A US firm (company U) is negotiating to buy aircraft engines from a British firm (company B). Under discussion is the price to be paid (in British pounds), quality (high or low), warranty (full or partial), and the delivery schedule (two, three, or five years). The spreadsheet that follows shows company U’s values in dollars and company B’s costs in British pounds for possible agreements. For instance, delivery of high-quality engines under full warranty in two years implies a cost (in pounds) to company B of 68 + 10 = £78 million. Company B receives £110 million (cell H13), implying a profit of 110 – 78 = £32 million (cell L13). In turn, company U’s value (in dollars) for the deal is $238 + $18 = $256 million. The exchange rate is $2 for each pound. Thus, company U’s final profit is 256 – (2)(110) = $36 million (cell K13).

a. Create a spreadsheet similar to the sample spreadsheet given. Put the numerical value of 1 in cell C7, C9, I7, or I9, and put zeros in the 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, or C14 to indicate the delivery schedule. Then compute company U’s profit (cell K13) according to the formula

= (C7*D7 + C9*D9 + I7*G7 + I9*G9

+ C12*D12 + C13*D13 + C14*D14) − 2*H13.

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.

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CID E|F| G 1|J| K LIM A BRITISH-AMERICAN CONTRACT Warranty Quality Full Partial CoUCo B 42 High 23868 180 Sum Low 0178 24 92 10 Delivery 2 Years1 3 Years00 5 Years -2418 Co U Co B U's Payment to B Co U's Co B's ProfitProfit 12 13 14 15 16 17 (Pounds) 110 36 32 Sum1