Question

Anne and Beth work for NET Financial (firm that sells Economic Forecasting Services - EFS). Their productivity measures and constraints per 40 hour work week are: Anne is capable of selling 10 EFS contracts she is capable of underwriting 20 EFS contracts; Beth is capable of selling 32 EFS contracts she is capable of underwriting 40 EFS contracts. Commission on the sale of an EFS contract is $500 per contract, and the underwriting fee for an EFS contract is $1000. To receive payment, the forecasting contract has to be sold and underwritten in the same week. What is the Maximum amount Anne and Beth can make per week working alone? What is the Gain from Cooperation if they trade services? What happens to the Dead Weight Loss if they cooperate? Explain the compensation payment necessary between Anne and Beth to get Cooperation? Show your table of calculations.

Answer 1

Working alone

Since to receive payment forecasting contract has to be sold and underwritten in the same week

Anne can receive payments for 10 forecasting contract in which she is able to sell and underwrite. Payment earned in a week = 10 * (1000+500) = $ 15000. Note - Selling contracts is a bottleneck for Anne.

Similarly, Beth is capable of receiving payment for 32 forecasting contracts. Payment earning in a week = $32 *1500 = $48000

Now, let's assume they can cooperate.

Anne focuses solely on underwriting contracts, in this case, she can underwrite 40 EFS contracts per week.

(ratio of selling to underwriting is 1:2, hence if Anne let's go of selling part, she can do twice as much underwriting, 20 underwriting done for 10 selling let go)

For every 10 contracts Beth underwrites, she can sell 8. Beth distributes her ~83.5% of the time of the week in selling. In that case, Beth will be able to sell, 83.5% of 64 = 53 contracts and underwrite 13 contracts

(If Beth solely focuses on selling, she can sell a total of 64 contracts, addition of 32 contracts sold for letting go of 40 underwriting work)

Collectively, both can underwrite 53 (40+13) contracts and sell 53 contracts.

AMount earned = 53*1500 = 79500

Gain = 79500 - 48000 - 15000 = $16500

The dead weight loss due to inefficiency by working alone reduces.

Maximum contracts that can be sold and underwritten alone = 10 + 32 = 42

Extra contracts that are fulfilled due to collaboration = 53-42 = 11

So, payment of these 11 contracts must be divided equally and added to individual earning capacity.

Hence Anne earns = 15000 + 11/2 * (1500) = 15000 + 8250 = 23250

Beth earns = 48000 + 8250 = 56250