Question

1. Consider the following equations: T B = 314X − 1.6X2 MB = 314 − 3.2X T C = 50X + 1.7X2 MC = 50 + 3.4X a) Calculate total benefit, total cost, marginal benefit, and marginal cost for values of X ranging from 35 to 45. b) Graph total benefit and total cost on one graph, and marginal benefit and marginal cost on the other graph. c) Find the optimal value of X.

Answer 1

TB = 314X − 1.6X²

MB = 314 - 3.2X

TC = 50X + 1.7X²

MC = 50 + 3.4X

a)

X	TB	MB	TC	MC
35	9030.00	202.00	3832.50	169.00
36	9230.40	198.80	4003.20	172.40
37	9427.60	195.60	4177.30	175.80
38	9621.60	192.40	4354.80	179.20
39	9812.40	189.20	4535.70	182.60
40	10000.00	186.00	4720.00	186.00
41	10184.40	182.80	4907.70	189.40
42	10365.60	179.60	5098.80	192.80
43	10543.60	176.40	5293.30	196.20
44	10718.40	173.20	5491.20	199.60
45	10890.00	170.00	5692.50	203.00

b)

12000.00 11000.00 10000.00 9000.00 TB & TC 8000.00 7000.00 6000.00 5000.00 -TB ---TC 4000.00 3000.00 2000.00 1000.00 35 36 37 38 39 40 41 42 43 44 45 46

210.00 200.00 190.00 MC MB 180.00 MB MC 170.00 160.00 150.00 35 36 37 38 39 40 41 42 43 44 45 46 х

c) The optimal value of X is where MB = MC. From the table and graph it is seen that the optimal value of X is 40.