# Optimal Pricing Strategies

(See attached file for full problem description)

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Problem 7:

In your job overseeing pricing and marketing of software for a major U.S. manufacturer of software (Macrotuff), your staff develops the following data on the willingness to pay for two of your products (Doors and Traveler) for three groups of potential customers in two different countries, the United States and Japan. Given cultural differences, the different groups have different values for willingness to pay for each program. The number of people is the same in each group.

U.S. Market Japanese Market .

Doors Traveler Doors Traveler

Group 1 $90 $15 Group A 6500 Y 5500 Y

Group 2 $60 $30 Group B 5000 Y 5000 Y

Group 3 $50 $45 Group C 3500 Y 3500 Y

The marginal cost of producing Doors is zero and the marginal cost of Traveler is zero. Assume that the market segments are so different that people in one market do not know what is going on in the other segment. That is they don't know the goods are the same and that they might potentially have different prices in each market. Assume that the current exchange rate is 100 yen per dollar.

Questions:

1. Considering just separate pricing or pure bundling, what is the profit-maximizing pricing strategy in the U.S.? What is the U.S.-market profit from this strategy in dollars? Tell me the optimal dollar price/prices for the optimal strategy. If there is no difference between separate pricing and pure bundling, then go with separate pricing.

2. Considering just separate pricing or pure bundling, what is the profit-maximizing pricing strategy in Japan? What is the Japanese-market profit from this strategy in dollars? Tell me the optimal yen price/prices for the optimal strategy. If there is no difference between separate pricing and pure bundling, then go with separate pricing.

3. If the two markets are not separate and people in one market know the prices, know that the products are the same in the two markets and can buy products in one market and ship them to the other market at zero cost, then how will the pricing schemes given above work? That is, if the markets are not segmented and you keep the prices given in your answers to 1 and 2 above, then who will pay what and what will be the dollar profit in the two markets combined? Assume that all people pick a product (or a bundle of products) in order to maximize their consumer surplus.

4. If the markets are not segmented and customers know the prices in the other market and can buy from the other market, then what is the optimal pricing scheme? Only consider separate pricing and pure bundling. What is the dollar profit for Macrotuff in this case?

Problem 8:

You produce a good in a competitive market in which the price doesn't change.

Your firm has the following monthly variable cost curve for production:

VCP = 5 Q + .025Q2,

where Q is the total production in a month (in thousands) and VCP is in thousands of dollars.

Although the price is stable, the number of orders for your product varies from one month to the next. In particular, the following is a list of the possible monthly demands and their probabilities.

Quantity Demanded (Q) Probability

100 .25

150 .25

200 .25

250 .25

Part 1:

a. What is the expected variable cost of production if you produce exactly what is demanded in each month? Hint: Answer this question the same way you would if there were only two possibilities, but now take the expected value over the four possible values instead.

b. If your demand were a constant equal to the expected demand, how much would your expected variable cost be per month?

Part 2:

You have estimated that you could add a warehouse that would allow you to smooth production in an effort to save production costs. The fixed cost of the warehouse is $50,000 per month. You have also estimated that the variable costs to running the warehouse depend upon the number of units you move in and out of the warehouse in a month. Specifically, the monthly variable cost is

VCI =.01 I2,

where I is the number of units (in thousands) you either move into the warehouse or the number of units you move out of the warehouse in a month. VCI is also in thousands of dollars.

Questions:

c. If you choose to smooth production and just produce the average demand each month, then what are the potential values of I and their probabilities given the variation in demand from Part 1?

d. Given your answer to c), what is the expected total warehousing cost per month?

e. Should you smooth production and invest in the warehouse? Why or why not?

Problem 9:

You work for a Korean manufacturer of personal computers. Currently your firm makes this product for sale in Korea and in the U.S. There are only minor differences in the models sold in Korea versus those in the US (the labeling is in Korean for one and in English for the other). However, there is no cost differential between the two models. In fact, both models are produced at the same factory and the marginal cost of producing one more of either model depends solely on the total amount (Korean models plus US models) produced. Most (all but one) of the components (labor and materials) come from Korea. However, one of the components comes from Japan.

The current exchange rates are 1200 won per dollar and 10 won per yen. At these current exchange rates, the total cost curve for your company is

TC = 240,000Q + 1,200Q2,

where Q is in thousands and TC is in won. Assume transportations costs are zero.

The demand curves for your product is given by the following:

Demand in Korea: PK = 960,000 - 4,800QK,

where PK is the price in won and QK is the quantity in thousands.

Demand in the U.S.: PU = 600 - 2QU,

where PU is the price in dollars and QU is the quantity in thousands.

Assume that if exchange rates change, the demand curves expressed in their home currency do not change.

Questions:

1. At the current exchange rates, what is the optimal production plan and pricing scheme for your product? What are your profits in won?

PK = ________________________ won, QK = ___________________________.

PU =____________________________$, QU = ___________________________.

Profit = ___________________________________won_.

2. The dollar devalues relative to the won with the exchange rate dropping to 1000 won per dollar. The exchange rate between won and yen, however, stays at 10 won per yen. How does the change in the exchange rate affect the optimal production and pricing plan? Indicate the appropriate answers below for each of the following variables. For each variable circle one answer. Explain all of your answers.

a. Dollar Price in US Increases Decreases Stays the same Can't tell

b. Won Price in Korea Increases Decreases Stays the same Can't tell

c. Output sold in US Increases Decreases Stays the same Can't tell

d. Output sold in Korean Increases Decreases Stays the same Can't tell

e. Total output Increases Decreases Stays the same Can't tell

f. Profit (in won) Increases Decreases Stays the same Can't tell

3. For this question, assume that the exchange rate between the won and the dollar did not change and is still 1200 won per dollar. Instead, the exchange rate between won and yen changes. In particular, the yen appreciates relative to the won. How does this affect the optimal pricing and production policy? Indicate the appropriate answers below for each of the following variables. For each variable circle one answer. Explain your answers.

g. Dollar Price in US Increases Decreases Stays the same Can't tell

h. Won Price in Korea Increases Decreases Stays the same Can't tell

i. Output sold in US Increases Decreases Stays the same Can't tell

j. Output sold in Korean Increases Decreases Stays the same Can't tell

k. Total output Increases Decreases Stays the same Can't tell

l. Profit (in won) Increases Decreases Stays the same Can't tell

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#### Solution Summary

Maximizing profit given different market conditions.