Suppose that the production function for Alfred Barbuda, a producer of fine violins, is given by the following: Q = 10K0.5L0.5.
a. Suppose that Alfred is currently using 1 unit of capital. If he hires 4 workers, how many violins will they produce?
b. Suppose that Alfred is currently using not 1, but 2 units of capital. How many workers must he hire to match the level of production you found in (a)?
c. Rework your answer to (b), assuming that Alfred is currently using 4 units of capital.
d. Plot the combinations of labor and capital you found in (a - c) as a production isoquant.
e. (A test of your math skills) A change in capital technology alters Alfred's production function. Now Alfred's output is given by Q = 10 K0.7L0.3. If Alfred employs 3 workers, how many machines will he have to use to achieve the production level you found in (a)? What happens to the isoquant you drew?