Isoquants

AGENDA

AGENDA Production Functions

Isoquants and Isocosts

Cost Minimization Problems

Recap: Production Function Q that is a function of two variables (K, L)

 Q depends on both L and K  Can not plot 3 variables (Q, L, and K) in a two dimensional plot, hence use isoquants (lines of constant production)

Production with Two Variable Inputs LABOR INPUT (L) Capital Input 1 2 3 4 5 1 20 40 55 65 75 2 40 60 75 85 90 3 55 75 90 100 105 4 65 85 100 110 115 5 75 90 105 115 120

● Isoquant: Curve showing

all possible combinations of inputs that yield the same output.

Production with two inputs

● isoquant map Graph combining a number of isoquants, used to

describe a production function.

Production with Two Variable Inputs (continued)

A set of isoquants, or isoquant map, describes the firm’s production function. Output increases as we move from isoquant q1 (at which 55 units per year are produced at points such as A and D), to isoquant q2 (75 units per year at points such as B) and to isoquant q3 (90 units per year at points such as C and E).

Show that two isoquants cannot intersect?

Assume that two isoquants can intersect as shown • Points A and C are on the same isoquant, and hence should produce the same output (Q1) Points B and C are on the same isoquant, and hence should produce the same output (Q2) This is a contradiction unless Q1 = Q2 which implies that we cannot have intersecting isoquants.

Q1

Q2

•

B

•

Capital (K)

A C

Labor (L)

Upward Sloping Isoquant What does this isoquant represent?

•

Points A and G are on the same isoquant, hence should produce same output But they use different combinations of L and K. In fact when you move from A to G, you increase both L and K simultaneously. Yet the output does not increase. This is not possible. Hence upward sloping isoquants are not realistic!

•

Capital (K)

G

•

A

Labor (L)

Cobb Douglas Production Function and Calculation of MPL and...