Automakers can produce cars using machinery and labor. In particular, 50 cars can be produced using the

Question:

Automakers can produce cars using machinery and labor. In particular, 50 cars can be produced using the following combinations of machinery and labor:

(a) If you were to graph these points on a figure with Machinery on the horizontal axis and Labor on the vertical axis, what would you be graphing? In other words, what do these different combinations of inputs represent?
(b) Suppose machinery costs $30/machine, while labor costs $40/worker. How much would each of these combinations cost? Perform a similar calculation if machinery costs $50 and labor $40; and if machinery costs $70 and labor $40.
(c) What is the lowest-cost combination of machinery and labor when the price of machinery is $30 and the price of labor is $40? When machinery costs $50 and labor costs $40? When machinery costs $70 and labor costs $40?
(d) As the price of machinery rises relative to the price of labor, what happens to the relative amounts of machinery and labor that minimize cost?
(e) As the price of machinery increases, while the price of labor stays constant, what happens to the minimum possible total cost of producing 50 cars?
(f) Suppose that the use of machinery causes pollution, while the use of labor does not. Machinery costs $30/machine if environmental costs are not considered, but each machine causes $20/machine of environmental damage; labor still costs $40. The environmental damage does not harm the manufacturer. If there is no regulation concerning pollution, what input combination would the automaker use, and what would be the automaker's costs?
(g) If automakers had to pay for the damages associated with machine use, what input combination would they use, and what would be their costs?
(h) If the government instead used a standard to limit machine use to 4 machines, what input combination would automakers use, and what would be their costs?