“Aggregate gives the inverse relationship between investment

“Aggregate
investment is independent of economic growth.” Explain and critically appraise
the economic theory underpinning this statement.

Investment is the net change in capital stock:
. In order to
explain the determinants of aggregate investment, a microfounded model is used
to determine what affects a firms’ investment decisions. The revenue of a firm generated by its capital stock given by ,
where  ,
with price, ,
and output, .
Assuming the real interest rate, ,
remains constant, the discounted net present value of the revenue stream is
given by .
A higher interest rate decreases  as the cost of borrowing is increased and it
will cost more for a firm to increase its capital stock, thus reducing investment;
this gives the inverse relationship between investment and the real interest
rate. A  firms’ objective is to maximise the
profits, so investment is chosen by the firm to maximise the net present value
of the profit stream generated by capital, ,
where  is the cost of investment. This maximisation
gives an optimal level of capital stock, ,
and a firm makes an investment to increase capital to this level. The following
models, Tobin’s Q model and the Accelerator model, act under different conditions
regarding competition, perfect or imperfect, and the presence of adjustment costs.
In Perfect competition, prices are exogenous, so investment has no effect on
the price. In imperfect competition, prices are endogenous and determined by
demand. Adjustment costs are the costs a firm incurs as a result of increasing the
capital stock.  For example, if the
capital stock is increased through the acquisition of new equipment, staff training
may be required in order to use it; this in an extra cost outside the purchase
of capital goods.

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The first model operates under the assumes
perfect competition and the presence of adjustment costs. Under perfect competition,
the scale of the firm is optimised so an increase in demand would increase the
price of a firms output. There are an infinite number of firms in the market,
so the investment is shown in the entry of new firms. As a result, at the
microfounded level, economic growth is independent of investment. Adjustment costs
are assumed to be convex; as capital stock increases, adjustment costs increase
sat a higher than proportional rate. In this model, the adjustment cost
function is quadratic, and the investment cost function is given by .  Furthermore, assume that the production
function is linear, . Firms will
choose investment to maximise , where  is the rate at which capital,, depreciates
each period . This maximisation gives , which can be
written as  , where q, or
marginal q, is given by ; this is Tobin’s
Q model. Marginal q is the ratio of marginal product of capital to the marginal
cost of capital, the interest and depreciation lost from investing in capital instead
of a financial asset; when profit is maximised, marginal revenue is equal to
marginal costs, and q is equal to 1.   If q > 1, the capital stock needs to be increased
to the optimal level. The amount of investment required depends on the marginal
cost of adjusting capital stock, . Given an
increase in the value of , the level of investment
decreases and the time taken for a firm to reach its optimal level,,
increases.  An increase in the relative
price of capital goods, , reduces the level
of investment, , for a given amount
of capital stock, . Likewise,
increasing the real interest rate, , results in a
higher opportunity cost from investing in capital. In this model, prices and depreciation
are held constant and only is endogenous. Therefore,
the inverse relationship of investment and real interest rate holds, meaning
that Tobin’s Q is a sufficient determinant of investment.

As q is a marginal value, it is difficult to measure, as marginal
values are not easily observable.

In this model, imperfect competition is assumed, so prices are
endogenous. For a monopolist firm, the representative firm in this model, the
demand function, which is downward-sloping, is . This gives the
price function, , where  is aggregate demand,  is the number of sectors and  is the firms’ output; in a monopoly each firm
is a sector;  is the elasticity of demand. Each sector is
assumed to be the same size,  is the average economic outp”Aggregate
investment is independent of economic growth.” Explain and critically appraise
the economic theory underpinning this statement.

Investment is the net change in capital stock:
. In order to
explain the determinants of aggregate investment, a microfounded model is used
to determine what affects a firms’ investment decisions. The revenue of a firm generated by its capital stock given by ,
where  ,
with price, ,
and output, .
Assuming the real interest rate, ,
remains constant, the discounted net present value of the revenue stream is
given by .
A higher interest rate decreases  as the cost of borrowing is increased and it
will cost more for a firm to increase its capital stock, thus reducing investment;
this gives the inverse relationship between investment and the real interest
rate. A  firms’ objective is to maximise the
profits, so investment is chosen by the firm to maximise the net present value
of the profit stream generated by capital, ,
where  is the cost of investment. This maximisation
gives an optimal level of capital stock, ,
and a firm makes an investment to increase capital to this level. The following
models, Tobin’s Q model and the Accelerator model, act under different conditions
regarding competition, perfect or imperfect, and the presence of adjustment costs.
In Perfect competition, prices are exogenous, so investment has no effect on
the price. In imperfect competition, prices are endogenous and determined by
demand. Adjustment costs are the costs a firm incurs as a result of increasing the
capital stock.  For example, if the
capital stock is increased through the acquisition of new equipment, staff training
may be required in order to use it; this in an extra cost outside the purchase
of capital goods.

The first model operates under the assumes
perfect competition and the presence of adjustment costs. Under perfect competition,
the scale of the firm is optimised so an increase in demand would increase the
price of a firms output. There are an infinite number of firms in the market,
so the investment is shown in the entry of new firms. As a result, at the
microfounded level, economic growth is independent of investment. Adjustment costs
are assumed to be convex; as capital stock increases, adjustment costs increase
sat a higher than proportional rate. In this model, the adjustment cost
function is quadratic, and the investment cost function is given by .  Furthermore, assume that the production
function is linear, . Firms will
choose investment to maximise , where  is the rate at which capital,, depreciates
each period . This maximisation gives , which can be
written as  , where q, or
marginal q, is given by ; this is Tobin’s
Q model. Marginal q is the ratio of marginal product of capital to the marginal
cost of capital, the interest and depreciation lost from investing in capital instead
of a financial asset; when profit is maximised, marginal revenue is equal to
marginal costs, and q is equal to 1.   If q > 1, the capital stock needs to be increased
to the optimal level. The amount of investment required depends on the marginal
cost of adjusting capital stock, . Given an
increase in the value of , the level of investment
decreases and the time taken for a firm to reach its optimal level,,
increases.  An increase in the relative
price of capital goods, , reduces the level
of investment, , for a given amount
of capital stock, . Likewise,
increasing the real interest rate, , results in a
higher opportunity cost from investing in capital. In this model, prices and depreciation
are held constant and only is endogenous. Therefore,
the inverse relationship of investment and real interest rate holds, meaning
that Tobin’s Q is a sufficient determinant of investment.

As q is a marginal value, it is difficult to measure, as marginal
values are not easily observable.

In this model, imperfect competition is assumed, so prices are
endogenous. For a monopolist firm, the representative firm in this model, the
demand function, which is downward-sloping, is . This gives the
price function, , where  is aggregate demand,  is the number of sectors and  is the firms’ output; in a monopoly each firm
is a sector;  is the elasticity of demand. Each sector is
assumed to be the same size,  is the average economic output for each firm,
and  and  are fixed parameters. For a given level of
demand, increasing in capital stock and therefore the scale of the firm, would
result in a decline in the prices of output. As a result, investment will be
chosen by maximising , where, to
simplify the model, there are no adjustment costs and ; therefore, the marginal,
and average, product of capital is constant.  The maximisation gives . Given a small
value for ,  is equal to economic growth; given the
interest rate, , is constant, this
is the accelerator model for investment. As investment is determined by an
increase in aggregate demand, it is not independent of economic growth in this
model.

ut for each firm,
and  and  are fixed parameters. For a given level of
demand, increasing in capital stock and therefore the scale of the firm, would
result in a decline in the prices of output. As a result, investment will be
chosen by maximising , where, to
simplify the model, there are no adjustment costs and ; therefore, the marginal,
and average, product of capital is constant.  The maximisation gives . Given a small
value for ,  is equal to economic growth; given the
interest rate, , is constant, this
is the accelerator model for investment. As investment is determined by an
increase in aggregate demand, it is not independent of economic growth in this
model.