Numerous empirical studies have sought to evaluate the relationship between market structure and performance. The traditional structure-conduct-performance approach (SCP) alone seems hard to reconcile with the true development of the relationship. There are two main stream of hypothesis that studies the relationship between. On one hand, the collusion hypothesis, widely known as SCP (Bain, 1995), stipulates that as a result of market concentration which facilitates the collusion between firms of the industry, greater benefits like higher firm profits arise. On the other hand, Demsetz (1973) provide an alternative reasoning for the positive relationship between concentration and profitability. The efficient structure hypothesis suggests that market structure is dictated by the efficiency of the operating firms. The most efficient firms reap higher profitability and market share which eventually lead to higher market concentration. This review will present some literature findings which are either in favour of or against Demsetz view of efficiency hypothesis.

Efficient-structure hypothesis stipulates that bigger market share is the outcome of efficient operations of the firms. It is subdivided into two forms of hypothesis. Under X-efficiency hypothesis, firms with superior management or production processes operate at lower costs and eventually gain more profits. Following-on higher market shares may result in higher market concentration. On another hand, scale-efficiency hypothesis posits that firms have comparable management technology and production but operate at respective optimal levels of economies of scale. A company’s cost position relies upon its relative market share. The higher the relative market share, the lower the company’s unit costs are and the higher the profit margins.
Banks
The efficient-structure theory also includes two hypotheses – the X-efficiency and scale efficiency hypotheses. The X-efficiency hypothesis argues that banks with better management and practices control costs and raise profit, moving the bank closer to the best-practice, lowerbound cost curve. The scale-efficiency hypothesis argues some banks achieve better scale of operation and, thus, lower costs. Lower costs lead to higher profit and faster growth for the scale-efficient banks.

Demsetz
Demsetz (1973, 1974) : positive relationship between market concentration and profitability reflects the exercise of market power, then it should affect all firms equally.

According to the efficiency hypothesis, market share is the consequence of efficiency rather than its cause. Differences in profitability among firms are due to higher efficiency. Efficient firms obtain large market share and earn high profits induce a causal association between size and profitability. Firms offering products that offer customers greater value enjoy gains in market share. Better managed firms that have a competitive advantage grow faster than rival firms. Firms with superior skill and foresight gain market share through lower prices or through better products. Caves and Porter (1977) and Woo and Cooper (1981,1982) provide evidence that smaller-share competitors are equally or even more profitable than larger rivals. Efficiency

1. More efficient producers typically enjoy higher profits because they are able to charge lower prices and thus capture larger market shares and economic rents. There are two measures of efficiency, namely X-efficiency and scale efficiency which give rise to profitability. Large firms more profitable than small firms.

According to efficient hypothesis, banks attain higher profits by having efficiency in their superior management or large scale, cost reduction production technologies.
Berger (1995) devised a model that incorporates two forms of efficiency hypothesis and two forms of collusion hypothesis using data of bank over the 1980 to 1989 period. They use income statement data and individual bank balance sheet to approximate a frontier cost function to derive the assessment of efficiency .Profitability is measured using both return on assets and return on equity. Independent variables comprise of concentration measured by HH index, measures of efficiency effects on managerial aptitude and measures of effect on average cost of economies of scale. There is support for X-efficiency, not for scale-efficiency. Profitability is not related to concentration but positively related to market share.

Gale (1972) studies the effect of market share on the rate of return of selected firms operating in different market environments.

The table above demonstrates the effect of share and quality on relative direct costs (the estimated per-unit materials, production, and distribution costs of the business as a percentage of the costs of its competitors, with administrative and marketing expenses excluded). By altering 1 standard deviation in the share index, relative direct costs for both groups change by 1-2%. From the share/relative direct cost results he concludes that higher-share businesses tend to be more profitable largely due to having lower direct costs. This is in line with the X-efficiency hypothesis. http://heinonline.org/HOL/Page?handle=hein.journals/antibull27&div=5&g_sent=1&collection=journals http://econpapers.repec.org/article/tprrestat/v_3a54_3ay_3a1972_3ai_3a4_3ap_3a412-23.htm

Using the PIMS database, Buzzell, Gale and Sultan (1975) study found a positive relationship between market share and profitability. The discovery from PIMS data is that a firm with a market share of 40 percent will reign a profit margin twice as high as the competitor 10 percent of the market (Simon 2010). Therefore, the strategic implication of these findings is that firms should strive to achieve a higher market share in order to reap the advantages of higher economies of scale and experience.
[Buzzell, R.D, B.T. Gale and R.G.M. Sultan (1975), Market Share – A Key to Profitability, Harvard Business Review, 53 (January – February), 97-106] https://hbr.org/1975/01/market-share-a-key-to-profitability/ar/1

2. Some paper support SCP which is not in line with Demsetz view. Collusion hypothesis stipulates concentration affects profitability as a result of market power. There is positive relationship between profitability and concentration, and no relationship between profitability and market share. Concentration ratio proxies collusion.

Using call report data from Federal Reserve Bank of Chicago, Jeon and Miler (2005) study the relationship between several measures of bank concentration at the state level and average performance of banks within that state from 1976 to 2000. The average return on equity of all banks in the state is the profit measure. The % of assets held by the five largest and ten largest banks in a state along with Herfindahl-Hirschman index of concentration in each state and the District of Columbia are the three measures of concentration. They find a positive relationship between bank concentration in a state and the average return on equity within that state, even after tuning for economic environment within that state. Temporal causality tests infers that bank concentration causes bank profitability. http://digitalcommons.uconn.edu/cgi/viewcontent.cgi?article=1066&context=econ_wpapers
In an analysis of statistics for a cross section of 32 four-digit food manufacturing industries for 1958, Collins and Preston (1966) concludes that average industry price-cost margins are positively correlated to the degree of concentration. The relationship are continuous and curvilinear. Initially, there is no systematic increases in price-cost margins as concentration rises in the lower ranges, however as concentration reaches above a certain level (in the 30 to 40% range for four firms) price-cost margins quickly picks up. http://www.jstor.org/stable/2097552?origin=JSTOR-pdf http://www.jstor.org/stable/2097552

Molyneux & Llyod-Williams (1994) conduct a study with respect to Spanish banking industry using pooled and annual data from year 1986–1988. The results generally support the traditional SCP hypothesis as justification for the market behaviour of Spanish banks. This proposes that the support of additional concentration in Spanish banking by government and Bank of Spain might unambiguously reduce the level of competition in the system and cannot be warranted on efficiency grounds. http://www.sciencedirect.com/science/article/pii/0378426694900027 Concentration may be the result of the greater efficiency of major companies large firm has higher profits than small firms in the same concentrated industry The variation of profitability among large and small firms illustrates the role of efficiency in the positive structure-profit relationship.Large firms make higher returns due to their efficiency. 3. There is no relationship between concentration and profitability.
Lawrence & Anoop (1995) study the relationship between concentration and performance for largest European banks using the test developed in Berger and Hannan (1993) but with different approach. First, they estimate the deviations from a stochastic cost frontier under the assumption that errors are distributed half-normal. The error terms are then taken to obtain the measures of X-efficiency for each bank. The stochastic cost frontier is also used to retrieve measures of scale-inefficiency. They do not use data of individual bank branches or very insignificant banks. Hence, the expected signs of the coefficients in the estimation of Eq. (1) are as follows: X-EFFi > 0, S-EFFi > 0, CONC = 0 and MS = 0. More efficient firms will have higher profits and the signs of the coefficients of X-EFF, and S-EFFI should be positive. If net interest margin is used as the measure of performance, the signs of the efficiency measures should be negative because more efficient banks should be able to offer more attractive loan and deposit rates to customers. In spite of the competitive interest margins, banks will still generate larger profits than those that are operating inefficiently. Although efficiency leads to higher market shares and market concentration, the zero coefficients indicate that market structure has no direct effect on prices and profits. By using a model which incorporates efficiency directly, we assume the following: prices are set competitively and efficiency is a function of strictly lower costs and banks operating at efficient scale levels; and market structure variables CONC and MS have no relationship with profits conditional on efficiency (Berger and Hannan, 1993).

Demsetz (1973,1974) states that if the profitability of large firms in concentrated industries is greater than the profitability of small firms in concentrated industries, then the relationship between profitability and concentration is due to a relationship between efficiency and profitability. Using the data on 1963 US Internal Revenue Service data for 95 industries, he finds that the profitability of firms in size classes R1, R2 and R3 is not related to concentration. Nevertheless, for the largest size class, R4 profitability and concentration exhibits positive relationship.
Ravenscraft (1983) approaches the firm size issue indirectly by taking into account the relative effects of market share and concentration on profits. In an analysis of 1975 US Data for 3186 lines of business (LOB) in 258 Federal Trade Commission (FTC), price-cost margins are positively related to LOB market shares, nonetheless the opposite holds true for seller concentration. Ravenscraft conjectures that profit concentration relationship in industry regressions reveals the upper hand of large sellers reaping more profits relative to smaller competitors. Having higher returns to advertising and assets for sellers with more market shares, it reflects the positive market share-profit relationship.

4. There is positive relationship between market share and profitability where market share act as a proxy for efficiency/ When market share, concentration and profitability are regressed, market share will outweigh concentration.
Gale (1972) finds that high market share is associated with high rates of return and that the effect of share on profitability depends on other firm and industry characteristics. The bigger the firm or the more concentrated or moderate growth the competitive environment is, the greater the influence of share on profitability. http://www.jstor.org/stable/1924568
Smirlock (1985) models bank profitability as a function of market share, concentration and an interaction term between market share and concentration as well as several control variables for over 2700 unit state banks from time period 1973-1978. http://www.jstor.org/stable/1992507

The equation is estimated with market share (MS) as the only structural variable, that is, with the restriction a2 = a3 = 0 imposed. These results are reported in the middle three rows of Table 1. Across all profit rate meanings, the coefficient on market share is significant and positive at 1 percent level where the coefficient on concentration is negative, giving the control variables are in line with anticipations. The explanatory power of these equations beats those where concentration (CR) is the market structure variable. Once market share is accounted for properly, concentration means nothing to explaining bank profit rates. He finds that market share is positively related to profitability while there is no relationship between concentration and profitability.

Gale & Branch (1982) test the relationship between profitability, market share and concentration using data covering period from 1970 to 1979 in some cases and four years of data in most cases. ROI is the proxy for profitability index.

Although explanatory power of concentration is statistically significant at 99% level, its relation to ROI is very modest (R² of less than 2%). When market share and concentration are inputted concurrently, the concentration coefficient falls to insignificance and changes signs, whereas the share coefficient is still highly significant. An interaction term (the product of share and concentration) do not pass a significance test with or without concentration in the equation. Hence, market share variable greatly dominates concentration which has explanatory power of almost 20% against concentration which is less than 2%, and eventually reaches zero once share has explained what it can.

This review is centred on Demsetz view of efficient structure paradigm where several literature written by researchers who support the efficient structure model criticise the SCP model since the relationship between market share, concentration and efficiency is excluded.

Three recent studies, one of which used company-wide data 0 did, however, find a positive relationship between ROI and market share. B. Gale, "Market Share and the Rate of Return," Review of Economics and Statistics 54 (November 1972): 412-23; R. Buzzell, B. Gale, and G. Sultan, "Market Share-A Key to Profitability," Harvard Business Review 53 (January-February 1975): 97-106; R. Caves, B. Gale, and M. Porter, "Interfirm Profitability Differences: Comment," Quarterly Journal of Economics 91 (November 1977): 667-75.