Summary 271equal QF). However, total production must match total sales:
QHQFDHDF.
a. Create a spreadsheet (based on the accompanying example) to model
the firm’s worldwide operations. Find the firm’s profit-maximizing
outputs, sales quantities, and prices. Are chips shipped overseas?
(Hint:The key to maximizing profit is to find sales and output
quantities such that MRHMRFMCHMCF. Also note that MCH
is constant. When using your spreadsheet’s optimizer, be sure to
include the constraint that cell F9—extra output—must equal zero.
That is, total sales must exactly equal total output.)
b. Answer the questions in part (a) under an “antidumping” constraint;
that is, the company must charge the sameprice in both markets.
(Hint:Include the additional constraint that cell F12, the price gap,
must equal zero.)
S3. The accompanying spreadsheet depicts the pricing options (cells C10
and C18) for a best seller that is released in hardback and as an e-book.
The demand curve for the hardback version is described by the
equation: Q 80 2.4P 2PE, where PEdenotes the e-book price. In
turn, the demand curve for the e-book is given by: QE 80 4PE. (Both
quantities are denominated in thousands of units.) Note that lowering
the e-book price by $1.00 increases e-book sales by 4 thousand units but
also reduceshardbook sales by 2 thousand books. In short, each
additional e-book sold replaces .5 hardback sales.
The profit cells are calculated based on the economic facts noted
earlier in the chapter. (1) Revenues for the e-book are split 70–30
between book publisher and online seller. The marginal cost of
producing and delivering additional e-books is essentially zero. (2)
Revenues for the print book are split 50–50 between the book publisher
and the book retailer. The publisher incurs $3.50 per hardback in
production and related costs. (3) For both book types, the publisher pays
a 15 percent author royalty based on total retail revenue.
a. Re-create the spreadsheet shown. If e-books did not exist (set
PE$20 so that QEis 0), what is the publisher’s profit-maximizing
hardback price?
b. Before 2010 when Amazon was free to set the e-book price, what price
should Amazon have set? In response, what is the publisher’s profit-
maximizing price for the hardback?
c. Alternatively, if the publisher sets both book prices, what are the
optimal prices? Why does the publisher prefer a higher e-book price
than the online seller?
d. Suppose that each e-book sale replaces onehardback sale. This
cannibalization rate is described by the hardback demand curve:
Q 40 2.4P 4PE. Using this demand curve, re-answer the
questions in parts (b) and (c). Confirm that this worsens the pricingc06CostAnalysis.qxd 9/29/11 1:46 PM Page 271