9781118041581

Summary 665

remaining three cells. The placement of the 1 (a so-called dummy

variable) specifies the exact agreement. For instance, putting the 1 in

cell C7 indicates high-quality engines under full warranty. Similarly, put

a 1 in cell C12, C13, orC14 to indicate the delivery schedule. Then

compute company U’s profit (cell K13) according to the formula

This formula works because all zero-valued dummies disappear, leaving

only the values (238 plus 18) for the actual agreement. Company B’s

profit is computed as its revenue payment minus its cost by an

analogous formula.

b. Find the zone of agreement by maximizing company U’s profit subject

to company B’s profit being equal to 0, and vice versa. Use your

spreadsheet’s optimizer, listing U’s payment and the seven dummy

variables as the adjustable cells. Include the constraints that all dummies

must be greater than or equal to 0. In addition, the sum of the first four

dummies (computed in cell K8) must equal 1, and the sum of the last

three dummies (computed in cell C16) must also equal 1. Finally, do not

forget the constraint that one firm’s profit is equal to 0.

c. Find one or more points on the efficient frontier, setting one

company’s profit equal to a positive value and maximizing the other’s

profit. What agreement terms are efficient? Explain.

C12D12C13D13C14D14) 2 H13.

(C7D7C9D9I7G7I9G9

ABCD EFG H IJ K L M

1

2 A BRITISH-AMERICAN CONTRACT

3

4 Warranty

5 Quality Full Partial

6 Co U Co B Co U Co B

7 High 1 238 68 180 42 0 Sum

8 1

9 Low 0 178 24 92 18 0

10

11 Delivery Co U Co B U’s Payment to B Co U’s Co B’s

12 2 Years 1 18 10 (Pounds) Profit Profit

13 3 Years 0 00 110 36 32

14 5 Years 0  24  18

15

16 Sum 1

17

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