Economic Impact Analysis pot

Solving this equation in the usual way by pre-multiplying both sides by I – A -1 an equation relating final demands to gross industry outputs can be obtained: This equation can be used t

© Harry Campbell & Richard Brown

School of Economics The University of Queensland

BENEFIT-COST ANALYSIS

Financial and Economic

Appraisal using Spreadsheets

Ch 13: Economic Impact Analysis

What is the difference between Net Present Value

and Economic Impact?

Keynes gives the example of land, labour and capital used in two alternative ways:

1 To dig a hole in the ground;

2 To build a hospital.

The two projects have the same economic impact, in terms of

generating income for factors of production and inducing additional

expenditures, but the hospital has a higher net present value than the

hole in the ground.

Figure 13.1 The Circular Flow of Income

$ GOODS GOVERNMENT FACTORS $

HOUSEHOLDS

FIRMS

The Circular Flow of National Income

The National Income Multiplier

Consider three models which can be used to derive the national income multiplier:

1 A closed economy, no taxes;

2 A closed economy, with exogenous taxes;

3 An open economy, with endogenous taxes.

Symbols:

Y = national income; C = consumption expenditure;

T = tax revenues; G = government expenditure;

X = value of exports; M = value of imports

Model 1: Closed economy, no taxes

Y = C + I + G

C = A* + bY,

where A* is autonomous consumption expenditure, and

investment and government expenditure are exogenous.

Substitute to get:

Y = A* + bY + I* + G*

where “ * ” indicates a variable which is exogenous to the model (i.e is assumed to be constant).

Solve to get:

Y = (1/(1-b))(A* + I* +G*),

where (1/(1-b) is the national income multiplier.

Now dY = (1/(1-b) dG*

Model 2: Closed economy, with exogenous taxes

Y = C + I + G

C = A + b(Y - T)

Substitute:

Y = A* + b(Y - T*) + I* + G*

Solve:

Y = (1/(1-b)(A* + I* + G* - bT*)

Now:

dY = (1/(1-b)(dG* - bdT*)

Note that if extra government expenditure is financed

by increasing tax revenues, dG* = dT*,

dY = dG*

i.e the balanced budget multiplier is 1.

Model 3: Open economy, with endogenous taxes

Y = C + I + G + X - M

Note that X is added because income is generated in production

of exports, but the component of C+I+G that represents imports (M) is subtracted because no domestic income is generated by imports.

C = A + b(Y - T)

T = tY

M = mY

Substitute:

Y = A* + b(Y - tY) + I* +G* + X* - mY

Solve:

Y = [1/(1-b(1-t)+m)](A* + I* + G* + X*)

Using plausible values: t=0.3; m=0.25; b=0.9, the multiplier

takes the value 1.45.

The Employment Multiplier

Suppose that average per worker income is $y The number of

‘jobs’ in the economy is, therefore: L = kY, where k = 1/y.

The extra number of jobs resulting from an increase in

government expenditure is, therefore: dL = kdY , which, from Model 3, can be written as: dL = k[1/(1-b(1-t)+m)]dG* ,

where k[1/(1-b(1-t)+m)] is the employment multiplier

Some points to note:

1 The size of the multiplier is inversely related to the size of the

‘leakages’: (1-b), t, m.

The smaller the region (extent of the referent group) the larger the

leakage caused by imports, and the smaller the multiplier.

2 National income, Y, is expressed in nominal terms We can think of Y being the product of the average price of goods and

services, P, times the quantity produced, Q.

Y = PQ

An increase in Y could be caused by changes in P and/or Q:

dY = dP.Q + P.dQ

but only changes in Q generate changes in real income

In other words, some of the multiplier effect could represent

inflation.

3 Any project involving the use of scarce factors of production will generate income and, hence, expenditures and a multiplier effect In

comparing the economic impact of projects, it is the relative

multiplier effects that count, and these may not differ significantly

4 Multiplier effects may be particularly associated with the

construction phase of a project, and, in that case, will be of limited

duration.

5 Multiplier effects can be considered a benefit of the project only

in so far as they are ‘real’ (i.e represent the value of extra output

net of any additional opportunity costs), and would not have

occurred in the absence of the project (i.e would not have been

generated by an alternative project).

Table 13.1: Inter-Industry Structure of a Small Closed Economy

_

Sales Final Demand Gross Output

_ Purchases 1 100 400 300 200 1000

_ Value Added 900 1200 1200 3300

_ Gross Output 1000 2000 3000

_

Inter-Industry Analysis

The fixed coefficients of an input-output model

Where yi is final demand for the output of industry I.

If the coefficient aij is used to represent

the sales of industry i to industry j per

dollarÕs worth of ou tput of industry j, t hen

total sales of i ndustry i t o industry j can be

represented by:

And t otal value of ou tput of industry i can

be written as:

x i a x ij y

j

We can write a set of equations determining the gross output of each industry:

a 11 x 1 + a 12 x 2 + a 13 x 3 + y 1 = x 1

a 21 x 1 + a 22 x 2 + a 23 x 3 + y 2 = x 2

a 31 x 1 + a 32 x 2 + a 33 x 3 + y 3 = x 3

This set of equations can be simplified to:

(1- a 11 ) x 1 - a 12 x 2 - a 13 x 3 = y 1

-a 21 x 1 + (1- a 22 ) x 2 - a 23 x 3 = y 2

-a 31 x 1 - a 32 x 2 + (1- a 33 )x 3 = y 3

which can be written in matrix form as:

(I – A)X = Y

where I is the identity matrix (a matrix with ‘1’ on the diagonal and ‘0’ elsewhere), A is the matrix of inter-industry coefficients, a ij , X is the vector of industry

gross output values, and Y is the vector of values of

final demands for industry outputs

Solving this equation in the usual way (by

pre-multiplying both sides by (I – A) -1) an equation relating final demands to gross industry outputs can be obtained:

This equation can be used to predict the effect on industry output of any change in final demand For example, if a private investment project were to involve specified increases in final demands for the outputs of the three industries, the effects on gross industry outputs could be calculated

The input-output model can be modified to incorporate multiplier effects by adding a set of equations which play the same role as the consumption function in the multiplier model Suppose that the final demand for the outputs of the three industries are given by:

Where y is the level of national income and g i are the autonomous levels of demand for the output of each industry Each of the above equations can be thought

of as an industry-specific consumption function,

where the coefficient on y plays the role of the coefficient b in the aggregate consumption function and g i plays the role of A* By summing the equations

we can see that:

y i y g

where 0.9 is the marginal propensity to consume, as

in our earlier illustrative model of national income

Now consider the system of inter-industry

equations Y = (I – A)X, and replace Y by the set of

industry-specific expenditure functions and rearrange

to get:

We now have a set of three equations in four

unknowns, the x i and y In order to close the system

we need to add the condition that the value of final demand output should equal the value added in producing this output – the value of factor incomes paid by the industries The values added can be expressed as proportions of the values of the outputs

of the three industries:

When this equation is added to the other three and

the system solved for national income, y, the following

result is obtained:

Inter-industry Analysis and Employment

Suppose that the level of input of factor of production i

to industry j is given by:

v ij = b ij x j

Where b ij is a coefficient and x j is gross output of

industry j as before Supposing that there are two

inputs, labour and capital for example, total input levels are given by:

v 1 = b 11 x 1 + b 12 x 2 + b 13 x 3

v 2 = b 21 x 1 + b 22 x 2 + b 23 x 3

Or, in matrix notation, V = BX, where V is the vector of factor inputs, B the matrix of employment coefficients, and X the vector of industry outputs However, we already know that X = (1 – A) -1 Y and so we can write

levels of inputs of the two factors to the levels of final demand for the three goods Any change in the level

of autonomous demand for any of the three goods can be traced back through this system of equations

to calculate the effects on the levels of the factor

General Equilibrium Analysis

A computable general equilibrium (CGE) model can be constructed to determine the equilibrium values of prices and quantities traded in the economy, and to calculate the changes in these values which would result from some change in an exogenous variable, such as the level of investment

Simple CGE models can be constructed from information contained in the input-output model Our simple input-output model was of a closed economy producing three commodities and using two factors of production, and was solved for the equilibrium values

of the two inputs and the three outputs In a general equilibrium model values are calculated as the product of two variables - price and quantity Equilibrium in such a model with three commodities and two factors consists of five equilibrium prices and five equilibrium quantities In order to solve for the values of these 10 variables, a system of 10

Three of the required equations can be obtained

from the input-output coefficients by assuming that competition in the economy ensures that total revenue equals total cost; this means that for each industry the value of its sales equals the value of the intermediate inputs and factors of production used to

produce the quantity of the commodity sold Two

more equations are obtained from the factor markets where factor prices have to be set at levels at which the quantities of factors supplied by households equal

the quantities demanded by industries Three

equations are obtained from the markets for commodities in final demand; commodity prices must

be at a level at which the quantities demanded by households are equal to the final demand quantities

supplied by industries An income equation is

required to ensure that the income households receive from the supply of factors of production to industries is equal to their expenditure on final demand goods Lastly, since the CGE model

determines relative prices only, the price of either

one commodity or one factor must be set at an arbitrary level This normalization adds one more

equation to the model and completes the system of