Question

If D(p)=100/p and c(y)=y²

what is the optimal level of output of the monopolist?

Answer 1

In order to find the optimal level of output of the monopolist, marginal revenue (MR) must be equal to marginal cost (MC). That is, $MR=MC$

In this equation, we will use the inverse elasticity rule for the demand curve $D(p)=\frac{100}{p}$. The demand curve has a constant elasticity of $-1$.

Here is how we will calculate the marginal revenue.

$MR=q=\frac{100}{p}$

$p=\frac{100}{q}$

$Revenue(R)=p(q)q$

$R=\frac{100}{q} \times q=100$

$MR=\frac{dR}{dq}=0$

$MR=0$

Therefore, for all levels of output, the marginal revenue will be 0. $MR\neq MC$

This indicates that profits are decreasing. The company can then generate the smallest amount of production possible, as profits will decline as a result, and profits will be maximized.