| Line 62: |
Line 62: |
| | {{clear}} | | {{clear}} |
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| − | :From the point (50,50) neither firm can increase its own profits by reducing its own output. So that is equilibrium. To check the answer, we can start from (75,75). From there, either firm can increase its profits by increasing its output, and it does. But from the new point the other firm can increase its profits by increasing its output, and the market ends up at where both firms have increased their output, with profits of (50,50). Spend a few minutes trying each approach to confirm that is the equilibrium - the Nash equilibrium. | + | :Unfortunately, there is a mistake in the ''ordering'' of the paired numbers used in this problem. The numbers were in the wrong order because a firm's profits should increase, not decrease, when it increases output in an oligopoly. As mistakenly written above, we can start from (50,50) and realize that firm B can increase its profits by reducing output, which takes us to (25,100). But then the other firm can increase its profits by reducing output, which takes us to equilibrium at (75,75). Any movement away from that point would start of chain of events that would lead back to that point, so it is a true equilibrium. But that is an uninteresting solution, and unrealistic in a free market. |
| | + | |
| | + | :The chart should have had the ordered pairs reversed: |
| | + | <div style=float:left; padding: 20px"> |
| | + | {|style="border-collapse:collapse" |
| | + | |- |
| | + | | |
| | + | | |
| | + | |style="border-style:solid; border-width:1px; padding:10px"|Firm A Does Not Reduce Output |
| | + | |style="border-style:solid; border-width:1px; padding:10px"|Firm A Reduces Output |
| | + | |- |
| | + | !rowspan=2 style="padding:10px"| |
| | + | |style="border-style:solid; border-width:1px; padding:10px"|Firm B Does Not Reduce Output |
| | + | |style="border-style:solid; border-width:1px; padding:10px"|(50,50) |
| | + | |style="border-style:solid; border-width:1px; padding:10px"|(25,100) |
| | + | |- |
| | + | |style="border-style:solid; border-width:1px; padding:10px"|Firm B Reduces Output |
| | + | |style="border-style:solid; border-width:1px; padding:10px"|(100,25) |
| | + | |style="border-style:solid; border-width:1px; padding:10px"|(75,75) |
| | + | |} |
| | + | </div> |
| | + | {{clear}} |
| | + | <br> |
| | + | |
| | + | :In the corrected version above, from the point (50,50) neither firm can increase its own profits by reducing its own output. So that is equilibrium. To check the answer, we can start from (75,75). From there, either firm can increase its profits by increasing its output, and it does. But from the new point the other firm can increase its profits by increasing its output, and the market ends up at where both firms have increased their output, with profits of (50,50). Spend a few minutes trying each approach to confirm that is the equilibrium - the Nash equilibrium. |
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| | 7. Monopolies: should the government regulate them? Or is regulation worse? | | 7. Monopolies: should the government regulate them? Or is regulation worse? |