Suppose that the production function for fine violins is given by the following: Q = 10K^.5 L^.5
(a) Suppose that the firm is currently using 1 unit of capital. If they hire 4 workers, how many violins will they produce?
(b) Suppose that now the first is currently using 2 units of capital. How many workers must the firm hire to match the level of production you found in (a)?
(c) Redo part (b), with the assumption that the firm is now employing 4 units of capital?
(d) Plot the combination of labor and capital you found in (a-c) as a production isoquant?
(e) A change in technology results in the production function becoming: Q = 10K^.7L^.3. If the firm employs 3 workers, how many machines will they have to use to achieve the production level you found in (a)? What happens to the isoquant you drew?