Jennifer Trucking Company operates a large rig transportation business in Texas that transports locally grown vegetables to San Diego, California. The company owns 5 large rigs and hires local drivers paid fixed salaries monthly, regardless of the number of trips or tons of cargo that each driver transports each month. The below table presents details about the number of drivers and the total cargo transported by the company at different staff levels. Drivers employed Total Cargo Transported (tons) 1 2 3 4 5 6 7 8 Total Cargo Transported (tons) 5 12 21 32 40 46 51 50 a. Which inputs are fixed and which are variable in the production function of Jennifer Trucking Company? Over what ranges do there appear to be increasing, constant and/or diminishing returns to the number of drivers employed? b. What number of drivers appears to be most efficient in terms of output per driver? c. What number of drivers appears to minimize the marginal cost of transportation assuming that all drivers are paid the same salary?
1. Jennifer Trucking Company operates a large rig transportation business in Texas that transports locally grown vegetables to San Diego, California. The company owns 5 large rigs and hires local drivers paid fixed salaries monthly, regardless of the number of trips or tons of cargo that each driver transports each month. The below table presents details about the number of drivers and the total cargo transported by the company at different staff levels. Drivers employed Total Cargo Transported (tons) 1 2 3 4 5 6 7 8 Total Cargo Transported (tons) 5 12 21 32 40 46 51 50
a. Which inputs are fixed and which are variable in the production function of Jennifer Trucking Company? Over what ranges do there appear to be increasing, constant and/or diminishing returns to the number of drivers employed?
b. What number of drivers appears to be most efficient in terms of output per driver?
c. What number of drivers appears to minimize the marginal cost of transportation assuming that all drivers are paid the same salary?
2. Over the past 12 months the Four Winds Novelty Company firm has recorded its internet sales (equals monthly output levels) and its monthly total variable costs (TVC) for a particular novelty item as shown in the following table. Sales have grown over this period with relatively few shocks due to uncontrollable weather, political and sporting events. This online retailer carries no inventories; when it receives a pre-paid on-line order from a customer, it simply buys the product from a supplier and ships it out to the customer. Sales = Output 102,813 176,163 196,121 222,885 226,356 296,416 378,446 450,666 579,696 607,082 624,680 636,133 TVC ($) 201,953 340,608 377,940 432,863 441,714 629,267 867,596 1,103,807 1,701,125 1,917,861 2,195,352 2,479,195
a. Using regression analysis, find an equation that best fits the data to represent the TVC function.
b. At what sales/output level will marginal costs (MC) reach a minimum?
c. Estimate the value of TVC for sales/output level 250,000 units, and calculate the 95% confidence interval for your estimate.
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