marginal propensity to consume than the owners of capital. And there is no particular reason why this would be the case. Moreover, unless the demand for labor is less than unitary elastic with respect to the real wage rate, the aggregate wage payments to labor will not increase in response to an increase in the wage rate.

Furthermore, even if the demand for labour is less than unitary elastic and workers have a greater marginal propensity to spend than the owners of capital, the rise in the wage rate will be passed on in part to consumers in the form of a higher price level. This will reduce the real quantity of money, causing the LM curve to shift to the left. The real interest rate will rise and investment and output will decline. It is thus true that the price level will rise, but the effect on the quantity of aggregate output demanded (ignoring the income-distribution effects above) will be negative.

In the Classical-Keynesian Synthesis model the LM curve is flatter the greater the income elasticity of demand for money. True or False? Explain your answer.

False. The equation of the aggregate demand curve can be written

P = M/L(r,Y) = M/L[Z(Y,G,T),Y]

where Z(Y,G,T) is a rearrangement of the income-expenditure (IS) equation that puts the real interest rate r on the left-hand side, L[r,Y] is the demand function for money, and taxes and government expenditure are incorporated in the simplest Keynesian fashion. [See the derivation of the IS curve in the answer to the next question.] The greater the income elasticity of demand for money, the greater the partial derivative of L[r,Y] with respect to Y and, hence, the greater the increase in the denominator of the expression M/L[Z(Y,G,T),Y] as Y increases. When the denominator increases by more as Y increases, the price falls be more as Y increases. Thus, a rise in Y will have a bigger downward effect on P, the bigger the income elasticity of demand for money, making the AD curve steeper.

In the Classical-Keynesian Synthesis model the IS curve is flatter the greater the marginal propensity to consume. True or False? Explain your answer.

True. The IS curve in traditional closed-economy models (as well as open economy models) is derived by substituting the consumption function

C = a + b Y

and the investment function

I = v - u r + h Y

into the standard income-expenditure equation

Y = C + I + G.

This yields

Y = a + b Y + v - u r + h Y + G.

Subtracting (b Y + h Y) from both sides we obtain

(1 - b - h)Y = a + v - u r + G

which can be reorganized to yield

Y = m (a + b) - m u r + m G

where m = 1/(1 - b - h) is the traditional Keynesian multiplier (which equals the reciprocal of a term equal to one minus the marginal propensity to consume, b, minus the marginal propensity to invest, h). This negative relationship between r and Y is the equation of the IS curve.

It can now be easily seen that a bigger value for b, the marginal propensity to consume, will imply a bigger value for the multiplier m, with the result that the effect of a fall in r on Y as we move down along the IS curve will be bigger. Y will thus increase by more, and the IS curve will therefore be flatter, the larger is the marginal propensity to consume.

The fixed wage aggregate aggregate supply curve KAS is flatter the greater the decline in the marginal physical product of labour as the level of employment increases, holding the stock of capital constant. True or False? Explain your answer.

False. Let

Y = F(N)

be the production function, where N is the level of employment and the stock of capital employed is constant and therefore embedded in the form of the function. The demand function for labor can be written

W/P = dF(N)/dN = F'(N).

The marginal product of labour, given by F'(N) declines as N increases. Rearranging the production function to express N as a function of Y,

N = J(Y),

we can rewrite the demand function for labor as

W/P = F'[J(Y)] = G(Y).

Rearranging this equation, we can express the price level as

P = W/G(Y).

This is the equation of the fixed-wage aggregate supply curve. An increase in Y is associated with an increase in employment, a consequent decline in the marginal product of labour and a decline in the real wage rate that takes the form of an increase in P holding W constant. The greater the decline in F'(N) as Y and N increase, the greater will be the rise in the price level and the steeper the KAS curve. Another way of stating this is to note that when there are diminishing returns the supply curve of output is upward sloping---the greater the diminishing returns, the steeper the slope.

The same result holds for the expectations augmented short-run aggregate supply curve, EAS, which is a redefinition of the KAS curve when wages are set according to rational expectations on the part of workers and firms based on their existing knowledge of economic conditions. The Keynesian aggregate supply curve, KAS, simply assumes that the wage rate is fixed.

A monetary expansion will lower the interest rate in a closed economy but have no effect on the interest rate in an open economy. True or False? Explain your answer.

True if the open economy is small, in which case the interest rate is determined in the rest of the world. If the open economy is large, an expansion of its money supply will cause the world interest rate (and hence its own interest rate) to fall. In a closed economy, an expansion of the money supply will cause the LM curve to shift to the right and the interest rate to fall. All this assumes, of course, that nominal wages are fixed. The interest rate will fall in the short run but not in the long run when wages and prices are flexible.