Maximizing Revenue for an Oil-producing Country

What is the optimal price to maximize revenue for an oil-producing country?

An oil-producing country can sell 7 million barrels of oil a day at a price of $120 per barrel. If each $1 price increase will result in a sales decrease of 100,000 barrels per day, what price will maximize the country's revenue?

Answer:

To maximize revenue, the price should be set at $35 per barrel.

Optimizing revenue for an oil-producing country involves finding the price point at which the demand and supply are in equilibrium, resulting in the highest possible revenue. In this case, the initial price of $120 per barrel with a quantity of 7 million barrels per day can be used to calculate the optimal price.

Since the demand decreases by 100,000 barrels per day for each $1 increase in price, a linear demand function can be created: Qd = -100,000P + 7,000,000, where P is the price and Qd is the quantity demanded. The revenue function can be expressed as R = P * Q, where R is the revenue.

By substituting the demand function into the revenue function, the parabolic revenue function can be formed: R = -100,000P^2 + 7,000,000P. To find the price that maximizes revenue, the vertex of the parabolic function must be determined. The x-coordinate of the vertex represents the price that maximizes revenue.

Applying the formula x = -b / (2a) to the revenue function, where a = -100,000 and b = 7,000,000, the optimal price is calculated as $35 per barrel. Setting the price at this point will lead to the maximum revenue for the oil-producing country.