Problem
Deriving cost curves, verbal description of production. (9 points) Joey operates a lemonade stand. His cost of the lemons, sugar, and water per glass is $0.15. Joey's fixed cost is $180. Joey sells five glasses of lemonade per hour.
(a) When he was eight years old, Joey had a near zero opportunity cost of time. What was Joey's total cost function, T C(Q) where Q represents the number of glasses of lemonade?
(b) Joey is now 17. If he were not selling lemonade, he would be working the first six hours a day at $6 per hour and he would be spending the remainder of the day with his friends. Joey's total value of the time he spends with his friends, t, is 6t + t 2 , where time is measured in hours. Assuming that the descripion of his lemonade business continues to hold, what is Joey's total cost function T C(Q)? The total cost function should be a function of numbers and Q alone, which means you should substitute out for t.
HINT: The total cost funtion will have 2 pieces, when Q = Qthreshold matching what happens when Joey sells for 6 hours or less and when Q > Qthreshold matching what happens when he sells for more than 6 hours. For each piece, consider the opportunity costs in terms of glasses of lemonade (in addition to the costs in part (a)).
The response should include a reference list. Double-space, using Times New Roman 12 pnt font, one-inch margins, and APA style of writing and citations.