13.10 In Example 13.3, we computed the general short-run total cost curve for Hamburger Heaven as STC
4v  .

a. Assuming this establishment takes the price of hamburgers as given (P), calculate its profit function (see the extensions to Chapter 13),
* (P, v, w).

b. Show that the supply function calculated in Example 13.3 can be calculated as
*/P 

q (for w  v  4).

c. Show that the firm’s demand for workers, L, is given by 
*/w.

d. Show that the producer surplus calculated in Example 13.5 can be computed as 
P*
0
*/Pdp for w
v
4.

e. Show how the approach used in part

(d) can be used to evaluate the increase in producer surplus (and in short-run profits) if P rises from $1 to $1.50.