Question 5 (1) and (2)

Question 5 Brawndo Corp. is the monopoly producer of Brawndo an electrolyte rich energy drink (\"it has what plants crave'). It is produced using a combination of labor and electrolytes. If L denotes the amount of labor (measured in hours) used and E the number of gallons of electrolytes, Brawndo's production function is f (L, E) = min{L, E} Each gallon of electrolytes costs Brawndo Corp. $1 dollar per gallon to purchase. The supply of labor in the city in which Brawndo Corp.'s manufac- turing facility is located, increases with the hourly wage offered. If Brawndo Corp. were to offer a wage of 71) per hour, it will be able to acquire aw hours of labor where a > 0, is a constant to be specied later. Brawndo Corp. does not sell its energy drink directly to consumers but through a retailer, Buy More, at a wholesale price of a per gallon of Brawndo. BuyMore in turn sets the price per gallon to the nal consumer. The inverse demand curve for Brawndo that BuyMore faces is p(q) = 1000.5q where q is the quantity of Brawndo supplied by BuyMore. Selling Brawndo at the retail level also requires labor. For every unit of Brawndo that Buy- More sells it must employ half an hour of labor. The supply of labor that BuyMore has access to, differs from the one that Brawndo Corp. pulls from. The supply of labor hours that BuyMore faces increases with the hourly wage offered. If BuyMore were to offer a wage of 11) per hour, it will be able to acquire 0.51:; hours of labor. 1. Determine Brawndo Corp.'s cost function. Specically, if Cl(h) is the minimum cost in curred to produce h units of Brawndo, what is 01(h) as a function of h and a. If done correctly, for a = 1, you should have 01 (0.5) = 0.75. 2. Determine BuyMore's cost function. Specically, if 02(q) is the minimum cost incurred to sell (1 units of Brawndo, what is 02(q) as a function of q and u. If done correctly, for u = 1, you should have 02(2) = 4