I. Explain Cobb- Douglas Production Function?
The task of a production function is
to organize a production process- a process of combining the different factors
in some proportion so that those inputs can be efficiently transformed into
products or outputs.
Various
terms are used for inputs and outputs.
Inputs
Outputs
-------- -----------
factors
Quantity(Q)
factors
of production Total product(P)
resources Product
A
production function defines the relationship between inputs and maximum amount
that can be produced within a given period of time with a given level of
technology. Decision on input and output are taken after considering various
technological specifications. The technological information is summarized as
Q
= Q(L, N, K, .........)
Production
function states that Q is the the maximum amount of output which the firm can
produce if it combines the inputs( Land L, Labour N and Capital K). The ratio
of the the factor-combination depends on the form of the estimated production
function. Mathemaqtically, the production function can be shown as
Q=
f(X1, X2,.......Xk)
where
Q = Output
X1..........Xk
=input used
For
the purpose of analysis, the equation can be reduced to two inputs X and Y as,
Q
= f(X,Y)
where
Q = output
X = Labour
Y
= Capital
Two
special features of production function are,
a. Labour
and capital are are both inevitable inputs to produce any quantity of goods.
b. Labour
and capital are substitutes to each other in production.
Short
-run and Long-run Production function
Some
quantity of of both inputs is required to produce a given quantity of output. A
two variable input -lon-run production function for quantities of labour and
capital up to 10 units can be expressed in the form as in the table:
Labour(L) Capital(K)
0 1 2 3 4 5 6 7 8 9 10
0 0 0 0 0 0 0 0 0 0 0 0
1 0 5 15 35 47 55 62 61 59 56 52
2 0 12 31 49 58 66 72 77 72 74 71
3 0 35 48 59 68 75 82 87 91 89 87
4 0 48 59 68 72 84 91 96 99 102 101
5 0 56 68 76 85 92 99 104 108 111 113
6 0 55 72 83 91 99 107 112 117 120 122
7 0 53 73 89 97 104 111 117 122 125 127
8 0 50 72 91 100 107 114 120 124 127 129
9 0 46 70 90 102 109 116 121 125 128 130
10 0 40 67 89 103 110 117 122 126 129 131
If capital was
the fixed input in the short-run, then each column of the table represents a short-run
production function with respect to a specific quantity of the fixed
(Capital)input. for example for K=4 the short-run production function would be
Labour
(L) 0 1 2 3 4 5 6 7 8 9 10
Output
(Q) 0 47 58 68 72 85 91 97 100 102 103
Cobb-Douglas
Production Function
-------------------------------------------------------
The
most popular form of production function is Cobb-Douglas function.
Suppose
Q = Q(L, K)
this
means, the physical output level, Q depends upon qunatities of Labour (L) and
Capital (K).
The
Cobb-Douglas form is
Q = ALpoweralpha Kpower (1-
alpha)
where 0 < a <
1 A and a are constants.
2. Analyse the determinants of
investment?
Inducement to
Invest' or the investment function is the second component of Aggregate demand.
Investment, according to Keynes, is the addition to real capital assets.
According to classical economists investment demand was simply a decreasing
function of rate of interest. Inducement to invest depends upon two factors (i)
Marginal efficiency of capital and (ii) Rate of interest. Thus I = f (r, i).
The marginal efficiency of capital
(MEC) is the higher rate of return over cost expected from the employment of a
marginal or additional unit of capital asset. MEC means the expected rate of
profitability of a new brand machine. It may be defined as the highest rate of
return over cost expected from the marginal or additional unit of a capital
asset. The MEC depends on two factors.
(i)
Prospective yield "from the capital assets
(ii)
The supply price of the capital asset.
The MEC is the
ratio of their two factors.
The prospective yield means the
total net returns which an entrepreneur expects of obtain from selling the
output of the capital asset over its life time. Running expenses are deducted
from their returns. If the total expected life of a capital asset is divided
into a series of years, the annual returns represented by Rp R2,
R3 R, are added. The investor also takes into account the supply
price of the asset it is the cost price of a new capital good. Supply price is
also known as replacement cost.
The investment decisions are
governed by the prospective yield aid the supply price of an asset. By
comparing their two concepts we can arrive at the MEC of a particular asset.
The MEC of a particular type of asset means what an investor expects to earn
from an additional unit of it compared with what it costs him.
In other words the MEC is the rate
at which the prospective yield is to be discounted if it is to equal the supply
price of the asset. Given the supply price, the marginal efficiency of capital
is influenced by future expectations.
The low rate of interest induces
investment and high rate of interest discourages it. Rate of interest, in term,
is determined by the quantity of money and the liquidity preference. Given the
quantity of - money the rate of interest mainly depends, on the strength of
liquidity preference of two determinants MEC is the most important one to
determine investment.
Investment
demand curve:-
The MEC
progressing declines as more and more units of that asset are produced. As more
and more units of an asset are produced, they will compete against each other
to meet consumers' demand and by this the prospective yield will decline.
With the decline in the prospective
yield, the supply price of such as asset is likely to go up it more and more
units of such asset are produced because of the rising cost. The decline in the
prospective yield and the increase in supply price of an asset will result in
lower MEC with an increased investment.
In the above diagram MEC and rate of
interest are measured in the OY-axis. Along OX-axis is measured investment. The
equilibrium will be established at the point where MEC becomes equal to the given
current rate of interest. Thus if the rate of interest is Op then OM investment
will be under taken because at OM, level of stock of capital MEC of Capital is
equal to the rate of interest OP.
If the rate of interest falls to OP,
investment will rise to ON since at ON level of investment the new rate of
interest is equal to the marginal efficiency of capital. Thus it is seen that
the curve of MEC shows the demand for investment or inducement to invest at
various rates of interest. Hence MEC curve represents the investment demand
curve. The Investment Demand Curve shows the amount of investment expenditure
at various rates of interest.
If the investment curve (MEC curve)
is less elastic, then investment demand will not increase very fetch with the
fall in the rate of interest. If the investment demand curve is elastic, the
changes in the rate of interest will lead to larger change in investment
demand.
When expectations regarding profit
change, the whole curve of the marginal efficiency of investment will shift. It
profit expectation falls or rises, the MEC curve (Investment Curve) will shift
downward or upward.
