This is an MBA-level Managerial Economics course. I am working on a homework assignment and have a couple problems that I don't really know how to get started. Here is another:

Assume that a drug manufacturer sells a major drug in Europe and the U.S. Because of legal restrictions, the drug cannot be bought in one country and sold in another. The demand curve for the drug in Europe is:

Pe = 10 - Qe

where Pe is the price (in dollars per pound) in Europe and Qe is the amount (in millions of pounds) sold there. The demand curve for the drug in the U.S. is:

Pu = 20 - 1.5Qu

where Pu is the price (in dollars per pound) in the United Statees and Qu is the amount (millions of pounds) sold there. Marginal costs are a constant $2 for all quantities sold. Assume that fixed costs are zero.

a. Calculate the optimum price, quantity, and profit for the firm if price discrimination is not possible and Pe = Pu.

b. Now assume that the firm can price discriminate in the two markets and charge separate prices in the two markets. Compare optimum prices, quantities, and resulting profits. Compare the total profits for both cases. Provide an explanation for the different pricing strategies when price discrimination is possible.

If someone could at least tell me where to get started (i.e. how to approach the problem, etc.) I would greatly appreciate it. Thanks!

First b)

Always, always, always -- maximize profits where MC=MR. In Europe, MR is 10-2Qe. As MC=2, then 2=10-2Qe. Solve for Qe. Repeat for US, cept MR=20-3Qu

Now then a gets a little tricky as there is a kink in the demand curve. For P above 10, the combined demand is simply the US demand curve. At 10, Q=6,66667. For each $ drop below 10, total output goes up by 2.5 So, the slope of the demand line is 1/2.5 = 0.4 -- which means that if extended back to the y-axis, the line would cross the y-axis at 10+(6.6667*.4) = 12.6667. So, MR for the combined case is 12.6667-5Q. Solve for Q

Ok, so for Question B, would these answers be right?

Europe:
MC = MR
2 = 10 - 2Qe
2Qe = 8
Qe = 4

Pe = 10 - Qe
Pe = 10 - 4
Pe = 6

Profit:
10Qe - Qe^2 - 2Qe
8Qe - Qe^2
8(4) - 4^2
32 - 16
$16

So, Europe should produce 4 million pounds of the drug & charge $6/pound. Total profit would be $64,000,000 ($16/pound x 4 million pounds).

US:

MC = MR
2 = 20 - 3Qu
3Qu = 18
Qu = 6

Pu = 20 - 1.5Qu
Pu = 20 - 1.5(6)
Pu = 11

Profit:
20Qu - 1.5Qu^2 - 2Qu
18Qu - 1.5Qu^2
18(6) - 1.5(6)^2
108 - 1.5(36)
108 - 54
$54

So, the US should produce 6 million pounds of the drug & charge $11/pound. Total profit would be $324,000,000 ($54/pound x 6 million pounds).

I just wanted to make sure I used the information you gave me correctly on this part of the question. Thanks! :)

To approach this problem, we need to first understand the concept of price discrimination. Price discrimination refers to the practice of charging different prices to different groups of customers for the same product or service, based on their willingness to pay. In this case, the firm has the ability to sell the drug at different prices in Europe and the U.S.

a. First, let's consider the scenario where price discrimination is not possible. This means that the price in Europe (Pe) is equal to the price in the U.S. (Pu). In this case, we need to find the optimal price, quantity, and profit for the firm.

To do this, we can start by finding the demand and marginal revenue functions for each market:

In Europe:
Demand: Pe = 10 - Qe
Marginal Revenue: MR = ∂TR/∂Qe = ∂(Pe * Qe)/∂Qe = Pe - Qe (∂ symbol denotes partial derivative)

In the U.S.:
Demand: Pu = 20 - 1.5Qu
Marginal Revenue: MR = ∂TR/∂Qu = ∂(Pu * Qu)/∂Qu = Pu - 1.5Qu

Since marginal cost is a constant $2 for all quantities sold, the profit function can be expressed as:
Profit = Total Revenue - Total Cost
Profit = (Pe * Qe) - (MC * Qe) + (Pu * Qu) - (MC * Qu)

To find the optimum price and quantity, we need to set the marginal revenue equal to the marginal cost. So we set MR = MC in both markets and solve the resulting equations simultaneously.

After finding the optimum price and quantity in each market, you can calculate the total profit for the firm by substituting those values into the profit function.

b. Now, let's consider the scenario where the firm can price discriminate in the two markets. This means that the firm can charge different prices in Europe and the U.S. Now we need to find the optimal prices, quantities, and resulting profits under price discrimination.

To do this, we follow a similar approach as in part a. However, this time we need to differentiate between Europe and the U.S. Let's calculate the marginal revenue in each market separately and then set it equal to the marginal cost.

After finding the optimal prices and quantities in each market, you can calculate the respective profits. To find the total profit for the firm, simply add the profits obtained in Europe and the U.S.

In summary, to solve this problem:
- Start by understanding the concept of price discrimination.
- Set up the demand and marginal revenue functions for each market.
- Set the marginal revenue equal to the marginal cost to find the optimum price and quantity in each market.
- Calculate the profit for each market, considering the fixed costs are zero.
- Compare the results between the scenarios where price discrimination is not possible and where it is, analyzing the different pricing strategies and their impact on profits.