Lectures in Microeconomics-Charles W. Upton Mathematical Cost Functions(2) C= 10+20q+4q 2.
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Transcript of Lectures in Microeconomics-Charles W. Upton Mathematical Cost Functions(2) C= 10+20q+4q 2.
Lectures in Microeconomics-Charles W. Upton
Mathematical Cost Functions(2)
C= 10+20q+4q2
Mathematical Cost Functions(2)
A Problem
C= 10+20q+4q2
Mathematical Cost Functions(2)
C= 10+20q+4q2
• Compute TC, AC, and MC when q=10
Mathematical Cost Functions(2)
C= 10+20q+4q2
• Compute TC, AC, and MC when q=10
• Find where MC = AC
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?
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?
Mathematical Cost Functions(2)
C= 10+20q+4q2
• Compute TC, AC, and MC when q=10
TC= 10+20(10)+4(10)2
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
Mathematical Cost Functions(2)
C= 10+20q+4q2
Compute AC
Mathematical Cost Functions(2)
C= 10+20q+4q2
q
qqAC
q
qCAC
242010
)(
Compute AC
Mathematical Cost Functions(2)
C= 10+20q+4q2
Compute AC
AC
q
qqAC
q
qCAC
42010
42010
)(
2
Mathematical Cost Functions(2)
C= 10+20q+4q2
Compute AC
61)10(42010
10
42010
42010
)(
2
AC
AC
q
qqAC
q
qCAC
Mathematical Cost Functions(2)
C= 10+20q+4q2
C= 10+20q+4q2
•The derivative of
ax2 + bx + c
is
2ax+b
Mathematical Cost Functions(2)
C= 10+20q+4q2
•The derivative of
ax2 + bx + c
is
2ax+b
MC = 8q + 20
MC = 100
Mathematical Cost Functions(2)
C= 10+20q+4q2
Find where MC = AC
AC 42010
MC = 8q+20
Mathematical Cost Functions(2)
C= 10+20q+4q2
Find where MC = AC
AC 42010
MC = 8q+20
20842010
qqq
Mathematical Cost Functions(2)
C= 10+20q+4q2
Find where MC = AC
AC 42010
MC = 8q+20
qqq
410
20842010
Mathematical Cost Functions(2)
C= 10+20q+4q2
Find where MC = AC
58.15.2
410
410
2
q
q
Mathematical Cost Functions(2)
C= 10+20q+4q2
What level of output minimizes AC?
AC 42010
Mathematical Cost Functions(2)
C= 10+20q+4q2
What level of output minimizes AC?
0410
42010
2
qdq
dAC
AC
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
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
Mathematical Cost Functions(2)
C= 10+20q+4q2
When is MC = 60?
MC = 8q +20
8q + 20 = 60
8q = 40
q = 5
Mathematical Cost Functions(2)
End
©2003 Charles W. Upton