10. cost in a multiproduct firm15 Ralph is toying with concepts of cost. A two product firm, with quantities denoted q1and q2, is being studied. Three distinct cost functions are being explored: (1) C1(q; P) = 10q1 + 5q2; (2) C2(q; P) =

6q1 + q2 1 + 8q2 + q2 2; and (3) C3(q; P) = 7q1 + 9q2 + q1q2.

(a) As a warm-up exercise, Ralph decides you should fill in the following table for each of the cost functions. (Incremental cost refers to the incremental cost of one additional unit of output.)

output total average cost marginal cost inc. cost q1 q2 cost of q1 of q2 of q1 of q2 of q1 of q2 100 50 60 50 40 50 30 10 30 50 30 70

(b) Plot each of the functions.

(c) Write a brief paragraph about your observations on this exercise.

(d) Also write a brief paragraph on each of the following two questions:
(i) what is the economic significance of nonlinearities in the cost functions; and (ii) what is the economic significance of interactions in a cost function (e.g., the q1q2 term in C3(q; P))?