further optimization of economic...
TRANSCRIPT
![Page 1: Further Optimization of Economic Functionsmizu.lecture.ub.ac.id/files/2016/06/14.-Further-Optimization-of.pdfObjectives Show that, at the point of maximum profit, marginal revenue](https://reader031.vdocument.in/reader031/viewer/2022022807/5cec3d5388c9935f398b6c7b/html5/thumbnails/1.jpg)
![Page 2: Further Optimization of Economic Functionsmizu.lecture.ub.ac.id/files/2016/06/14.-Further-Optimization-of.pdfObjectives Show that, at the point of maximum profit, marginal revenue](https://reader031.vdocument.in/reader031/viewer/2022022807/5cec3d5388c9935f398b6c7b/html5/thumbnails/2.jpg)
Objectives Show that, at the point of maximum profit, marginal
revenue equals marginal cost. Show that, at the point of maximum profit, the slope of
the marginal revenue curve is less than that of marginalcost. Maximize profits of a firm with and without price
discrimination in different markets. Show that, at the point of maximum average product of
labour, average product of labour equals marginalproduct of labour.
5/6/2013 2
![Page 3: Further Optimization of Economic Functionsmizu.lecture.ub.ac.id/files/2016/06/14.-Further-Optimization-of.pdfObjectives Show that, at the point of maximum profit, marginal revenue](https://reader031.vdocument.in/reader031/viewer/2022022807/5cec3d5388c9935f398b6c7b/html5/thumbnails/3.jpg)
The previous section demonstrated how mathematics can be usedto optimize particular economic functions. Those examples
suggested two important results:
The previous section demonstrated how mathematics can be usedto optimize particular economic functions. Those examples
suggested two important results:
5/6/2013 3
![Page 4: Further Optimization of Economic Functionsmizu.lecture.ub.ac.id/files/2016/06/14.-Further-Optimization-of.pdfObjectives Show that, at the point of maximum profit, marginal revenue](https://reader031.vdocument.in/reader031/viewer/2022022807/5cec3d5388c9935f398b6c7b/html5/thumbnails/4.jpg)
5/6/2013 4
![Page 5: Further Optimization of Economic Functionsmizu.lecture.ub.ac.id/files/2016/06/14.-Further-Optimization-of.pdfObjectives Show that, at the point of maximum profit, marginal revenue](https://reader031.vdocument.in/reader031/viewer/2022022807/5cec3d5388c9935f398b6c7b/html5/thumbnails/5.jpg)
5/6/2013 5
![Page 6: Further Optimization of Economic Functionsmizu.lecture.ub.ac.id/files/2016/06/14.-Further-Optimization-of.pdfObjectives Show that, at the point of maximum profit, marginal revenue](https://reader031.vdocument.in/reader031/viewer/2022022807/5cec3d5388c9935f398b6c7b/html5/thumbnails/6.jpg)
5/6/2013 6
![Page 7: Further Optimization of Economic Functionsmizu.lecture.ub.ac.id/files/2016/06/14.-Further-Optimization-of.pdfObjectives Show that, at the point of maximum profit, marginal revenue](https://reader031.vdocument.in/reader031/viewer/2022022807/5cec3d5388c9935f398b6c7b/html5/thumbnails/7.jpg)
5/6/2013 7
![Page 8: Further Optimization of Economic Functionsmizu.lecture.ub.ac.id/files/2016/06/14.-Further-Optimization-of.pdfObjectives Show that, at the point of maximum profit, marginal revenue](https://reader031.vdocument.in/reader031/viewer/2022022807/5cec3d5388c9935f398b6c7b/html5/thumbnails/8.jpg)
Example 1
5/6/2013 8
![Page 9: Further Optimization of Economic Functionsmizu.lecture.ub.ac.id/files/2016/06/14.-Further-Optimization-of.pdfObjectives Show that, at the point of maximum profit, marginal revenue](https://reader031.vdocument.in/reader031/viewer/2022022807/5cec3d5388c9935f398b6c7b/html5/thumbnails/9.jpg)
Solution
5/6/2013 9
![Page 10: Further Optimization of Economic Functionsmizu.lecture.ub.ac.id/files/2016/06/14.-Further-Optimization-of.pdfObjectives Show that, at the point of maximum profit, marginal revenue](https://reader031.vdocument.in/reader031/viewer/2022022807/5cec3d5388c9935f398b6c7b/html5/thumbnails/10.jpg)
Hence
5/6/2013 10
![Page 11: Further Optimization of Economic Functionsmizu.lecture.ub.ac.id/files/2016/06/14.-Further-Optimization-of.pdfObjectives Show that, at the point of maximum profit, marginal revenue](https://reader031.vdocument.in/reader031/viewer/2022022807/5cec3d5388c9935f398b6c7b/html5/thumbnails/11.jpg)
5/6/2013 11
![Page 12: Further Optimization of Economic Functionsmizu.lecture.ub.ac.id/files/2016/06/14.-Further-Optimization-of.pdfObjectives Show that, at the point of maximum profit, marginal revenue](https://reader031.vdocument.in/reader031/viewer/2022022807/5cec3d5388c9935f398b6c7b/html5/thumbnails/12.jpg)
5/6/2013 12
![Page 13: Further Optimization of Economic Functionsmizu.lecture.ub.ac.id/files/2016/06/14.-Further-Optimization-of.pdfObjectives Show that, at the point of maximum profit, marginal revenue](https://reader031.vdocument.in/reader031/viewer/2022022807/5cec3d5388c9935f398b6c7b/html5/thumbnails/13.jpg)
Ada pertanyaan?
5/6/2013 13
![Page 14: Further Optimization of Economic Functionsmizu.lecture.ub.ac.id/files/2016/06/14.-Further-Optimization-of.pdfObjectives Show that, at the point of maximum profit, marginal revenue](https://reader031.vdocument.in/reader031/viewer/2022022807/5cec3d5388c9935f398b6c7b/html5/thumbnails/14.jpg)
5/6/2013 14
![Page 15: Further Optimization of Economic Functionsmizu.lecture.ub.ac.id/files/2016/06/14.-Further-Optimization-of.pdfObjectives Show that, at the point of maximum profit, marginal revenue](https://reader031.vdocument.in/reader031/viewer/2022022807/5cec3d5388c9935f398b6c7b/html5/thumbnails/15.jpg)
5/6/2013 15
![Page 16: Further Optimization of Economic Functionsmizu.lecture.ub.ac.id/files/2016/06/14.-Further-Optimization-of.pdfObjectives Show that, at the point of maximum profit, marginal revenue](https://reader031.vdocument.in/reader031/viewer/2022022807/5cec3d5388c9935f398b6c7b/html5/thumbnails/16.jpg)
5/6/2013 16
![Page 17: Further Optimization of Economic Functionsmizu.lecture.ub.ac.id/files/2016/06/14.-Further-Optimization-of.pdfObjectives Show that, at the point of maximum profit, marginal revenue](https://reader031.vdocument.in/reader031/viewer/2022022807/5cec3d5388c9935f398b6c7b/html5/thumbnails/17.jpg)
Evaluate the profit under eachpolicy
5/6/2013 17
![Page 18: Further Optimization of Economic Functionsmizu.lecture.ub.ac.id/files/2016/06/14.-Further-Optimization-of.pdfObjectives Show that, at the point of maximum profit, marginal revenue](https://reader031.vdocument.in/reader031/viewer/2022022807/5cec3d5388c9935f398b6c7b/html5/thumbnails/18.jpg)
5/6/2013 18
![Page 19: Further Optimization of Economic Functionsmizu.lecture.ub.ac.id/files/2016/06/14.-Further-Optimization-of.pdfObjectives Show that, at the point of maximum profit, marginal revenue](https://reader031.vdocument.in/reader031/viewer/2022022807/5cec3d5388c9935f398b6c7b/html5/thumbnails/19.jpg)
5/6/2013 19