Transcript Example 7.2

Example 7.2
Pricing Models
Background Information

We continue looking at the Madison company, but we
now assume that Madison manufactures its product
in the United States and sells it in Germany.

Given the prevailing exchange rate in dollars per
Deutsche Mark (DM), Madison wants to determine
the price in DM it should charge in Germany so that
its profit in dollars is maximized.

The company also wants to see how the optimal
price and the optimal profit depend on exchange rate
fluctuations.
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PRICING2.XLS

The model appears on the next slide.

This file can be used to build the model.

It is very similar to the previous model, so we will
highlight only the new features.

The exchange rate in the ExRate cell indicates the
number of dollars required to purchase one DM.

As this exchange rate decreases, we say that the
dollar gets stronger; as it increases, the dollar gets
weaker.

The model development is straightforward.
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Developing the Model

To develop this model, proceed as follows.
– Inputs. The inputs for this model are the unit cost (in
dollars), the exchange rate, and the parameters of the
company’s demand function for the German market. These
latter values would need to be estimated exactly as we
discussed in the previous example. We chose them
arbitrarily for this example.
– Unit cost in DM. Although Madison’s unit cost occurs in the
United States and is expressed in dollars, it is convenient to
express it in DM. Do this in the UnitCostDM cell with the
formula =UnitCost/ExRate.
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Developing the Model –
continued
– Price, demand. As in the previous example, enter any price
in the Price cell (now it is in DM), and calculate the demand
from the demand function.
– Profit. The profit should be in dollars, so enter the formula
=(Price*ExRate-UnitCost)*Demand in the Profit cell. Note
that the unit cost is already in dollars, but the revenue from
German sales needs to be converted to dollars.
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Using the Solver

The Solver dialog box is set up exactly as before,
except that the constraint on price is now
Price>=UnitCostDM, so that DM are compared to
DM.
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Solution – continued
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The optimal solution, with an exchange rate of 0.63,
says that Madison should charge about 136 DM per
unit in Germany.

This will create demand for about 209 units, and the
profit in dollars will be approximately $7450.
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Sensitivity Analysis

What happens when the dollar gets stronger or
weaker?
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We use SolverTable with exchange rate as the single
input, allowing it to vary from 0.50 to 0.90 in
increments of 0.05, and we keep track of price,
demand, and profit.

As the results showed, as the dollar strengthens,
Madison charges more in DM for the product, but it
obtains a lower profit.
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Sensitivity Analysis – continued
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The opposite is true when the dollar weakens.
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Are these results in line with your economic intuition?
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Note that when the dollar strengthens, DM are not
worth as much to an American company.
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Therefore, when we convert the DM revenue to
dollars in the profit cell, the profit tends to decrease.

But in this case, why does the optimal price in DM
increase. We’ll say no more here – except that this
should be a good question for discussion.
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