Example 7.2 Pricing Models

| 7.3 | 7.4 | 7.5 | 7.6 | 7.7 | 7.8 | 7.9 | 7.10 | Background Information n 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. n 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. n The company also wants to see how the optimal price and the optimal profit depend on exchange rate fluctuations.

| 7.3 | 7.4 | 7.5 | 7.6 | 7.7 | 7.8 | 7.9 | 7.10 | PRICING2.XLS n The model appears on the next slide. n This file can be used to build the model. n It is very similar to the previous model, so we will highlight only the new features. n The exchange rate in the ExRate cell indicates the number of dollars required to purchase one DM. n As this exchange rate decreases, we say that the dollar gets stronger; as it increases, the dollar gets weaker. n The model development is straightforward.

| 7.3 | 7.4 | 7.5 | 7.6 | 7.7 | 7.8 | 7.9 | 7.10 |

| 7.3 | 7.4 | 7.5 | 7.6 | 7.7 | 7.8 | 7.9 | 7.10 | Developing the Model n 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.

| 7.3 | 7.4 | 7.5 | 7.6 | 7.7 | 7.8 | 7.9 | 7.10 | 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.

| 7.3 | 7.4 | 7.5 | 7.6 | 7.7 | 7.8 | 7.9 | 7.10 | Using the Solver n 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.

| 7.3 | 7.4 | 7.5 | 7.6 | 7.7 | 7.8 | 7.9 | 7.10 | Solution – continued n The optimal solution, with an exchange rate of 0.63, says that Madison should charge about 136 DM per unit in Germany. n This will create demand for about 209 units, and the profit in dollars will be approximately $7450.

| 7.3 | 7.4 | 7.5 | 7.6 | 7.7 | 7.8 | 7.9 | 7.10 | Sensitivity Analysis n What happens when the dollar gets stronger or weaker? n 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. n As the results showed, as the dollar strengthens, Madison charges more in DM for the product, but it obtains a lower profit.

| 7.3 | 7.4 | 7.5 | 7.6 | 7.7 | 7.8 | 7.9 | 7.10 | Sensitivity Analysis – continued n The opposite is true when the dollar weakens. n Are these results in line with your economic intuition? n Note that when the dollar strengthens, DM are not worth as much to an American company. n Therefore, when we convert the DM revenue to dollars in the profit cell, the profit tends to decrease. n 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.