• Asia Marketing Journal
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• v.14 no.1
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• pp.83-98
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• 2012

In a market where new and used cars are competing with each other, we would run the risk of obtaining biased estimates of cross elasticity between them if we focus on only new cars or on only used cars. Unfortunately, most of previous studies on the automobile industry have focused on only new car models without taking into account the effect of used cars' pricing policy on new cars' market shares and vice versa, resulting in inadequate prediction of reactive pricing in response to competitors' rebate or price discount. However, there are some exceptions. Purohit (1992) and Sullivan (1990) looked into both new and used car markets at the same time to examine the effect of new car model launching on the used car prices. But their studies have some limitations in that they employed the average used car prices reported in NADA Used Car Guide instead of actual transaction prices. Some of the conflicting results may be due to this problem in the data. Park (1998) recognized this problem and used the actual prices in his study. His work is notable in that he investigated the qualitative effect of new car model launching on the pricing policy of the used car in terms of reinforcement of brand equity. The current work also used the actual price like Park (1998) but the quantitative aspect of competitive price promotion between new and used cars of the same model was explored. In this study, I develop a model that assumes that the cross elasticity between new and used cars of the same model is higher than those amongst new cars and used cars of the different model. Specifically, I apply the nested logit model that assumes the car model choice at the first stage and the choice between new and used cars at the second stage. This proposed model is compared to the IIA (Independence of Irrelevant Alternatives) model that assumes that there is no decision hierarchy but that new and used cars of the different model are all substitutable at the first stage. The data for this study are drawn from Power Information Network (PIN), an affiliate of J.D. Power and Associates. PIN collects sales transaction data from a sample of dealerships in the major metropolitan areas in the U.S. These are retail transactions, i.e., sales or leases to final consumers, excluding fleet sales and including both new car and used car sales. Each observation in the PIN database contains the transaction date, the manufacturer, model year, make, model, trim and other car information, the transaction price, consumer rebates, the interest rate, term, amount financed (when the vehicle is financed or leased), etc. I used data for the compact cars sold during the period January 2009- June 2009. The new and used cars of the top nine selling models are included in the study: Mazda 3, Honda Civic, Chevrolet Cobalt, Toyota Corolla, Hyundai Elantra, Ford Focus, Volkswagen Jetta, Nissan Sentra, and Kia Spectra. These models in the study accounted for 87% of category unit sales. Empirical application of the nested logit model showed that the proposed model outperformed the IIA (Independence of Irrelevant Alternatives) model in both calibration and holdout samples. The other comparison model that assumes choice between new and used cars at the first stage and car model choice at the second stage turned out to be mis-specfied since the dissimilarity parameter (i.e., inclusive or categroy value parameter) was estimated to be greater than 1. Post hoc analysis based on estimated parameters was conducted employing the modified Lanczo's iterative method. This method is intuitively appealing. For example, suppose a new car offers a certain amount of rebate and gains market share at first. In response to this rebate, a used car of the same model keeps decreasing price until it regains the lost market share to maintain the status quo. The new car settle down to a lowered market share due to the used car's reaction. The method enables us to find the amount of price discount to main the status quo and equilibrium market shares of the new and used cars. In the first simulation, I used Jetta as a focal brand to see how its new and used cars set prices, rebates or APR interactively assuming that reactive cars respond to price promotion to maintain the status quo. The simulation results showed that the IIA model underestimates cross elasticities, resulting in suggesting less aggressive used car price discount in response to new cars' rebate than the proposed nested logit model. In the second simulation, I used Elantra to reconfirm the result for Jetta and came to the same conclusion. In the third simulation, I had Corolla offer $1,000 rebate to see what could be the best response for Elantra's new and used cars. Interestingly, Elantra's used car could maintain the status quo by offering lower price discount ($160) than the new car ($205). In the future research, we might want to explore the plausibility of the alternative nested logit model. For example, the NUB model that assumes choice between new and used cars at the first stage and brand choice at the second stage could be a possibility even though it was rejected in the current study because of mis-specification (A dissimilarity parameter turned out to be higher than 1). The NUB model may have been rejected due to true mis-specification or data structure transmitted from a typical car dealership. In a typical car dealership, both new and used cars of the same model are displayed. Because of this fact, the BNU model that assumes brand choice at the first stage and choice between new and used cars at the second stage may have been favored in the current study since customers first choose a dealership (brand) then choose between new and used cars given this market environment. However, suppose there are dealerships that carry both new and used cars of various models, then the NUB model might fit the data as well as the BNU model. Which model is a better description of the data is an empirical question. In addition, it would be interesting to test a probabilistic mixture model of the BNU and NUB on a new data set.

• Magazine of the Korean Society of Agricultural Engineers
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• v.11 no.4
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• pp.1775-1782
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• 1969

The results of the study on the consumptine use of irrigated water in paddy fields during the growing season of rice plants are summarized as follows. 1. Transpiration and evaporation from water surface. 1) Amount of transpiration of rice plant increases gradually after transplantation and suddenly increases in the head swelling period and reaches the peak between the end of the head swelling poriod and early period of heading and flowering. (the sixth period for early maturing variety, the seventh period for medium or late maturing varieties), then it decreases gradually after that, for early, medium and late maturing varieties. 2) In the transpiration of rice plants there is hardly any difference among varieties up to the fifth period, but the early maturing variety is the most vigorous in the sixth period, and the late maturing variety is more vigorous than others continuously after the seventh period. 3) The amount of transpiration of the sixth period for early maturing variety of the seventh period for medium and late maturing variety in which transpiration is the most vigorous, is 15% or 16% of the total amount of transpiration through all periods. 4) Transpiration of rice plants must be determined by using transpiration intensity as the standard coefficient of computation of amount of transpiration, because it originates in the physiological action.(Table 7) 5) Transpiration ratio of rice plants is approximately 450 to 480 6) Equations which are able to compute amount of transpiration of each variety up th the heading-flowering peried, in which the amount of transpiration of rice plants is the maximum in this study are as follows: Early maturing variety ; Y=0.658+1.088X Medium maturing variety ; Y=0.780+1.050X Late maturing variety ; Y=0.646+1.091X Y=amount of transpiration ; X=number of period. 7) As we know from figure 1 and 2, correlation between the amount evaporation from water surface in paddy fields and amount of transpiration shows high negative. 8) It is possible to calculate the amount of evaporation from the water surface in the paddy field for varieties used in this study on the base of ratio of it to amount of evaporation by atmometer(Table 11) and Table 10. Also the amount of evaporation from the water surface in the paddy field is to be computed by the following equations until the period in which it is the minimum quantity the sixth period for early maturing variety and the seventh period for medium or late maturing varieties. Early maturing variety ; Y=4.67-0.58X Medium maturing variety ; Y=4.70-0.59X Late maturing variety ; Y=4.71-0.59X Y=amount of evaporation from water surface in the paddy field X=number of period. 9) Changes in the amount of evapo-transpiration of each growing period have the same tendency as transpiration, and the maximum quantity of early maturing variety is in the sixth period and medium or late maturing varieties are in the seventh period. 10) The amount of evapo-transpiration can be calculated on the base of the evapo-transpiration intensity (Table 14) and Tablet 12, for varieties used in this study. Also, it is possible to compute it according to the following equations with in the period of maximum quantity. Early maturing variety ; Y=5.36+0.503X Medium maturing variety ; Y=5.41+0.456X Late maturing variety ; Y=5.80+0.494X Y=amount of evapo-transpiration. X=number of period. 11) Ratios of the total amount of evapo-transpiration to the total amount of evaporation by atmometer through all growing periods, are 1.23 for early maturing variety, 1.25 for medium maturing variety, 1.27 for late maturing variety, respectively. 12) Only air temperature shows high correlation in relation between amount of evapo-transpiration and climatic conditions from the viewpoint of Korean climatic conditions through all growing periods of rice plants. 2. Amount of percolation 1) The amount of percolation for computation of planning water requirment ought to depend on water holding dates. 3. Available rainfall 1) The available rainfall and its coefficient of each period during the growing season of paddy fields are shown in Table 8. 2) The ratio (available coefficient) of available rainfall to the amount of rainfall during the growing season of paddy fields seems to be from 65% to 75% as the standard in Korea. 3) Available rainfall during the growing season of paddy fields in the common year is estimated to be about 550 millimeters. 4. Effects to be influenced upon percolation by transpiration of rice plants. 1) The stronger absorbtive action is, the more the amount of percolation decreases, because absorbtive action of rice plant roots influence upon percolation(Table 21, Table 22) 2) In case of planting of rice plants, there are several entirely different changes in the amount of percolation in the forenoon, at night and in the afternoon during the growing season, that is, is the morning and at night, the amount of percolation increases gradually after transplantation to the peak in the end of July or the early part of August (wast or soil temperature is the highest), and it decreases gradually after that, neverthless, in the afternoon, it decreases gradually after transplantation to be at the minimum in the middle of August, and it increases gradually after that. 3) In spite of the increasing amount of transpiration, the amount of daytime percolation decreases gadually after transplantation and appears to suddenly decrease about head swelling dates or heading-flowering period, but it begins to increase suddenly at the end of August again. 4) Changs of amount of percolation during all growing periods show some variable phenomena, that is, amount of percolation decreases after the end of July, and it increases in end August again, also it decreases after that once more. This phenomena may be influenced complexly from water or soil temperature(night time and forenoon) as absorbtive action of rice plant roots. 5) Correlation between the amount of daytime percolation and the amount of transpiration shows high negative, amount of night percolation is influenced by water or soil temperature, but there is little no influence by transpiration. It is estimated that the amount of a daily percolation is more influenced by of other causes than transpiration. 6) Correlation between the amount of night percoe, lation and water or soil temp tureshows high positive, but there is not any correlation between the amount of forenoon percolation or afternoon percolation and water of soil temperature. 7) There is high positive correlation which is r=+0.8382 between the amount of daily percolation of planting pot of rice plant and amount and amount of daily percolation of non-planting pot. 8) The total amount of percolation through all growin. periods of rice plants may be influenced more from specific permeability of soil, water of soil temperature, and otheres than transpiration of rice plants.