Chapter 6

Production

The Production Function

A production function tells us the maximum output a firm can produce (in a given period) given available inputs. It is the economist’s way of describing technology or engineering relationships.

,Q f K L

Production Jargon

Factors of production: Inputs used in production (for example, K and L).

Production set: The set of points (combinations of inputs and outputs) that are feasible according to the production function.

Technically inefficient: feasible production points that yield less than the maximum possible for given amounts of inputs.

Technically efficient: feasible production points that yield the maximum possible output for given amounts of inputs.

Total Product

If we plot Q as a function of one input, say L, this is a total product curve.

,Q f K L

Marginal Product

The marginal product of labor (at a point on the total product curve) can be interpreted as the slope of the total product function.

LK K

QMP

L

Average Product

The average product of labor (at a point on the total product curve) can be interpreted as the slope of a ray from the origin to a point on the total product function.

( , )L

Q f K LAP

L L

Average and Marginal Products

Average and marginal products are related in the following ways: When the average product is increasing in labor,

marginal product is greater than average product. When the average product is decreasing in labor,

marginal product is less than average product. When the average product is neither increasing

nor decreasing in labor (it is at a maximum) then marginal product is equal to average product.

Marginal Returns to an Input

Along the total product curve, as L is increased, we may have increasing or decreasing marginal returns to labor (as marginal product is increasing or decreasing when L rises).

Production with 2 Inputs Varying

Marginal products can be defined for both capital and labor (and more) inputs:

LK K

QMP

L

KL L

QMP

K

Isoquants

Isoquant: A curve that shows all of the combinations of labor and capital that can produce a given level of output. Isoquants are normally negatively sloped (as

indifference curves were).

Marginal Rate of Technical Substitution

The (absolute value of the) slope of an isoquant is called the marginal rate of technical substitution:

,L KQ Q

KMRTS

L

More on the Slope of an Isoquant

For a movement along an isoquant, the following must hold:

0L KMP L MP K

K LMP K MP L

L

K

MPK

L MP

Elasticity of Substitution

The elasticity of substitution is defined as:

,

% Change

% Change L K

KL

MRTS

Special Cases: Elasticity of Substitution

Consider the special cases of L-shaped (fixed proportions) isoquants and straight-line (perfect substitutes) isoquants. In the first case, a change in the capital labor ratio

can have large impact of the MRTS, and the elasticity of substitution is small.

In the second case, a change in the capital labor ratio does not change MRTS, and the elasticity of substitution is large.

CES Production Function

The function below (do not bother to memorize) is the constant elasticity of substitution production function Special cases include Cobb-Douglas, fixed

proportions, linear (perfect substitutes) production functions.

1 1 1

Q aL bK

Special Cases

1b bQ AK L

min ,2

HQ O

Q aK bL

Returns to Scale

Suppose all inputs in production increase by a factor . If output goes up by more than in proportion to , the

production function has increasing returns to scale. If output goes up by less than in proportion to , the

production function has decreasing returns to scale. If output goes up exactly in proportion to , the production

function has constant returns to scale (CRS). The Cobb-Douglas production function is CRS if + = 1.

Iclicker Question

A production function describes A: The minimum output that can be produced with

given inputs. B: The maximum output that can be produced

with given inputs. C: The cost of producing output when labor

varies, holding capital fixed. D: The cost of producing output when labor

varies, holding capital fixed.

Iclicker Question

A production function describes A: The minimum output that can be produced with

given inputs. B: The maximum output that can be produced

with given inputs. C: The cost of producing output when labor

varies, holding capital fixed. D: The cost of producing output when labor

varies, holding capital fixed.

Iclicker Question

True or False? All points in the production set are technically efficient. A: True B: False

Iclicker Question

True or False? All points in the production set are technically efficient. A: True B: False

Iclicker Question

A total product curve plots: A: Output versus all inputs. B: Output versus the quantity of a single input. C: Input combinations that yield a given output

level D: The cost of production versus total output.

Iclicker Question

A total product curve plots: A: Output versus all inputs. B: Output versus the quantity of a single input. C: Input combinations that yield a given output

level D: The cost of production versus total output.

Iclicker Question

What is the correct defintion of the marginal product of labor?

LK K

QMP

L

( , )L

f K LMP

L

A:

B:

Iclicker Question

What is the correct defintion of the marginal product of labor?

LK K

QMP

L

( , )L

f K LMP

L

A:

B:

Iclicker Question

Which statement is correct: A: The marginal product of labor is measured by

the slope of a ray from the origin to a point on the total product curve.

B: The average product of labor is measured by the slope of the total product curve at a point.

C: The average product of labor is measured by the slope of a ray from the origin to a point on the total product curve.

None of the above.

Iclicker Question

Which statement is correct: A: The marginal product of labor is measured by

the slope of a ray from the origin to a point on the total product curve.

B: The average product of labor is measured by the slope of the total product curve at a point.

C: The average product of labor is measured by the slope of a ray from the origin to a point on the total product curve.

None of the above.

Iclicker Question

Which is the correct expression for the slope of an isoquant?

L

K

MPK

L MP

K

L

MPK

L MP

A:

B:

Iclicker Question

Which is the correct expression for the slope of an isoquant?

L

K

MPK

L MP

K

L

MPK

L MP

A:

B:

The End