Question

4.   a)   Suppose that there is a permanent collapse in consumer confidence causing

households to spend a smaller portion of their incomes on goods and

      services (i.e., consume less and save more). Use the IS-LM/PC model to explain and illustrate the short-run effect.

b)   Now illustrate the medium-run effect incorporating the Fed’s reaction. What component of demand rises to fill the gap left by the decline in consumption, and what causes this to happen?

c)   What will be the long-run effect of this change in saving/investment? That is, what will be the effect on K*/N and Y*/N? Explain and illustrate using the Solow model of chapters 10 and 11.

d)   In what sense is there a tradeoff between current consumption and future consumption?

Answer 1

ans ..

a

Consumers can change their savings rate (C):

If consumers decide to save more (marginal propensity to consume declines) then consumer spending declines and the IS curve shifts left.

c) In the long run, investment will also increase because increased savings will be invested.

We begin by using an economy-wide production function in Cobb-Douglas form with constant returns to scale:

Y* = f(L,K) = AL?K 1-?

As a first step, we modify this expression to put it into a form that represents thestandard of living (simply the ratio of output to labor input):

y* = Y*/L = f(1,K/L) = A(K/L)1-? = Ak1-?.

The term 'k' represents the capital/labor ratio better understood as the amount of capital available per unit of labor input. We would expect that greater amounts of capital per labor-unit would make that labor more productive and thus raise the living standards within a particular nation.

Capital is unique in that over time it wears out. This factor input is subject to the effects of friction, obsolescence and climate such that at some future date it ceases to make a useful contribution to the production process. This is known as depreciation. The reciprocal of the life-span of a unit of capital is then defined as the rate of depreciation '?'. The implication of this is that without replacement (via investment expenditure) the capital-labor ratio would naturally decline over time. In order to maintain this ratio, the required level of investment 'Irequired' (a flow variable) must be equal to the depreciation in the capital stock:

Irequired = ?K

It must be noted that with greater amounts of capital in place, greater levels of investment are required to maintain a particular capital-labor ratio (i.e., the more capital that exists, the more capital there is to wear out in a given time period).

With growth in the size of the labor force (due to population growth and increasing labor-force participation rates), additional investment is also necessary to maintain the capital-labor ratio (K/L) at a particular level. Thus, the level of investment must exceed rate of depreciation by an amount equal to the growth-rate 'n' in the labor-force:

Irequired = (n + ?)K

or if we divide both sides by 'L'

irequired = (n + ?)k

Investment is possible only if a given country makes resources available for this accumulation of capital. These resources, known as savings, represent those goods produced in the current time period not devoted to final private or public consumption. In a closed economy, we could write the following:

Savings: S = Y* - C - G
S = sY*

where 's' represents the proportion of output not devoted to private consumption 'C' or public (Government) consumption 'G'. With efficient financial and capital markets, these savings could then be made available for investment in new capital:

Savings = Irequired

or in per-capita terms:

sy* = (n+?)kd) It is a trade off between current consumption and future consumption because more of the current consumption means less of future consumption and vice versa.