Question

Draw isoquant curve for the following production functions.

Here ?Kdenotes quantity of capital input and ?Ldenotes the quantity of labor input.

In the graph, let ?Kbe on the vertical axis and ?Lbe on the horizontal axis.

(a) ?(?,?)=?⋅?=?¯,F(K,L)=K⋅L=Q¯,where

(1) ?¯=100,Q¯=100,

(2) ?¯=200,Q¯=200,

(3) ?¯=300.Q¯=300.

This production function is an example of Cobb-Douglas production technology.

(b) ?(?,?)=2?+5?=?¯,F(K,L)=2K+5L=Q¯,where

(1) ?¯=100,Q¯=100,

(2) ?¯=200,Q¯=200,

(3) ?¯=300.Q¯=300.

This production function is an example of perfect substitutes production technology.

(c) ?(?,?)=min{2?,5?}=?¯,F(K,L)=min{2K,5L}=Q¯,where

(1) ?¯=100,Q¯=100,

(2) ?¯=200,Q¯=200,

(3) ?¯=300.Q¯=300.

This production function is an example of perfect complements production technology.

Answer 1

Part A

Cobb Douglas Q= KL

In this case Isoquant will be rectangular hyperbola as KL = constant

PART B

Perfect Substitutes Q = 2K + 5L

PART C

Perfect Compliment Q= Min (2K, 5L)

We require 2K = 5L

Let K = 5L/2

PLEASE LIKE THE ANSWER IF YOU FIND IT HELPFUL OR YOU CAN COMMENT IF YOU NEED CLARITY / EXPLANATION ON ANY POINT.