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

qq

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

qq

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

qq

AC 42010

MC = 8q+20

Mathematical Cost Functions(2)

C= 10+20q+4q2

Find where MC = AC

qq

AC 42010

MC = 8q+20

20842010

qqq

Mathematical Cost Functions(2)

C= 10+20q+4q2

Find where MC = AC

qq

AC 42010

MC = 8q+20

qq

qqq

410

20842010

Mathematical Cost Functions(2)

C= 10+20q+4q2

Find where MC = AC

58.15.2

410

410

2

q

q

qq

Mathematical Cost Functions(2)

C= 10+20q+4q2

What level of output minimizes AC?

qq

AC 42010

Mathematical Cost Functions(2)

C= 10+20q+4q2

What level of output minimizes AC?

0410

42010

2

qdq

dAC

qq

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

qq

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

qq

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