Doublespeak Press has offered Mr. Hawthorne, a writer, a contract under which he

Question

Doublespeak Press has offered Mr. Hawthorne, a writer, a contract under which he would receive 50% of net profits from the sale of his book for which Doublespeak would have exclusive publishing rights. Publishing cost is 20Q. Currently demand is unknown, but thought to have equal likelihood of being

P = 100 – Q

      or                                                      P = 100 – (1/3)Q.

Additional market research will reveal the true demand curve prior to the time of publication, but it is unknown to both Doublespeak and Hawthorne at the time of the contract.

Hawthorne has current income of $100 and his von Neumann-Morgenstern utility index is:

                                                                  U = I1/2.

(a). How much can Hawthorne expect to receive under the Doublespeak offer?

(b). A competing publisher, Alpha Books, believes that by offering Hawthorne a fixed fee it can give up less of its expected profit than Doublespeak and yet offer Hawthorne a contract more favorable than that offered by Doublespeak. Is it possible? Explain. What is the minimum fee that Hawthorne would require to accept Alpha’s offer over that of Doublespeak?

(c). If Mr. Hawthorne’s von Neumann-Morgenstern utility index were

U = 12I,

would your answer to (b) change? Explain.

Explanation / Answer

(a)

P = 100 - Q or P = 100 - (1/3)Q

Expected demand = 0.50 x (100 - Q) + 0.5 x [100 - (1/3)Q] = 100 - (2/3)Q

Expected revenue, TR = P x Q = 100Q - (2/3)Q2

Marginal revenue, MR = 100 - (4/3)Q

Total cost, TC = 20Q

Marginal cost, MC = dTC / dQ = 20

Equating MR = MC:

100 - (4/3)Q = 20

(4/3)Q = 80

Q = 80 x 3/4 = 60

So, P = 100 - (2/3)Q = 100 - (2/3) x 60 = 60

So, TR = P x Q = 60 x 60 = 3,600

TC = 20Q = 20 x 60 = 1,200

Expected profit = TR - TC = 2,400

So, Expected income for Hawthrone = 50% x 2,400 = 1,200

(b)

This proposition is not feasible because, in order to make it possible, the demand has to be known with certainty to assess a fixed fee to be paid. But in this case, only the expected value of revenue and profit can be evaluated, therefore a fixed fee cannot be evaluated.

Hawthrone's current income = $100

Expected income = $1,200 [part (a)]

Total (expected) income = $1,300

This is the minimum fee that would be acceptable by Hawthrone.

[Utility = I1/2 = 13001/2 = 36]

(c) U = 12(I)

Since the utility function depends on expected value of profits, a change in N-M Utility index will not affect the decision.

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