5. large break-even and output calculations17 Ralph’s cost curve is piece-wise linear. For output of 0 ≤ q ≤ 1, 000 units it is given by C(q; P) = 1, 000 + 6q; for 1, 000 ≤ q ≤ 2, 000 it is given by C(q; P) = 3, 000 + 4q; and for 2, 000 ≤ q it is given by C(q; P) = −5, 000 + 8q.

(a) Plot Ralph’s cost curve.

(b) Suppose the selling price is
P = 7 per unit. Plot the implied total revenue curve on your graph in (a); also locate Ralph’s break-even point. Repeat for cases where the selling price is

P = 8 and
P = 9.

(c) Again assume the selling price is
P = 7. Locate Ralph’s optimal output.

(d) Now approximate Ralph’s cost curve with an LLA of 3, 000+4q;

notice this approximation is consistent with the optimal output chosen above as well as the original break-even calculation.

Suppose the selling price unexpectedly drops to
P = 4.8. Using the LLA of 3, 000 + 4q, calculate Ralph’s best choice of output

(somewhere between shutdown and a maximum of 2, 000 units).

(e) What mistake has Ralph made in part

(d) above?