Managerial Economics (chapter 6)

Chapter 6 Production Theory and Estimation

Managerial Economics Instructor: Maharouf Oyolola

Introduction • Managers are required to make decisions about the employment of the various types of resources within the firm. • Production decisions include the determination of the type and amount of resources or inputssuch as land, labor, raw and processed materials, factories, machinery, equipment, and managerial talent- to be used in the production of a desired quantity of output.

Introduction • The objective of the private sector manager is to combine the resources of the firm in the most efficient manner to contribute to the goal of maximizing shareholder wealth. • This chapter discusses the use of the theory of production in making wealthmaximizing production decisions

Production • It refers to the transformation of inputs or resources into outputs of goods and services.

Example 1 • IBM hires workers to use machinery, parts, and raw materials in factories to produce personal computers. • The final output in this example is the IBM computer.

Inputs • These are resources used in the production of goods and services. • There are four types of inputs - Labor - Capital - Land - Entrepreneurship

Production • The creation of any good or service that has value to either consumers or other producers. • This definition includes production of transportation services, legal advice, education (teaching students), and invention

The Production Function • A mathematical model, schedule, or graph that relates the maximum quantity of output that can be produced from given amounts of various inputs. • Letting X and Y represent the quantities of inputs used in producing a quantity Q of output, a production function can be represented in the form of a mathematical model as: • Q= f( X, Y)

Input • A resource or factor of production, such as a raw material, labor skill, or piece of equipment, that is employed in a production process

Example • The production of a house requires the use of many different labor skills (carpenters, plumbers, and electricians), raw materials (bricks, lumber), and types of equipment (bulldozers, saws, and cement mixers)

The Cobb-Douglas production function • One commonly used function is the CobbDouglas production function:

β1

Q = αL K

β2

Where L is the amount of labor and K is the amount of capital used in the production process (α,, β1 and β2 are constants )

Short-Run • The period of time in which one (or more) of the resources employed in a production process is fixed or incapable of being varied. • For example, for a production plant of fixed size and capacity, the firm can increase output only by employing more labor, such as by paying workers overtime or by scheduling additional shifts.

Long-run • The period of time in which all the resources employed in a production process can be varied.

The production function with one variable input • In this section, we present the theory of production when only one input is variable. Thus, we are in the short-run. • We assume, for instance, that capital input does not vary in the short-run. Only labor changes

Total, Average and Marginal Product • Total Product (TP) of the variable input •

∆ TP MPL = ∆ L TP APL = L

Production or output elasticity %∆ Q EL = %∆ L ∆Q Q ∆ Q L MPL EL = = • = ∆L ∆ L Q APL L

Production or output elasticity • EL measures the percentage change in output divided by the percentage change in the quantity of labor used.

Total, Marginal, and Average Product of Labor, and Output Elasticity Labor (number of Workers)

Output or total Marginal product product of Labor

Average Product of Labor

Output Elasticity of Labor

0

0

-

-

-

1

3

3

3

1

2

8

5

4

1.25

3

12

4

4

1

4

14

2

3.5

0.57

5

14

0

2.8

0

6

12

-2

2

-1

Total product 16 Total output (TP)

14 12 10 8

TP

6 4 2 0 0

2

4 Labor (L)

6

8

Marginal Product and Average product 6 5 MPL and APL

4 3 2

MPL

1

APL

0 -1 0

2

4

-2 -3 Labor

6

8

Interpretation of the graphs • Law of Diminishing Marginal Returns: Given that the amount of all other productive factors remains unchanged, the use of increasing amount of a variable factor in the production process beyond some point will eventually result in diminishing marginal increases in total output.

Interpretation of the graphs • In analyzing the production function, economists have identified three different stages of production. • Stage I: the range of X over which average product is increasing. • Stage II: corresponds to the range of X from the point at which the average product is a maximum to the point where the marginal product declines to zero. The endpoint of stage II thus corresponds to the point of maximum output on the TP curve. • Stage III: encompasses the range of X over which the total output is declining, or equivalently, the marginal product negative.

Optimal use of the variable input • How much labor (the variable in our previous section) should the firm use in order to maximize profits? • The answer is that the firm should employ an additional unit of labor as long as the extra revenue generated from the sale of the output exceeds the extra cost of hiring the unit of labor (i.e., until the extra revenue equals the extra cost).

Example • If an additional unit of labor generates $30 in extra revenue and costs an extra $20 to hire, it pays for the firm to hire this unit of labor. Therefore, its total profit will increase by $10. • However, it does not pay for the firm to hire an additional unit of labor if the extra revenue it generates falls short of the extra cost incurred.

Marginal Revenue Product of Labor • This equals the marginal product of labor (MPL) times the marginal revenue (MR) from the sale of the extra output produced. • This is the extra revenue generated by the use of an additional unit of labor

MRPL = ( MPL )( MR )

Marginal Resource cost of Labor • The extra cost of hiring an additional unit of labor (MRCL) is equal to the increase in the total cost to the firm resulting from hiring the additional unit of labor. That is,

∆TC MRC L = ∆L

• A firm should continue to hire labor as long as MRPL>MRCL and until MRPL=MRCL.

Marginal Revenue product and Marginal Factor cost- Deep Creek Mining Company Labor (Number of workers)

TP

Marginal revenue of labor (tons per worker)

Total revenue TP=P.Q ($)

Marginal revenue ($/ton)

Marginal revenue product MRPx=MPx* MRQ

Marginal factor cost ($/worker)

0

0

-

0

-

-

-

1

6

6

60

10

60

50

2

16

10

160

10

100

50

3

29

13

290

10

130

50

4

44

15

440

10

150

50

5

55

11

550

10

110

50

6

60

5

600

10

50

50

7

62

2

620

10

20

50

8

62

0

620

10

0

50

Comments • As it can be seen in the table above, the optimal input is X*=6 workers because MRP=MFC=$50 at this point

The Production Function with two variable inputs • We now examine the production function when there are two variable inputs. • An Isoquant shows the various combinations of inputs (labor and capital) that the firm can use to produce a specific level of output. • A higher isoquant refers to a larger output, while a lower isoquant refers to a smaller output.

Marginal Rate of Technical Substitution • The rate at which one input may be substituted for another input in producing a given quantity of output.

MRP and MFC

Optimal use of labor 160 140 120 100 80 60 40 20 0

MRP MFC

0

2

4

6 Labor

8

10

Optimal combination of inputs • Suppose that a firm uses only labor and capital in production. The total costs or expenditures of the firm can then be represented by • C=wL + rK where • C=total costs • W=wage rate of labor • L=quantity of labor • R=rental price capital • K=quantity of capital used

Optimization problem • One can solve for the combination of inputs that either • (1) minimizes total cost subject to a given constraint on output • (2) maximizes output subject to a given total cost constraint

Returns to scale • Returns to scale refers to the degree by which output changes as a result of a given change in the quantity of all inputs used in the production. • There are 3 types of returns to scale: constant, increasing, and decreasing.

Example • If the quantity of all inputs used in the production is increased by a given proportion, We have Constant returns to scale if output increases in the same proportion; increasing returns to scale if output increases by a greater proportion; and decreasing returns to scale if output increases by a smaller proportion. • (see figure 6-14 page 252)

Constant Returns to Scale capital

6

B 200Q A

3

100Q 3

6

labor

Increasing returns to scale

capital

6

C 300Q

3

A 100Q 3

6

Labor

Decreasing Returns to Scale capital

6

D 150Q

3

A 100Q

3

6

labor