Question

Could someone help with 4B? I would like a fresh new answer please.

4. (10 pts.) Assume two changes to the fast food industry: 1) a new machine that allows customers to make their own orders at the counter has been introduced (rental rate = $25/hr), and 2) fast food works finally convinced congress to pass a law mandating a $15 minimum wage (w = $15/hr). As a manager of McDonalds, you are interested in your optimal input mix for taking food orders and your food order production is: Q = 25K - 10K2 - KL + 6L - 0.2L2 a. What are the equations for APK and MPK? b. Assuming each McDonalds can only purchase 1 machine and that the average order from McDonalds is worth $5 (that is, P=$5), what is the optimal number of workers to hire? How much output is produced? What is the profit? c. Would you prefer 0, 1, or 2 machines? Explain.

Answer 1

42 Production function is Q=25k-lok²_K2+62-0.22² 62 Now, marginal product of labor (MPL) 22- -*+6-0:42 and Marginal product of capital (MPK) = 24 - 25- 20k - 2 Now, et in me Donald purchases only 1 machine then K= 1 Now optimal input mir condition is gum by: where w= hage rate = $15 the $25/hr andmscapar rental rate - $45th. $ 15/hr.

NOWO 2S -k 76-0.42 = 21 25-20k-2 - To Now substituting k=1 we qet! - » -146-0142 25=120217-2 - - => 5o me can 15- 12L = 25-52 a> -10 --3.82 1. =) L= 2.6 tuce the optimal run by of worku s will be 2=2.6. output will be froud by substituting L=2.6 and kal in the production functions Q = 85k-10K--K2+62-0.242 = Q = 25 (1) - 10/19 (1x 2.6) +(6x2.6) -0.21206)2 Q5 - 10-2'6 + 65 15.6 - 1.352 = 26.648 in'ts a 26.6 mit P= 45Pp ## we be: T = To tal reue une- To tal cosa Total costa whtok дии 1 Now 2*2 (5x 2.6) +(1541) Scanned with CamScanner 80

Now, total revenue = PxQ = $( 5 X 26.6) E $33 Profit will be Now, Total cosa = To tal revime - = $ (133-80) = $ 53 Scanned with CamScanner