lectures in microeconomics-charles w. upton mathematical cost functions(2) c= 10+20q+4q 2
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![Page 1: Lectures in Microeconomics-Charles W. Upton Mathematical Cost Functions(2) C= 10+20q+4q 2](https://reader030.vdocuments.site/reader030/viewer/2022032704/56649d405503460f94a1a4d3/html5/thumbnails/1.jpg)
Lectures in Microeconomics-Charles W. Upton
Mathematical Cost Functions(2)
C= 10+20q+4q2
![Page 2: Lectures in Microeconomics-Charles W. Upton Mathematical Cost Functions(2) C= 10+20q+4q 2](https://reader030.vdocuments.site/reader030/viewer/2022032704/56649d405503460f94a1a4d3/html5/thumbnails/2.jpg)
Mathematical Cost Functions(2)
A Problem
C= 10+20q+4q2
![Page 3: Lectures in Microeconomics-Charles W. Upton Mathematical Cost Functions(2) C= 10+20q+4q 2](https://reader030.vdocuments.site/reader030/viewer/2022032704/56649d405503460f94a1a4d3/html5/thumbnails/3.jpg)
Mathematical Cost Functions(2)
C= 10+20q+4q2
• Compute TC, AC, and MC when q=10
![Page 4: Lectures in Microeconomics-Charles W. Upton Mathematical Cost Functions(2) C= 10+20q+4q 2](https://reader030.vdocuments.site/reader030/viewer/2022032704/56649d405503460f94a1a4d3/html5/thumbnails/4.jpg)
Mathematical Cost Functions(2)
C= 10+20q+4q2
• Compute TC, AC, and MC when q=10
• Find where MC = AC
![Page 5: Lectures in Microeconomics-Charles W. Upton Mathematical Cost Functions(2) C= 10+20q+4q 2](https://reader030.vdocuments.site/reader030/viewer/2022032704/56649d405503460f94a1a4d3/html5/thumbnails/5.jpg)
Mathematical Cost Functions(2)
C= 10+20q+4q2
• Compute TC, AC, and MC when q=10
• Find where MC = AC
• What level of output minimizes AC?
![Page 6: Lectures in Microeconomics-Charles W. Upton Mathematical Cost Functions(2) C= 10+20q+4q 2](https://reader030.vdocuments.site/reader030/viewer/2022032704/56649d405503460f94a1a4d3/html5/thumbnails/6.jpg)
Mathematical Cost Functions(2)
C= 10+20q+4q2
• Compute TC, AC, and MC when q=10
• Find where MC = AC
• What level of output minimizes AC?
• When is MC = 60?
![Page 7: Lectures in Microeconomics-Charles W. Upton Mathematical Cost Functions(2) C= 10+20q+4q 2](https://reader030.vdocuments.site/reader030/viewer/2022032704/56649d405503460f94a1a4d3/html5/thumbnails/7.jpg)
Mathematical Cost Functions(2)
C= 10+20q+4q2
• Compute TC, AC, and MC when q=10
TC= 10+20(10)+4(10)2
![Page 8: Lectures in Microeconomics-Charles W. Upton Mathematical Cost Functions(2) C= 10+20q+4q 2](https://reader030.vdocuments.site/reader030/viewer/2022032704/56649d405503460f94a1a4d3/html5/thumbnails/8.jpg)
Mathematical Cost Functions(2)
C= 10+20q+4q2
• Compute TC, AC, and MC when q=10
TC= 10+20(10)+4(10)2
TC= 10+200+400 = 610
![Page 9: Lectures in Microeconomics-Charles W. Upton Mathematical Cost Functions(2) C= 10+20q+4q 2](https://reader030.vdocuments.site/reader030/viewer/2022032704/56649d405503460f94a1a4d3/html5/thumbnails/9.jpg)
Mathematical Cost Functions(2)
C= 10+20q+4q2
Compute AC
![Page 10: Lectures in Microeconomics-Charles W. Upton Mathematical Cost Functions(2) C= 10+20q+4q 2](https://reader030.vdocuments.site/reader030/viewer/2022032704/56649d405503460f94a1a4d3/html5/thumbnails/10.jpg)
Mathematical Cost Functions(2)
C= 10+20q+4q2
q
qqAC
q
qCAC
242010
)(
Compute AC
![Page 11: Lectures in Microeconomics-Charles W. Upton Mathematical Cost Functions(2) C= 10+20q+4q 2](https://reader030.vdocuments.site/reader030/viewer/2022032704/56649d405503460f94a1a4d3/html5/thumbnails/11.jpg)
Mathematical Cost Functions(2)
C= 10+20q+4q2
Compute AC
AC
q
qqAC
q
qCAC
42010
42010
)(
2
![Page 12: Lectures in Microeconomics-Charles W. Upton Mathematical Cost Functions(2) C= 10+20q+4q 2](https://reader030.vdocuments.site/reader030/viewer/2022032704/56649d405503460f94a1a4d3/html5/thumbnails/12.jpg)
Mathematical Cost Functions(2)
C= 10+20q+4q2
Compute AC
61)10(42010
10
42010
42010
)(
2
AC
AC
q
qqAC
q
qCAC
![Page 13: Lectures in Microeconomics-Charles W. Upton Mathematical Cost Functions(2) C= 10+20q+4q 2](https://reader030.vdocuments.site/reader030/viewer/2022032704/56649d405503460f94a1a4d3/html5/thumbnails/13.jpg)
Mathematical Cost Functions(2)
C= 10+20q+4q2
C= 10+20q+4q2
•The derivative of
ax2 + bx + c
is
2ax+b
![Page 14: Lectures in Microeconomics-Charles W. Upton Mathematical Cost Functions(2) C= 10+20q+4q 2](https://reader030.vdocuments.site/reader030/viewer/2022032704/56649d405503460f94a1a4d3/html5/thumbnails/14.jpg)
Mathematical Cost Functions(2)
C= 10+20q+4q2
•The derivative of
ax2 + bx + c
is
2ax+b
MC = 8q + 20
MC = 100
![Page 15: Lectures in Microeconomics-Charles W. Upton Mathematical Cost Functions(2) C= 10+20q+4q 2](https://reader030.vdocuments.site/reader030/viewer/2022032704/56649d405503460f94a1a4d3/html5/thumbnails/15.jpg)
Mathematical Cost Functions(2)
C= 10+20q+4q2
Find where MC = AC
AC 42010
MC = 8q+20
![Page 16: Lectures in Microeconomics-Charles W. Upton Mathematical Cost Functions(2) C= 10+20q+4q 2](https://reader030.vdocuments.site/reader030/viewer/2022032704/56649d405503460f94a1a4d3/html5/thumbnails/16.jpg)
Mathematical Cost Functions(2)
C= 10+20q+4q2
Find where MC = AC
AC 42010
MC = 8q+20
20842010
qqq
![Page 17: Lectures in Microeconomics-Charles W. Upton Mathematical Cost Functions(2) C= 10+20q+4q 2](https://reader030.vdocuments.site/reader030/viewer/2022032704/56649d405503460f94a1a4d3/html5/thumbnails/17.jpg)
Mathematical Cost Functions(2)
C= 10+20q+4q2
Find where MC = AC
AC 42010
MC = 8q+20
qqq
410
20842010
![Page 18: Lectures in Microeconomics-Charles W. Upton Mathematical Cost Functions(2) C= 10+20q+4q 2](https://reader030.vdocuments.site/reader030/viewer/2022032704/56649d405503460f94a1a4d3/html5/thumbnails/18.jpg)
Mathematical Cost Functions(2)
C= 10+20q+4q2
Find where MC = AC
58.15.2
410
410
2
q
q
![Page 19: Lectures in Microeconomics-Charles W. Upton Mathematical Cost Functions(2) C= 10+20q+4q 2](https://reader030.vdocuments.site/reader030/viewer/2022032704/56649d405503460f94a1a4d3/html5/thumbnails/19.jpg)
Mathematical Cost Functions(2)
C= 10+20q+4q2
What level of output minimizes AC?
AC 42010
![Page 20: Lectures in Microeconomics-Charles W. Upton Mathematical Cost Functions(2) C= 10+20q+4q 2](https://reader030.vdocuments.site/reader030/viewer/2022032704/56649d405503460f94a1a4d3/html5/thumbnails/20.jpg)
Mathematical Cost Functions(2)
C= 10+20q+4q2
What level of output minimizes AC?
0410
42010
2
qdq
dAC
AC
![Page 21: Lectures in Microeconomics-Charles W. Upton Mathematical Cost Functions(2) C= 10+20q+4q 2](https://reader030.vdocuments.site/reader030/viewer/2022032704/56649d405503460f94a1a4d3/html5/thumbnails/21.jpg)
Mathematical Cost Functions(2)
C= 10+20q+4q2
What level of output minimizes AC?
58.1
104
0410
42010
2
2
q
q
qdq
dAC
AC
![Page 22: Lectures in Microeconomics-Charles W. Upton Mathematical Cost Functions(2) C= 10+20q+4q 2](https://reader030.vdocuments.site/reader030/viewer/2022032704/56649d405503460f94a1a4d3/html5/thumbnails/22.jpg)
Mathematical Cost Functions(2)
C= 10+20q+4q2
What level of output minimizes AC?
58.1
104
0410
42010
2
2
q
q
qdq
dAC
AC
58.1q
MC = AC at the minimum of AC
![Page 23: Lectures in Microeconomics-Charles W. Upton Mathematical Cost Functions(2) C= 10+20q+4q 2](https://reader030.vdocuments.site/reader030/viewer/2022032704/56649d405503460f94a1a4d3/html5/thumbnails/23.jpg)
Mathematical Cost Functions(2)
C= 10+20q+4q2
When is MC = 60?
MC = 8q +20
8q + 20 = 60
8q = 40
q = 5
![Page 24: Lectures in Microeconomics-Charles W. Upton Mathematical Cost Functions(2) C= 10+20q+4q 2](https://reader030.vdocuments.site/reader030/viewer/2022032704/56649d405503460f94a1a4d3/html5/thumbnails/24.jpg)
Mathematical Cost Functions(2)
End
©2003 Charles W. Upton