An Analysis of the Economic Outcome of Financial Liberalization

Abstract

In the last chapter, we have considered the impact of financial reforms program and the channels through which such outcomes were transmitted. Particularly, we have assessed the performance of various indicators expected to capture improvements in efficiency, competitiveness and allocational enhancements following the adoption of liberalized financial policies in our sample countries. From these results and assessments based on almost all conventionally used aggregates, it is observable that there has been modest contribution of financial liberalization in terms of promoting economic growth in Kenya and Malawi. Importantly, in both these two countries the monopolistic structure of the commercial banking system has limited the depth and breadth of the financial services offered even under liberalized financial regime. This chapter considers this issue further. Firstly, it provides a simple model within the framework of imperfectly competitive banking industry and looks at the behaviour of the interest rate spread. The strategy is to analyse the level of spread together with the impact of an entry by a new firm. In doing so, the model solution is initially given for liberalized market system and then extended for the case of repressed financial environment. Applying the solutions from these exercises, adverse effect of higher fixed (overhead) costs in terms of serving as a barrier to entry of new established financial institutions is considered. Secondly, with this theoretical treatment the chapter also provides empirical evidence on the issue of high fixed costs which explain the lack of entry by effective competitors in these economies.

Appendices

Appendix A 5.1: Deriving the Market Equilibrium Condition for Loan Equation

To define our market equilibrium level of loan in the region between A and B, let us consider ${\bar{r} }$ in the critical. Does ${L = \bar {L}- \beta \bar{r} }$ satisfy the condition for market equilibrium? For firm i:

$${{\pi _i} = \left[ {\bar{r} - \frac{1}{\alpha }\left( {\bar{L}- \beta \bar{r} } \right)} \right]{L_i}}$$

What happens if L_i increases by one unit?

$$\Delta {\pi _i} = \bar{r} - \frac{1}{\alpha }\left( {\bar{L}- \beta \bar{r} } \right) - \left( {\frac{1}{\alpha } + \frac{1}{\beta }} \right)\frac{L}{n}$$

Substituting L in this equation we get:

$$\Delta {\pi _i} = \bar{r} - \frac{1}{\alpha }\left( {\bar {L}- \beta \bar{r} } \right) - \left( {\frac{1}{\alpha } + \frac{1}{\beta }} \right)\left( {\frac{{\bar{L}- \beta \bar{r} }}{n}} \right)$$

If this change has a non-increasing effect on the profit function then:

$${\bar{r} \left( {1 + \frac{\beta }{n}\left( {\frac{{\left( {n + 1} \right)}}{\alpha } + \frac{1}{\beta }} \right)} \right) - \frac{1}{n}\left( {\frac{{\left( {n + 1} \right)}}{\alpha } + \frac{1}{\beta }} \right)\bar{L}\le 0}$$

Without any difficulty and undertaking little manipulation we finally derive that:

$${\bar{r} \le \left( {\frac{{\left( {n + 1} \right)\beta + \alpha }}{{\left( {n + 1} \right)\left( {\alpha + \beta } \right)}}} \right)\frac{{\bar{L}}}{\beta } \equiv {r^*}}$$

Since this condition holds, this implies that as long as ${\bar{r} \le {r^*}}$ we will be operating on our loan curve while the condition for market equilibrium is satisfied.

What happens if L_i decreases by one unit? This will imply that:

$$\Delta {\pi _i} = \left( {\bar{r} - \frac{1}{\alpha }\left( {\bar{L}- \beta \bar{r} } \right)} \right)\left( { - 1} \right) + \frac{1}{\alpha }\frac{L}{n} \le 0$$

$${- \bar{r} + \left( {\frac{1}{\alpha } + \frac{1}{{\alpha n}}} \right)\left( {\bar{L}- \beta \bar{r} } \right) \le 0}$$

With little manipulation while further simplifying this equation and collecting terms we can derive:

$${ - \bar{r} \left( {\frac{{n\alpha + \beta \left( {n + 1} \right)}}{{n\alpha }}} \right) + \frac{{\left( {n + 1} \right)}}{{n\alpha }}\bar{L}\le 0}$$

Through reformulation and simplification we observe a familiar equation such that:

$${\bar{r} \ge \left( {\frac{{\left( {n + 1} \right)}}{{n\alpha + \beta \left( {n + 1} \right)}}} \right)\bar{L}\equiv \mathop {{\bar r\,^c}}}$$

Again since this condition holds, this indicates that as long as ${\bar{r} }$ is equal to or greater than the critical level of interest rate, ${\mathop {{\bar{r}^c}}}$, we will be operating on the curve. Combined together, we observe that the profit function is non-increasing in both directions within the region of ${\mathop {{\bar{r}^c}} \le \bar{r} \le {r^*}}$, thus we will be moving along the ${L = \bar{L}- \beta \bar{r} }$ curve.

Appendix A 5. 2: Deriving the Fixed Cost Lines for Medium and Lower Regions at ${\mathop {{\bar r\,^c}}\ }$

${\mathop {{\bar r\,^c}}\ }$",6,1?>In Figure 5.8, it is necessary to investigate whether ${{F^{M1}} {F^{L1}}}$ along the ${\mathop {{\bar{r}^c}}}$ line. With the help of equation (5.21) and equation (5.22) while substituting the value of ${\bar{r} }$ at the critical, we can derive that:

$${{F^{L1}} = \frac{{\alpha \bar{{L}^2} }}{{{{\left[ {n\alpha + \left( {n + 1} \right)\beta } \right]}^2}}}}$$

((A1))

$${{F^{M1}} = \frac{{\bar{L}}}{n}\left( {\frac{{\alpha + n\beta }}{\alpha }} \right)\frac{{\left( {n + 1} \right)\bar{L}}}{{n\alpha + \left( {n + 1} \right)\beta }} - \frac{\beta }{n}\left( {\frac{{\alpha + \beta }}{\alpha }} \right)\frac{{{{\left( {n + 1} \right)}^2}\bar{{L}^2} }}{{{{\left[ {n\alpha + \left( {n + 1} \right)\beta } \right]}^2}}} - \frac{{\bar{{L}^2} }}{{n\alpha }}}$$

((A2))

Simplifying equation (A2) while collecting terms, it can be expressed as:

$${{F^{M1}} = \frac{{\bar{{L}^2} }}{{n\alpha }}\left[ {\frac{{\left( {\alpha + n\beta } \right)\left( {n + 1} \right)}}{{n\alpha + \left( {n + 1} \right)\beta }}} \right] - \frac{{\bar{{L}^2} }}{{n\alpha }}\left[ {\frac{{\beta \left( {\alpha + \beta } \right){{\left( {n + 1} \right)}^2}}}{{{{\left[ {n\alpha + \left( {n + 1} \right)\beta } \right]}^2}}} + 1} \right]}$$

With little manipulation and further substitution after collecting terms this equation is given as:

$${F^{M1}} = \frac{\alpha \bar{{L}^2}}{\left[ {n\alpha + \left( {n + 1} \right)\beta} \right]}^2 \left[ \begin{array}{c} \frac{\left( {n\alpha + \left( {n + 1} \right)\beta} \right)\left( {\alpha + n\beta } \right)\left( {n + 1} \right)} {n{\alpha ^2}}-\\ \frac{\beta \left( {\alpha + \beta } \right){{\left( {n + 1} \right)}^2} + {{\left[ {\left( {n\alpha + \left( {n + 1} \right)\beta } \right)} \right]}^2}}{n{\alpha ^2}}\\ \end{array}\right]$$

((A3))

Having derived this, since the first term in both equations is similar to that of equation (A1) it is understandable that if, in the second term the equation (A3) is greater than 1, that will imply that ${{F^{M1}} {F^{L1}}}$. To investigate further whether this holds, let us propose that:

$$\frac{\left( {n\alpha + \left( {n + 1} \right)\beta } \right)\left( {\alpha + n\beta } \right)\left( {n + 1} \right)}{n{\alpha ^2}} - \frac{\beta \left( {\alpha + \beta } \right){{\left( {n + 1} \right)}^2} + {{\left[ {\left( {n\alpha + \left( {n + 1} \right)\beta } \right)} \right]}^2}}{n{\alpha ^2}} < 1$$

((A4))

Rearranging the above equation we can calculate that:

$$\left( {n\alpha + \left( {n + 1} \right)\beta } \right)\left( {\alpha + n\beta } \right)\left( {n + 1} \right) n{\alpha ^2} + \beta \left( {\alpha + \beta } \right){\left( {n + 1} \right)^2} - {\left[ {\left( {n\alpha + \left( {n + 1} \right)\beta } \right)} \right]^2}$$

((A5))

Finally while taking the case of ${n = 2}$ for simplicity and convenience, we get:

$${6{\alpha ^2} - 21\alpha \beta + 18{\beta ^{^2}} - 2{\alpha ^2} - 3\alpha \beta }$$

This simplifies to:

$${4\alpha + 6\beta 0}$$

((A6))

Since we know that this is not true, it implies that the last term in equation (A3) is greater than unity, which again means that ${{F^{M1}} {F^{L1}}}$.

Appendix A 5. 3: Maximal Points for C and D Curves

To investigate whether the maximal points of curves C and D are greater or lesser than the specified fixed costs under liberalization (F^H1 and F^H2), let us take that:

$${{F^{M2}} = \frac{{\bar{L}}}{{n + m}}\left[ {1 + \frac{{2\beta }}{\alpha }} \right]\bar{r} - \frac{\beta }{{n + m}}\left( {1 + \frac{\beta }{\alpha }} \right){{\bar r^2}} - \frac{{\bar{{L}^2} }}{{\left( {n + m} \right)\alpha }}}$$

((A7))

$${{F^{H2}} = \frac{{\alpha \bar{{L}^2} }}{{16\beta \left( {\alpha + \beta } \right)}}}$$

((A8))

For simplicity, equation (A7) can be re-written as:

$${F = a\mathop r\limits^ - - b\mathop {{r^2}}\limits^ - - c}$$

where a, b and c represent the given terms with respect to ${\bar{r} }$ in the original equation. Deriving the first order condition, we will get:

$${\frac{{\partial F}}{{\partial \bar{r} }} = a - 2b\bar{r} = 0}$$

((A9))

Therefore, solving for ${\bar{r} }$ and substituting this value into equation (A7), we will have:

$${\bar{r} = \frac{a}{{2b}}{\rm{\ \ and\ \ }}F = \frac{{{a^2}}}{{4b}}{\rm{ }}}$$

((A10))

Taking n to represent two firms initially and with the help of equation (A10), we can simplify equation (A7) to be:

$${{F^{M2}} = {\left[ {\left( {\frac{{\alpha + 2\beta }}{\alpha }} \right)\frac{{\bar{L}}}{3}} \right]^2}\frac{1}{4}\left( {\frac{{\alpha + \beta }}{\alpha }} \right)\frac{3}{\beta } - \frac{{\bar{{L}^2} }}{{3\alpha }}}$$

((A11))

With little manipulation while collecting terms we derive:

$${{F^{M2}} = \frac{{{\alpha ^2}\bar{{L}^2} }}{{12\alpha \beta \left( {\alpha + \beta } \right)}}}$$

((A12))

When equation (A12) is greater than equation (A8), it implies that ${16\beta 12\beta }$ which actually holds. Thus the maximum point of curve C must be higher than F given under equation (A8).