Question

White truffles are a very prized and rare edible fungus that grow naturally in the countryside near Alba, Italy. Suppose that it costs $200 per day to search for white truffles. On an average day, the total number of white truffles (T) found in Alba is T = 20x − x 2 , where x is the number of people searching for white truffles on that day. White Truffles can be sold for $100 each. If there is no regulation, how many more people will be searching for white truffles than the socially optimal number?

Answer 1

If there is no regulation, any number of people searching for white truffles will be more than the socially optimal number of 0. This analysis is based on the private cost of searching for truffles and the marginal cost of each additional person searching.

Step-by-step explanation:

To determine how many more people will be searching for white truffles than the socially optimal number, we need to compare the individual's private cost with the social cost. The individual's private cost is $200 per day, while the social cost includes the private cost plus the cost to society from each additional person searching. The socially optimal number is the point where the social cost equals the private cost.

To find the socially optimal number, we need to determine the marginal cost of each additional person searching. The marginal cost is the change in the total cost divided by the change in the number of people searching. The equation for the total number of truffles found is T = 20x - x^2, so the marginal cost is the derivative of this equation, which is dT/dx = 20 - 2x.

Setting the marginal cost equal to the private cost of $200, we have 20 - 2x = 200. Solving for x, we get x = -90. Since we can't have a negative number of people searching, the socially optimal number is 0. This means that no one should be searching for truffles.

Therefore, if there is no regulation, any number of people searching for truffles will be more than the socially optimal number. However, it's important to note that this analysis assumes that the social cost of an additional person searching is constant and does not take into account any potential benefits or externalities.

Answer 2

Explanation: Take (t), if white truffles is $100 to sell, as x is the amount of people searching for truffles. you divide 100 by 20, that leaves, 5, x-x2 is x, so the answer would be, x equals 5.