11. Case and Lave (1970) analysed inland waterway costs in the United States. In their paper,...

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11. Case and Lave (1970) analysed inland waterway costs in the United States. In their paper, they identified two trends associated with inland waterway transport during the preceding three decades: a relatively constant cost per ton-mile and a trend for a small number of firms to garner a large share of the market, either through growth or merger. In order to examine these issues, the authors estimated the following Cobb-Douglas long-run average cost (LRAC) function: LRAC = ao(EBM) (SZ)-T Where EBM is "equivalent barge-miles", a measure of output, SZ is size of firm, measured by the number of towboats, and T is a time trend. ( = 1, . . ., 4) are parameters. Data for this study was based upon quarterly observations for five major inland water carriers between 1962 and 1966. The results of the analysis are shown in table 5.16. Table 5.16 Inland waterway regression results* Regressor Constant term Equivalent Barge Miles (EBM) Number of Towboats -0.200 Coefficient Estimate (t-statistics) -0.615 (-11.0) -0.074 (-1.3) 0.030 (0.88) Time Trend R2 = 0.865 Number of observations = 83 * The estimated model also included three seasonal variables for the first, second, and third quarters, as well as four dummy variables for firms 1, 2, 3, and 4. The constant term reflects the fourth quarter and firm 5. A t-statistic was not reported for the constant term. Source: Case and Lave (1970), table III, p. 188 a. Based upon the reported results, do inland waterway companies operate under increasing, decreasing, or constant returns to scale? b. The authors argue that the measure of firm size, Number of Towboats, should have a negative effect upon long-run average costs. What's the economic intuition behind this hypothesis, and do the reported results support this? 11. Case and Lave (1970) analysed inland waterway costs in the United States. In their paper, they identified two trends associated with inland waterway transport during the preceding three decades: a relatively constant cost per ton-mile and a trend for a small number of firms to garner a large share of the market, either through growth or merger. In order to examine these issues, the authors estimated the following Cobb-Douglas long-run average cost (LRAC) function: LRAC = ao(EBM) (SZ)-T Where EBM is "equivalent barge-miles", a measure of output, SZ is size of firm, measured by the number of towboats, and T is a time trend. ( = 1, . . ., 4) are parameters. Data for this study was based upon quarterly observations for five major inland water carriers between 1962 and 1966. The results of the analysis are shown in table 5.16. Table 5.16 Inland waterway regression results* Regressor Constant term Equivalent Barge Miles (EBM) Number of Towboats -0.200 Coefficient Estimate (t-statistics) -0.615 (-11.0) -0.074 (-1.3) 0.030 (0.88) Time Trend R2 = 0.865 Number of observations = 83 * The estimated model also included three seasonal variables for the first, second, and third quarters, as well as four dummy variables for firms 1, 2, 3, and 4. The constant term reflects the fourth quarter and firm 5. A t-statistic was not reported for the constant term. Source: Case and Lave (1970), table III, p. 188 a. Based upon the reported results, do inland waterway companies operate under increasing, decreasing, or constant returns to scale? b. The authors argue that the measure of firm size, Number of Towboats, should have a negative effect upon long-run average costs. What's the economic intuition behind this hypothesis, and do the reported results support this?