PRODUCTION

PREPARED BY –VANSHIKA AGRAWAL

Production Economics

Managers must decide not only what to produce for the market, but also how to produce it in the most efficient or least cost manner.

Economics offers widely accepted tools for judging whether the production choices are least cost.

A production function relates the most that can be produced from a given set of inputs. Production functions allow measures of the marginal

product of each input.

The Production Function A Production Function is the maximum quantity from any amounts of inputs If L is labor and K is capital, one popular functional form is known as the Cobb-Douglas Production Function

Q = • K • L is a Cobb-Douglas Production Function The number of inputs is often large. But economists simplify by suggesting some,

like materials or labor, is variable, whereas plant and equipment is fairly fixed in the short run.

The Short Run Production Function

Short Run Production Functions: Max output, from a n y set of inputs Q = f ( X1, X2, X3, X4, X5 ... )

FIXED IN SR VARIABLE IN SR _

Q = f ( K, L) for two input case, where K as Fixed A Production Function is has only one variable input, labor, is easily analyzed. The one variable input is labor, L.

Average Product = Q / L output per labor

Marginal Product =Q / L = dQ / dL output attributable to last unit of labor

applied Similar to profit functions, the Peak of MP

occurs before the Peak of average product When MP = AP, we’re at the peak of the

AP curve

Elasticities of Production The production elasticity of labor,

EL = MPL / APL = (Q/L) / (Q/L) = (Q/L)·(L/Q)

The production elasticity of capital has the identical in form, except K appears in place of L.

When MPL > APL, then the labor elasticity, EL > 1. A 1 percent increase in labor will increase output by

more than 1 percent.

When MPL < APL, then the labor elasticity, EL < 1. A 1 percent increase in labor will increase output by less

than 1 percent.

Short Run Production Function Numerical Example

L Q MP AP 0 0 --- --- 1 20 20 20 2 46 26 23 3 4 5

70 92 110

24 22 18

23.33 23 22

Marginal Product

L 1 2 3 4 5

Average Product

Labor Elasticity is greater then one,for labor use up through L = 3 units

When MP > AP, then AP is RISING IF YOUR MARGINAL GRADE IN THIS CLASS IS

HIGHER THAN YOUR GRADE POINT AVERAGE, THEN YOUR G.P.A. IS RISING

When MP < AP, then AP is FALLING IF YOUR MARGINAL BATTING AVERAGE IS LESS

THAN THAT OF THE NEW YORK YANKEES, YOUR ADDITION TO THE TEAM WOULD LOWER THE YANKEE’S TEAM BATTING AVERAGE

When MP = AP, then AP is at its MAX IF THE NEW HIRE IS JUST AS EFFICIENT AS THE

AVERAGE EMPLOYEE, THEN AVERAGE PRODUCTIVITY DOESN’T CHANGE

Law of Diminishing Returns

INCREASES IN ONE FACTOR OF PRODUCTION, HOLDING ONE OR OTHER FACTORS FIXED, AFTER SOME POINT, MARGINAL PRODUCT DIMINISHES.

A SHORT RUN LAW point of

diminishingreturns

Variable input

MP

Figure 7.4 on Page 306

Three stages of production

Stage 1: average product rising.

Stage 2: average product declining (but marginal product positive).

Stage 3: marginal product is negative, or total product is declining. L

Total Output

Stage 1

Stage 2

Stage 3

Optimal Use of the Variable Input

HIRE, IF GET MORE REVENUE THAN COST

HIRE ifTR/L > TC/L

HIRE if the marginal revenue product > marginal factor cost: MRP L > MFC L

AT OPTIMUM,MRP L = W MFC

MRP L MP L • P Q = W

optimal labor

MPL

MRPL

W W MFC

L

wage

•

MRP L is the Demand for Labor If Labor is MORE

productive, demand for labor increases

If Labor is LESS productive, demand for labor decreases

Suppose an EARTHQUAKEEARTHQUAKE destroys capital

MP L declines with less capital, wages and labor are HURT

D L

D’ L

S L

W

L’ L

Long Run Production Functions

All inputs are variable greatest output from any set of inputs

Q = f( K, L ) is two input example MP of capital and MP of labor are the

derivatives of the production function MPL = Q /L = Q /L

MP of labor declines as more labor is applied. Also the MP of capital declines as more capital is applied.

Isoquants & LR Production Functions

In the LONG RUN, ALL factors are variable

Q = f ( K, L ) ISOQUANTS -- locus of

input combinations which produces the same output (A & B or on the same isoquant)

SLOPE of ISOQUANT is ratio of Marginal Products, called the MRTS, the marginal rate of technical substitution

ISOQUANT MAP

B

A

C

Q1

Q2

Q3

K

L

Optimal Combination of Inputs

The objective is to minimize cost for a given output

ISOCOST lines are the combination of inputs for a given cost, C0

C0 = CL·L + CK·K K = C0/CK - (CL/CK)·L Optimal where:

MPL/MPK = CL/CK· Rearranged, this becomes the

equimarginal criterion

Equimarginal Criterion: Produce where MPL/CL = MPK/CK where marginal products per dollar are equal

Figure 7.9 on page 316

Q(1)

D

L

K

at D, slope of isocost = slope of isoquant

C(1)

Use of the Equimarginal Criterion

Q: Is the following firm EFFICIENT?

Suppose that: MP L = 30 MPK = 50 W = 10 (cost of labor) R = 25 (cost of capital)

Labor: 30/10 = 3 Capital: 50/25 = 2 A: No!

A dollar spent on labor produces 3, and a dollar spent on capital produces 2.

USE RELATIVELY MORE LABOR!

If spend $1 less in capital, output falls 2 units, but rises 3 units when spent on labor

Shift to more labor until the equimarginal condition holds.

That is peak efficiency.

Allocative & Technical Efficiency Allocative Efficiency – asks if the firm using the least cost combination of

input It satisfies: MPL/CL = MPK/CK

Technical Efficiency – asks if the firm is maximizing potential output from a given set of inputs When a firm produces at point T

rather than point D on a lower isoquant, they firm is not producing as much as is technically possible.

Q(1)

D

Q(0)T

Returns to Scale

A function is homogeneous of degree-n if multiplying all inputs by (lambda) increases

the dependent variable byn

Q = f ( K, L) So, f(K, L) = n • Q

Constant Returns to Scale is homogeneous of degree 1. 10% more all inputs leads to 10% more output.

Cobb-Douglas Production Functions are homogeneous of degree +

Cobb-Douglas Production Functions Q = A • K • L is a Cobb-Douglas Production Function

IMPLIES: Can be CRS, DRS, or IRS

if + 1, then constant returns to scaleif + < 1, then decreasing returns to scaleif + > 1, then increasing returns to scale

Coefficients are elasticities is the capital elasticity of output, often about .67 is the labor elasticity of output, often about .33

which are EK and E L

Most firms have some slight increasing returns to scale