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BENEFIT-COST ANALYSIS Financial and Economic Appraisal using Spreadsheets Ch 13: Economic Impact Analysis © Harry Campbell & Richard Brown School of Economics The University of Queensland 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. The Circular Flow of National Income Figure 13.1 The Circular Flow of Income HOUSEHOLDS $ GOODS GOVERNMENT FIRMS FACTORS $ 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; S = Savings; T = tax revenues; X = value of exports; C = consumption expenditure; I = investment expenditure; G = government expenditure; 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). Inter-Industry Analysis Table 13.1: Inter-Industry Structure of a Small Closed Economy _________________________________________________________________ Sales Final Demand Gross Output 1 2 3 _________________________________________________________________ Purchases 1 100 400 300 200 1000 2 0 400 900 700 2000 3 0 0 600 2400 3000 _________________________________________________________________ Value Added 900 1200 1200 3300 _________________________________________________________________ Gross Output 1000 2000 3000 _________________________________________________________________ The fixed coefficients of an input-output model 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: xij = aijxj , And t otal value of ou tput of industry i can be written as: x i a ij x j yi . j Where yi is final demand for the output of industry I. We can write a set of equations determining the gross output of each industry: a11x1 + a12x2 + a13x3 + y1 = x1 a21x1 + a22x2 + a23x3 + y2 = x2 a31x1 + a32x2 + a33x3 + y3 = x3 This set of equations can be simplified to: (1- a11) x1 - a12x2 - a13x3 = y1 -a21x1 + (1- a22) x2 - a23x3 = y2 -a31x1 - a32x2 + (1- a33)x3 = y3 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 interindustry coefficients, aij, 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 premultiplying both sides by (I – A)-1) an equation relating final demands to gross industry outputs can be obtained: Y = (I – A)-1 X. 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: y1 = 0.2 y + g1 y2 = 0.3 y + g2 y3 = 0.4y + g3 Where y is the level of national income and gi 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 gi plays the role of A*. By summing the equations we can see that: y i i 0.9 y g i i where 0.9 is the marginal propensity to consume, as in our earlier illustrative model of national income determination. 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: 0.9 x1 – 0.2 x2 - 0.1 x3 – 0.2 y = g1 0 x1 – 0.8 x2 - 0.3 x3 – 0.3 y = g2 0 x1 – 0 x2 - 0.8 x3 – 0.4 y = g3 We now have a set of three equations in four unknowns, the xi 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: y = 0.9 x1 + 0.6 x2 + 0.4 x3. When this equation is added to the other three and the system solved for national income, y, the following result is obtained: y = 10(g1 + g2 + g3). Inter-industry Analysis and Employment Suppose that the level of input of factor of production i to industry j is given by: vij = bij xj Where bij is a coefficient and xj 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: v1 = b11x1 + b12x2 + b13x3 v2 = b21x1 + b22x2 + b23x3 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)-1Y and so we can write F = B (1 – A)-1Y, a set of equations which relates the 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 inputs. 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 equations is required. 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 10 equations required to solve for the 10 variables.