00:01
Hello, to determine the optimal price for the pharmaceutical product in country a and country b, we need to find the price that maximizes the firm's profit in each country.
00:11
Profit is calculated as total revenue minus total cost.
00:19
In general, total revenue is equals to the price multiplied by quantity demanded which will be represented by x and total cost is equals to the marginal cost multiplied by quantity supplied or produced, it will be represented by x.
00:45
For country a, the demand function is p is equals to 84 less 2x, so total revenue will be p into x, it will be 84 minus 2x multiplied by x.
01:15
So, it will be 84x less 2x square and the total cost is equals to marginal cost multiplied by x, it will be 4x.
01:32
To maximize profit, we need to find the quantity that maximize the difference between the total revenue and total cost.
01:38
This can be done by taking the derivative of profit function with respect to x, x setting 2 equal to 0 and solving for x.
01:47
So, profit which is represented by pi is equals to total revenue minus total cost, it will be 84x minus 2x square less 4x, it will be 84x less 2x square less 4x and it will be 80x less 2x square.
02:20
Taking the derivative of profit with respect to x, it will be d pi by dx is equals to 80 minus 4x equals to 0.
02:53
So, setting this equal to 0 and solving for x, d pi by dx will be equals to 80 less 4x is equals to 0.
03:20
So, 4x is equals to 80, x is equals to 20.
03:29
Therefore, the optimal quantity in the country a is x equals to 20.
03:33
To find the optimal price, substitute this value back into the demand function, p is equals to 84 less 2x and the answer will be 84 less 40 that is 44...