Question

In Clean Water County, groundwater is the only source of water for household consumption and irrigated agricultural production. Residues of fertilizer, pesticides, and herbicides on farmland seep into the aquifer and lower water quality for residential use. The total cost of cleaning the polluted water

(C)
is a function of farm output in the county, y, given by
C = 0.01y²
Production cost of the farmers is given by:
C = 100 + 2y + 0.04y²
Farm output is sold in a competitive industry at price of $10 per unit of output. Answer the following:
a. If the farmers are not required to compensate for the water cleaning cost arising from their pollution of it, how much output will be produced?

Answer 1

When the farmers are not required to compensate for the water cleaning cost, approximately 100 units of output will be produced.

Step-by-step explanation:

To determine the amount of output that will be produced when the farmers are not required to compensate for the water cleaning cost, we need to find the level of output at which the production cost is equal to the revenue from selling the output.

First, let's calculate the production cost equation:

C = 100 + 2y + 0.04y²

Next, let's calculate the revenue equation:

R = 10y

Since the production cost is equal to the revenue, we set the two equations equal to each other:

100 + 2y + 0.04y² = 10y

Now, let's solve the equation:

0.04y² - 8y + 100 = 0

Using the quadratic formula, we find that y ≈ 100.

Therefore, when the farmers are not required to compensate for the water cleaning cost, approximately 100 units of output will be produced.