BigBook is a monopolist book publishing company, which sells books in Australia and New Zealand. Assume there is a 1:1 exchange rate between Australia and New Zealand. The inverse demand equations for Australia and New Zealand are as follows:
Australia: PA = 100 - 2.5QA
New Zealand: PZ = 80 - 12.5QZ
where PA is the price of a book in Australia, PZ is the price of a book in New Zealand, QA is the quantity of books consumed in Australia and QZ is the quantity of books consumed in New Zealand.
BigBook has one plant that produces books that is located in Australia. The cost of book production is as follows:
C= 5(QA+QB)
The cost of shipping books between New Zealand and Australia is $2 per book. However, there is a law prohibiting the resale of books between Australia and New Zealand.
BigBook decides to engage in third degree price discrimination.
What prices does BigBook set in Australia and New Zealand and what profit will be earned?
To find the prices that BigBook sets in Australia and New Zealand and the profit it will earn, we need to analyze the demand and cost equations.
First, let's find the optimal quantity and price for each market separately:
1. Australia:
Demand equation: PA = 100 - 2.5QA
To find the optimal quantity, we take the derivative of the demand equation with respect to QA and set it equal to zero:
d(PA)/d(QA) = -2.5 = 0
This implies that the optimal quantity in Australia is QA = 0.
Substituting the optimal quantity back into the demand equation, we can find the optimal price in Australia:
PA = 100 - 2.5(0) = 100
2. New Zealand:
Demand equation: PZ = 80 - 12.5QZ
Again, take the derivative of the demand equation with respect to QZ and set it equal to zero:
d(PZ)/d(QZ) = -12.5 = 0
This implies that the optimal quantity in New Zealand is QZ = 0.
Substituting the optimal quantity back into the demand equation, we can find the optimal price in New Zealand:
PZ = 80 - 12.5(0) = 80
Now let's calculate the profit:
Profit is equal to total revenue minus total cost. From the demand equations, we know that total revenue is given by:
TR = PA*QA + PZ*QZ
In this case, since both QA and QZ are zero, total revenue is zero as well.
Total cost (TC) is the sum of production cost and shipping cost:
TC = C + Shipping Cost
Shipping cost is given as $2 per book, and the production cost is C = 5(QA + QZ).
Since QA and QZ are both zero, the production cost is also zero.
Therefore, TC = 0 + Shipping Cost = 0 + 2(0) = 0
Hence, the profit earned by BigBook is:
Profit = TR - TC = 0 - 0 = 0
In this case, with no sales in either market, BigBook does not earn any profit.