1) Table 1 below describes the revenue that a monopolist is able to make for different levels of output (denoted by Q). The total cost (TC) for a given value of output Q is given by the formula: TC = 20 + Q + Q2 (in words, total cost is given by twenty plus the level output plus the square of the level of output).
a) Complete the table.
b) Determine the profit-maximizing level of output.
c) At the profit-maximizing level of output, what is the marginal revenue and what is the marginal cost? (Hint: the marginal revenue, for, say, is the extra revenue that can be obtained by producing an additional unit). Compute these values and show how they are related to the choice of the profit-maximizing level of output.
d) At the profit-maximizing level of output, what is the price the monopolist charges (assume that the monopolist charges the same price for each unit of output he sells)? Is this price higher or lower than the marginal cost? Is the quantity produced by the monopolist efficient? How is this outcome different from the outcome of a competitive market?
Table 1:
|
Output (Q)
|
Total Revenue
|
Total Cost (TC)
|
Profit
|
|
1
|
$90
|
_____
|
_____
|
|
2
|
160
|
_____
|
_____
|
|
3
|
210
|
_____
|
_____
|
|
4
|
240
|
_____
|
_____
|
|
5
|
248
|
_____
|
_____
|
|
6
|
240
|
_____
|
_____
|
|
7
|
210
|
_____
|
_____
|
|
8
|
160
|
_____
|
_____
|
|
9
|
90
|
_____
|
_____
|