Production functions, graphically. Suppose that a biotech firm makes diagnostic tests and has a fixed-proportions production function in which one unit of output (diagnostic test) is produced using one worker and two units of capital (machines). If the firm has an extra worker and no more capital, it can produce only one unit of output. Similarly, one more unit of capital with no extra labor produces no extra output.
(a) Draw 3 isoquants for this production function with labor on the horizontal axis. Label each with the associated total production. That is, label each with the appropriate Q = #. 1
(b) In the short run, the firm has 8 units of capital. Draw the short run production function and provide its formula. Hint: there will be two pieces.
(c) On a separate graph from part (b), draw the marginal product of labor and provide its formula. Again, this will have two pieces.
(d) On the same graph as part (c), draw the average product of labor and provide its formula. Again, this will have two pieces.