SÍNTESIS: RELACIÓN PRUEBA SABER PRUEBA ESTADO

% Dissertation model chapter#2- lowering tax on capital- AMENDED ( dt 7/22/09) % % 4 equations in 4 variables:- dKx_Kx, dLy_Ly, dPlo, dKy_Ky %

clear; clear all;

eq1 = 'A11*dKx_Kx + A12*dKy_Ky + A13*dLy_Ly + A14*dPlo = B1';

eq2 = 'A21*dKx_Kx +A22*dKy_Ky + A23*dLy_Ly + A24*dPlo = B2' ; eq3 = 'A31*dKx_Kx + A32*dKy_Ky + A33*dLy_Ly + A34*dPlo = B3' ;

eq4 = 'A41*dKx_Kx +A42*dKy_Ky + A43*dLy_Ly + A44*dPlo = B4' ; s = solve (eq1, eq2, eq3, eq4, 'dKx_Kx', 'dKy_Ky', 'dLy_Ly', 'dPlo');

dKx_Kx= s.dKx_Kx dKy_Ky = s.dKy_Ky dLy_Ly = s.dLy_Ly dPlo = s.dPlo % RESULTS % dKx_Kx =

-(A12*A23*A34*B4 - A12*A23*A44*B3 - A12*A24*A33*B4 + A12*A24*A43*B3 + A12*A33*A44*B2 - A12*A34*A43*B2 - A13*A22*A34*B4 + A13*A22*A44*B3 + A13*A24*A32*B4 - A13*A24*A42*B3 - A13*A32*A44*B2 + A13*A34*A42*B2 + A14*A22*A33*B4 - A14*A22*A43*B3 - A14*A23*A32*B4 + A14*A23*A42*B3 + A14*A32*A43*B2 - A14*A33*A42*B2 - A22*A33*A44*B1 + A22*A34*A43*B1 + A23*A32*A44*B1 - A23*A34*A42*B1 - A24*A32*A43*B1 + A24*A33*A42*B1) ---

(A11*A22*A33*A44 - A11*A22*A34*A43 - A11*A23*A32*A44 + A11*A23*A34*A42 + A11*A24*A32*A43 - A11*A24*A33*A42 -

A12*A21*A33*A44 + A12*A21*A34*A43 + A12*A23*A31*A44 - A12*A23*A34*A41 - A12*A24*A31*A43 + A12*A24*A33*A41 + A13*A21*A32*A44 - A13*A21*A34*A42 - A13*A22*A31*A44 + A13*A22*A34*A41 + A13*A24*A31*A42 - A13*A24*A32*A41 - A14*A21*A32*A43 + A14*A21*A33*A42 + A14*A22*A31*A43 - A14*A22*A33*A41 - A14*A23*A31*A42 + A14*A23*A32*A41)

dKy_Ky =

(A11*A23*A34*B4 - A11*A23*A44*B3 - A11*A24*A33*B4 + A11*A24*A43*B3 + A11*A33*A44*B2 - A11*A34*A43*B2 - A13*A21*A34*B4 + A13*A21*A44*B3 + A13*A24*A31*B4 - A13*A24*A41*B3 - A13*A31*A44*B2 + A13*A34*A41*B2 + A14*A21*A33*B4 - A14*A21*A43*B3 - A14*A23*A31*B4 + A14*A23*A41*B3 + A14*A31*A43*B2 - A14*A33*A41*B2 - A21*A33*A44*B1 + A21*A34*A43*B1 + A23*A31*A44*B1 - A23*A34*A41*B1 - A24*A31*A43*B1 + A24*A33*A41*B1) *DIVIDED BY*

--- (A11*A22*A33*A44 - A11*A22*A34*A43 - A11*A23*A32*A44 + A11*A23*A34*A42 + A11*A24*A32*A43 - A11*A24*A33*A42 - A12*A21*A33*A44 + A12*A21*A34*A43 + A12*A23*A31*A44 - A12*A23*A34*A41 - A12*A24*A31*A43 + A12*A24*A33*A41 + A13*A21*A32*A44 - A13*A21*A34*A42 - A13*A22*A31*A44 + A13*A22*A34*A41 + A13*A24*A31*A42 - A13*A24*A32*A41 - A14*A21*A32*A43 + A14*A21*A33*A42 + A14*A22*A31*A43 - A14*A22*A33*A41 - A14*A23*A31*A42 + A14*A23*A32*A41)

dLy_Ly =

-(A11*A22*A34*B4 - A11*A22*A44*B3 - A11*A24*A32*B4 + A11*A24*A42*B3 + A11*A32*A44*B2 - A11*A34*A42*B2 - A12*A21*A34*B4 + A12*A21*A44*B3 + A12*A24*A31*B4 - A12*A24*A41*B3 - A12*A31*A44*B2 + A12*A34*A41*B2 + A14*A21*A32*B4 - A14*A21*A42*B3 - A14*A22*A31*B4 + A14*A22*A41*B3 + A14*A31*A42*B2 - A14*A32*A41*B2 - A21*A32*A44*B1 + A21*A34*A42*B1 +

A22*A31*A44*B1 - A22*A34*A41*B1 - A24*A31*A42*B1 + A24*A32*A41*B1)*DIVIDED BY*

---

(A11*A22*A33*A44 - A11*A22*A34*A43 - A11*A23*A32*A44 + A11*A23*A34*A42 + A11*A24*A32*A43 - A11*A24*A33*A42 - A12*A21*A33*A44 + A12*A21*A34*A43 + A12*A23*A31*A44 - A12*A23*A34*A41 - A12*A24*A31*A43 + A12*A24*A33*A41 + A13*A21*A32*A44 - A13*A21*A34*A42 - A13*A22*A31*A44 + A13*A22*A34*A41 + A13*A24*A31*A42 - A13*A24*A32*A41 - A14*A21*A32*A43 + A14*A21*A33*A42 + A14*A22*A31*A43 - A14*A22*A33*A41 - A14*A23*A31*A42 + A14*A23*A32*A41)

dPlo =

(A11*A22*A33*B4 - A11*A22*A43*B3 - A11*A23*A32*B4 + A11*A23*A42*B3 + A11*A32*A43*B2 - A11*A33*A42*B2 - A12*A21*A33*B4 + A12*A21*A43*B3 + A12*A23*A31*B4 - A12*A23*A41*B3 - A12*A31*A43*B2 + A12*A33*A41*B2 + A13*A21*A32*B4 - A13*A21*A42*B3 - A13*A22*A31*B4 + A13*A22*A41*B3 + A13*A31*A42*B2 - A13*A32*A41*B2 - A21*A32*A43*B1 + A21*A33*A42*B1 + A22*A31*A43*B1 - A22*A33*A41*B1 - A23*A31*A42*B1 + A23*A32*A41*B1) *DVIDED BY*

CHAPTER III – THE CONSUMPTION TAX

The purpose of this chapter is to develop a model of the consumption tax and simulate tax competition in the OECD country, using a similar model set-up as in chapter two. The major variation is that instead of a tax on all capital in the OECD country, there is now a tax on consumption (not production) in the OECD. The tax initially drives a wedge between the price paid by the OECD consumer and producers on the one hand and between the prices paid by the ROW and OECD consumers on the other.

If total demand can be split as in chapter two in the following manner:

X = Xo + Xr , Y = Yo , and Z = Zo + Zr , then the tax applies to Xo , Yo and Zo only, not to Xr and Zr. Further, the price paid by the consumer in OECD is Px*(1+TCo), Py*(1+TCo)

and Pz*(1+TCo), the prices paid by the consumer in the ROW are Px and Pz and the prices

received by producers in both countries are also Px , Py and Pz . As before, Px , Py and Pz

are still initially equal to 1, and Px*(1+TCo), Py*(1+TCo) and Pz*(1+TCo) are ≠ 1. We will

continue with all the previous assumptions, except where specified.

PROFIT MAXIMIZATION BEHAVIOR BY FIRMS (SECTORS)

The production functions for each sector can be written as a function of productive resources:

X = f (Kx , Lx, G) Y = g (Ky, Ly, G) Z = h (Kz, Lz)

The sector is synonymous with the firm. Since CRS industries imply that the size of the firm is indeterminate, we speak of the sector and firm interchangeably, like each sector were one giant firm. However, we have also assumed perfect competition, so each firm (sector) acts like an atomistic price-taker in all markets. Specifically, we assume that firms do not recognize the externality associated with paying taxes that support the public good G. The main difference is that the tax is not imposed on capital. Since producers receive only the supply price, and they take the tax rate as a given constant, they seek to maximize the objective function based on the production functions:

X = f (Kx , Lx, ) Y = g (Ky, Ly, ) Z = h (Kz, Lz)

Where is taken as fixed and given at the historical level which is assumed unchanged.

The profit maximization problem can then be set up as:

FIRM (SECTOR) X

Maximize Π (profit) = { Px* f (Kx , Lx, ) - Pk*Kx – Plo*Lx } with respect to Kx and Lx

First order conditions:

1. Px* - Pk = 0

And

2. Px* - Plo = 0

Each firm pays each factor its marginal product at the current level of provision of the public good. The demand price includes the tax, but since the tax is assumed to go to the government and the tax rate is independent of the firm‟s actions, it does not enter the objective function. Revenue for a firm is independent of the tax, so even if we included the demand price in our objective function we would have to subtract tax payable. As in the previous chapter, the firm ignores the externality arising from changes in G.

FIRM (SECTOR) Y

Behaves in exactly the same way as X, and so we get = Pk and = Plo

FIRM (SECTOR) Z

Since there is no government good or tax in the ROW we have only the production function

Z = h (Kz, ) and the problem for firm Z:

Maximize Π (profit) = { Pz* h (Kz , ) - Pk*Kz - Plr* } with respect to Kz {since we

assume full employment always in both countries, choosing Lz is not a decision variable}

and we get = Pk

We have chosen to keep the total amount of labor fixed in ROW, and to maintain a full employment restriction to keep the model simple and transparent. To equate labor price in ROW to marginal products, and to allow labor to move between sectors in ROW, all we have to do is introduce two sectors in ROW instead of one. We will then have a 4 sector open economy model. Alternatively, we could have modeled labor supply in the

ROW on the lines of existing substantial under-employment in the informal and

agricultural sector, a la Arthur Lewis‟ famous model to give us an independent equation for labor in ROW. It will need to account for the fact that in competitive conditions in this model with full price and wage flexibility, unemployment should imply that Plr has to

be driven down to zero.

we leave this issue to a future extension of this model, and for the present, assume that full employment exists for ROW, there is a positive labor price and that dLz = 0. We

do this for two reasons. The first is to keep the model as transparent and simple as possible and incorporate only essential complications. This is in line with most of the significant previous literature that also assumes full employment in the OECD and ROW, albeit with more sectors. The second is that if we were to contemplate a fixed

compensation for labor in ROW, or allow Plr to fall to zero, we cannot capture the effect

noted in Harberger (1995): when the tax in the OECD is changed, capital flows into or out of the ROW, changing the marginal productivity of labor, especially for constant employment.

This has to mean that even if total labor supply in ROW is fixed, Plr is only fixed

for a given amount of capital. Thus, instead of assuming both in this chapter and in chapter two that movement of capital into and out of ROW changes the unemployment level with dPlr = 0 we prefer Lz = , we treat Plr as a residual determined by the level of

Kz and instead take Pz as the numeraire. However, we could have proceeded in both

chapters by using Plr as the numeraire instead of Pz , or by allowing Lz to vary in terms of

SUBSTITUTION

The elasticity of substitution is (with CRS and competition) defined as: Sx =

This can be rewritten as:

In document INSTITUTO COLOMBIANO PARA EL FOMENTO DE LA EDUCACIÓN SUPERIOR –ICFES- SOBRE LAS PRUEBAS SABER Y DE ESTADO: UNA MIRADA A SU FUNDAMENTACION Y ORIENTACION DE LOS INSTRUMENTOS (página 50-60)