Markup and efficiency of Indian banks: an input distance function approach

Abstract

This paper examines market power and efficiency in Indian banking using a unified theoretical framework based on the primal approach. Empirical results show that due to high level of concentration, large banks hold the capacity to impose higher prices, particularly on advances, and enjoy significant market power. Indian banks, particularly Indian private and foreign banks, are operating below their efficient scale and cost savings can be obtained by increasing their size of operations. The impact of financial deregulation led to a decline in average markup of banks initially, but this trend got reversed in 2002. The increasing trend of market power is mostly determined by bank size. Large banks enjoy greater market power due to either cost advantages or to their capacity to impose higher prices. Lower marginal cost and higher return of the so-called efficient structure have helped the large banks to maintain higher efficiency level. Finally, higher market power was also reflected in higher profit.

Appendices

Appendix 1: Monopoly pricing

In a single output case, under monopoly, $P>\hbox {MC}$. However, if there are multiple outputs, $p_m >\hbox {MC}_m$ might not hold for all m, even under monopoly especially if there is cross-subsidization. To see it formally, assume that $y_1 ({p_1, p_2 }),y_2 ({p_1, p_2 })$ are the demand functions for outputs $y_1 \hbox { and }y_2$. Define profit as $\pi =p_1 \times y_1 \left( {p_1, p_2 } \right) +p_2 \times y_2 \left( {p_1, p_2 } \right) -C\left( {w, y_1, y_2 } \right)$, where $C\left( {w,y_1 ,y_2 } \right)$ is the cost function. The first-order conditions are:

$$\begin{aligned} \frac{\partial \pi }{\partial p_1 }= & {} 0\hbox { gives }p_1 \frac{\partial y_1 }{\partial p_1 }+y_1 +\frac{\partial y_2 }{\partial p_1 }\nonumber \\= & {} \frac{\partial C}{\partial y_1 }\frac{\partial y_1 }{\partial p_1 }+\frac{\partial C}{\partial y_2 }\frac{\partial y_2 }{\partial p_1 }=\hbox {MC}_1 \frac{\partial y_1 }{\partial p_1 }+\hbox {MC}_2 \frac{\partial y_2 }{\partial p_1 } \end{aligned}$$

(1)

$$\begin{aligned} \frac{\partial \pi }{\partial p_2 }= & {} 0\hbox { gives }p_1 \frac{\partial y_1 }{\partial p_2 }+y_2 +\frac{\partial y_2 }{\partial p_2 }\nonumber \\= & {} \frac{\partial C}{\partial y_1 }\frac{\partial y_1 }{\partial p_2 }+\frac{\partial C}{\partial y_2 }\frac{\partial y_2 }{\partial p_2 }=\hbox {MC}_1 \frac{\partial y_1 }{\partial p_2 }+\hbox {MC}_2 \frac{\partial y_2 }{\partial p_2 } \end{aligned}$$

(2)

From (i) $(P_1 -\hbox {MC}_1) \frac{\partial y_1 }{\partial p_1 }=-y_1 -\left( {p_2 -\hbox {MC}_2 } \right) \frac{\partial y_2 }{\partial p_1 }$

$$\begin{aligned} \Rightarrow \frac{(P_1 -\hbox {MC}_1)}{p_1 }=\frac{1}{\eta _1 }+\frac{(P_2 -\hbox {MC}_2)}{p_1 }\frac{\partial y_2 }{\partial p_1 }\div \left( {-\frac{\partial y_1 }{\partial p_1}} \right) \end{aligned}$$

(3)

where $\eta _1 =-\frac{\partial y_1 }{\partial p_1 }\frac{p_1 }{y_1 }>0$ is the price elasticity of demand. If outputs $y_1$ and $y_2$ are complements then $\frac{\partial y_2 }{\partial p_1 }<0.$ Thus, even if markup in $y_2$ is positive, i.e., $(P_2 -\hbox {MC}_2)>0,$ markup in $y_1$ can be negative if the complementarity is strong (i.e., $\frac{\partial y_2 }{\partial p_1 }$ is a large negative number). Similarly, $P_2 -\hbox {MC}_2 \gtrless 0.$

Appendix 2

See Table 5.

Table 5 Estimated parameters of input distance functions)