Assume the role of the consultant hired to assist Cranston Coils in deciding whether or not to accept the offer that has been made.

Cranston Coils manufactures specialized metallic coils that are used in the construction of box spring mattresses. They have eighteen plants located primarily in Michigan, Texas and Washington. A new plant, considerably smaller than the others, was recently constructed in Connecticut and began operating this past March. Top level managers in Spokane, Washington, want to determine the cost structure of the new facility in order to more accurately anticipate its impact on cash flow. A team of staff economists was called in and told to estimate the various short-run cost equations (total cost, average cost, average variable cost and marginal cost). They are provided with data on the eighteen existing plants (the Connecticut plant is not included in the sample because of the possibility that minor technical problems which arose in April and May might distort the results), duplicated below. On the basis of the duality relationship between production and cost, the team decides that the best way to proceed is to determine the equation of the production function first. Then, using the equation of the production function, the cost equations will be derived algebraically by hand. Team leader Dhrymes approves the plan, stating "This approach will probably also make it easier to deal with the question of functional form since the statistical estimation of the production function is less complicated than that of the cost function. The Connecticut plant, which has a capital stock of 4100, is currently producing at the rate of 650 units of output per month and has enough orders in place to ensure continued operation at this level for the foreseeable future. The price of labor is $120 and the price of capital is $2.45. The cost per unit has been estimated by Brian Cella, the operations manager, as follows: Direct labor $66.19 Plant overhead $12.35 Administrative and selling expenses $ 3.11 TOTAL UNIT COST $81.65 A 20 percent mark-up ($16.33) is added to the unit cost in arriving at the firm's selling price of $97.98 (plus shipping). A 20 percent mark-up ($16.33) is added to the unit cost in arriving at the firm's selling price of $97.98 (plus shipping) In May, Cella was approached by a group of buyers from the Sleep Easy Company concerning the possible purchase of coils for delivery in August. Sleep Easy indicated that they would place an order for 50 units if the price did not exceed $70 each (plus shipping). Cella, unsure whether or not to accept the order, notified Spokane of the proposal and asked their advice. The chief accountant, after reviewing the facts, felt that the firm should not accept the order since price per unit was less than the total unit cost and contributed nothing to the firm's profits. Dhrymes, taking a break from the cost estimation project, happened to overhear the chief accountant and, turning from the water cooler, objected "There's nothing wrong with taking the order -- so long as the incremental revenue exceeds the incremental cost. In fact, I'm working on a project upstairs that should help you determine whether the order should be filled." Plant Labor 1 700 2 924 3 674.1 Output 1801 2128 1845 1792 2025 1506 2293 4 5 6 Capital 18890 16423 21268 14777 19041 15082 24194 10127 8042 23972 11668 12931 13115 27442 25000 738.2 812.6 650.3 851.3 486.9 575.7 7 8 1148 9 1109 2635 10 1024 11 12 1950 1477 1801 1755 900.6 615.2 783 13 14 606.4 15 1385 432.5 16 1644 18296 617.1 17 2105 17471 818.9 18 2201 15050 993.8 Cranston Coils manufactures specialized metallic coils that are used in the construction of box spring mattresses. They have eighteen plants located primarily in Michigan, Texas and Washington. A new plant, considerably smaller than the others, was recently constructed in Connecticut and began operating this past March. Top level managers in Spokane, Washington, want to determine the cost structure of the new facility in order to more accurately anticipate its impact on cash flow. A team of staff economists was called in and told to estimate the various short-run cost equations (total cost, average cost, average variable cost and marginal cost). They are provided with data on the eighteen existing plants (the Connecticut plant is not included in the sample because of the possibility that minor technical problems which arose in April and May might distort the results), duplicated below. On the basis of the duality relationship between production and cost, the team decides that the best way to proceed is to determine the equation of the production function first. Then, using the equation of the production function, the cost equations will be derived algebraically by hand. Team leader Dhrymes approves the plan, stating "This approach will probably also make it easier to deal with the question of functional form since the statistical estimation of the production function is less complicated than that of the cost function. The Connecticut plant, which has a capital stock of 4100, is currently producing at the rate of 650 units of output per month and has enough orders in place to ensure continued operation at this level for the foreseeable future. The price of labor is $120 and the price of capital is $2.45. The cost per unit has been estimated by Brian Cella, the operations manager, as follows: Direct labor $66.19 Plant overhead $12.35 Administrative and selling expenses $ 3.11 TOTAL UNIT COST $81.65 A 20 percent mark-up ($16.33) is added to the unit cost in arriving at the firm's selling price of $97.98 (plus shipping). A 20 percent mark-up ($16.33) is added to the unit cost in arriving at the firm's selling price of $97.98 (plus shipping) In May, Cella was approached by a group of buyers from the Sleep Easy Company concerning the possible purchase of coils for delivery in August. Sleep Easy indicated that they would place an order for 50 units if the price did not exceed $70 each (plus shipping). Cella, unsure whether or not to accept the order, notified Spokane of the proposal and asked their advice. The chief accountant, after reviewing the facts, felt that the firm should not accept the order since price per unit was less than the total unit cost and contributed nothing to the firm's profits. Dhrymes, taking a break from the cost estimation project, happened to overhear the chief accountant and, turning from the water cooler, objected "There's nothing wrong with taking the order -- so long as the incremental revenue exceeds the incremental cost. In fact, I'm working on a project upstairs that should help you determine whether the order should be filled." Plant Labor 1 700 2 924 3 674.1 Output 1801 2128 1845 1792 2025 1506 2293 4 5 6 Capital 18890 16423 21268 14777 19041 15082 24194 10127 8042 23972 11668 12931 13115 27442 25000 738.2 812.6 650.3 851.3 486.9 575.7 7 8 1148 9 1109 2635 10 1024 11 12 1950 1477 1801 1755 900.6 615.2 783 13 14 606.4 15 1385 432.5 16 1644 18296 617.1 17 2105 17471 818.9 18 2201 15050 993.8