Production functions: perfect substitutes, perfect complements and Cobb-Douglas production function

Summary

Perfect substitutes and perfect complements

• Two factors are perfect substitutes if every isoquant is a straight line
• Example:
• 20 Heavy oil 1 solid fuel
• 10 Light oil 1 solid fuel
• \(y=x_1/20+x_2/10\)
• Two factors are perfect complements if every isoquant is L-shaped where all corners lie on a straight line through the origin
• Example:
• 1 copper cable + 1 electronic circuit 1 red wire
• \(y=min \{ x_1,x_2 \}\)

Cobb-Douglas production function

• The production function

\[y=f\left( x_1,x_2 \right)=Ax_1^ax_2^b\]

• where \(A,a,b\) are constants is called the C obb-Douglas production function
• Example: \(y=100\sqrt{x_1x_2}\)