Cost Equation: Suppose that the cost of making 20 cell phones is $6800 and the cost of making 50 cell phones is $9500.

Question

(a) Find the cost equation.

(b) What is the fixed cost?
(c) What is the marginal cost of production?

(d) Draw the graph of the equation.

Answer 1

(2, 68), (5, 95) = (phones, cost) =(p, C) with phones measured in 10's, cost in $1000's

the two points graphically have slope (95-68)/(5-2) = 27/3 = 9

C = 9p + FC with FC = fixed cost = y or C intercept (0, FC)

plug in either point to solve for FC

68 =9(2) + FC

FC = 68-18 = 50 = $50,000 = fixed cost

Total Cost = C = 9p + 50

Marginal Cost = derivative of C = C'(p) = 9 = $9,000

the graph is a steep upward sloping straight line, starting at (0, 50) the y or C intercept