For each of the following examples, draw a representative isoquant. What can you say about the marginal rate of technical substitution in each case?
A firm can hire more workers to increase its output, or it can buy more machines. For each additional machine, the firm requires fewer workers per machine to maintain the same level of output.
A firm finds that it can always substitute 4 units of labor for 1 unit of capital and still keep output constant. After having drawn the graph, suppose the price of 1 unit of capital is 10 and that of labor is 2 dollars. What is the firm’s optimal combination of labor and capital in the production process?
A taxi firm requires exactly three full-time drivers to operate each car during a 24 hours interval. After having drawn the graph, suppose the firm’s yearly budget is 240,000 dollars, and the price of 1 car is 60,000 and the yearly salary of a driver after deductions is 20,000 dollars. What is the firm’s optimal combination of cars and drivers given its cost constraints and prices?