Maximizing Net Benefits in Economics

What level of Y will yield the maximum net benefits?

A. 600/64 B. 600/32 C. 300/64 D. 300/32

Final Answer:

To find the level of Y that will yield the maximum net benefits, subtract the total costs from the total benefits. Take the derivative of the net benefits equation and set it equal to 0. Solve for Y to find the level that maximizes net benefits.

Explanation: To find the level of Y that will yield the maximum net benefits, we need to calculate the difference between the total benefits (B(Y)) and the total costs (C(Y)). Net benefits are given by NB(Y) = B(Y) - C(Y). In this case, B(Y) = 600Y - 12Y² and C(Y) = 20Y².

Substituting the given values into the net benefits equation, we have NB(Y) = (600Y - 12Y²) - (20Y²). Simplifying further, NB(Y) = 580Y - 32Y².

To find the maximum net benefits, we need to find the value of Y that maximizes NB(Y). This can be done by taking the derivative of NB(Y) with respect to Y and setting it equal to 0. Solving this equation will give us the value of Y that yields the maximum net benefits.

Taking the derivative of NB(Y) with respect to Y, we have d(NB(Y))/dY = 580 - 64Y. Setting this equal to 0, we get 580 - 64Y = 0. Solving for Y, we find Y = 580/64.