Suppose a profit-maximizing monopolist can engage in perfect price discrimination and faces a...

There will be a loss of $24.

The monopolist can distinguish among customers and sell the same quantity of goods at different prices to customers. In this way, all the consumer surplus can be obtained till P = MC.

The MC function is {eq}MC = \frac{{dTC}}{{dQ}} = 4. {/eq}

So, P = MC = 4.

Thus, the quantity produced by the monopoly firm is:

{eq}\begin{align*} Q &= 20 - 5\left( 4 \right)\\ Q &= 20 - 20\\ Q &= 0 \end{align*} {/eq}

The amount of profits are:

{eq}\begin{align*} \pi &= TR - TC\\ &= \left( {P \times Q} \right) - \left( {24 + 4Q} \right)\\ &= \left( {4 \times 0} \right) - 24 - \left( {4 \times 0} \right)\\ &= - 24 \end{align*} {/eq}