INTERNATIONAL ECONOMICS: THEORY, APPLICATION, AND POLICY;  Charles van Marrewijk, 2012; 1

Constant returns to scale

K Suppose 5 labor and 15 capital can produce 10 X This is the isoquant associated with point

A

Under constant returns to scale a proportional increase in inputs leads to a proportional increase in output Suppose we increase K and L by 40% K from 15 to 21 and L from 5 to 7 21 15

A B

Then output also increases by 40% from X = 10 to X = 14 Thus, the isoquant at point

B

is X = 14 X = 14 X = 10 0 5 7 L

INTERNATIONAL ECONOMICS: THEORY, APPLICATION, AND POLICY;  Charles van Marrewijk, 2012; 2

Constant returns to scale

K

A’

Increasing the inputs at

A

with 40% is equivalent to increasing the length of a line from the origin through

A

with 40% But if A’ is another point on the X=10 isoquant we can use the same procedure to conclude that

B’

must be also

B’

on the X=14 isoquant This procedure can be repeated for

B

any arbitrary point on the X=10 isoquant; here are a few

A

The X = 14 isoquant is a radial blow-up X = 14 X = 10 0 L

INTERNATIONAL ECONOMICS: THEORY, APPLICATION, AND POLICY;  Charles van Marrewijk, 2012; 3

Constant returns to scale

K Under constant returns to scale the isoquants are radial blow-ups of each other, which implies that drawing 1 isoquant gives information on all others 21

A

For example, that if cost is minized at point

A

for X = 10, then it is also minimized at the 40% radial blow-up of

A

(

B

) for X = 14

B

Thus, the slope of the isoquant at point

A

is the same as at point

B

15 X = 14 X = 10 0 5 7 L

INTERNATIONAL ECONOMICS: THEORY, APPLICATION, AND POLICY;  Charles van Marrewijk, 2012; 4

Constant returns to scale

K Since the isoquants are radial blow-ups of one another and the slope at point

A

is the same as the slope at point

B

cost minimization is simpler.

21

A

If we know the cost minimizing input mix for

one

isoquant and any ratio of w/r, we also know it for any other production level.

B

You only have to multiply the input mix times the output ratio (we frequently use the isoquant X = 1) 15 X = 14 X = 10 0 5 7 L