(a) Using the Production function defined in (1) derive how much it would cost the firm to produce a particular level of production y. That is, find the cost function C(w, y).
(b) The video defines the Marginal Cost function of the firm (MC(w,y)) as how much it costs to produce an additional unit of output. Find the marginal cost function.
(c) Assume that w = 1 and represent MC(w,y) in a graph with y in the horizontal axis and $ in the vertical axis. Is the Marginal Cost function decreasing or increasing? How does this relate to the decreasing Marginal Product of x function we saw in part (1)?
(d) Calculate y∗ if w = 1 and p = 3. Draw this solution in the graph you made in part (b) by drawing an horizontal line representing p = 3 and identifying the firm’s optimal choice of output as the point in the graph where p = MC.
(e) Calculate y∗ if w = 1 and p = 6. Draw this solution in a graph as that in point (b).
(f) Calculate y∗ if w = 4 and p = 6. Draw this solution in a graph as that in point (b)
(g) We now ask you to forget about particular values of p and w. Following the method explained in the second video derive the optimal supply of output y∗(p,w).