7. FIRMS AND PRODUCTION

 

7.1. Firms and production

A firm is a unit or organization that convert inputs (raw material, workers,

and machine) into outputs.

7.2. Types of Firms

3 types of firms: sole proprietorship, partnership and cooperation.

1. Sole Proprietorship: firms owned and run by a single

individual.

2. Partnership: firms jointly owned and controlled by two or more

people.

The owners operate under a partnership agreement.

3. Corporations: firms owned by shareholders in proportion to the

numbers of shares of stock they hold. The shareholders elect a

board of directors who run the firm. In turn, the board of directors

usually hires managers who make short-term decisions and long-

term plans. 

The owner will make decisions for a firm. His objective is to maximize

profit (p).

p = Revenue – Cost

Revenue = PQ

A necessary condition for maximizing profit is to have an efficient

production process. An efficient production process is defined that the

firm cannot produce more output with the existing knowledge, or that the

firm cannot produce same output by using less inputs. If a firm is

produced efficiently, then it cannot be maximizing its profit.

There are three major categories of inputs:

Capital (K): building, machine, equipment, etc.

Labor (L): managers, skilled workers, or unskilled workers.

Material (M): oil, water, steel, iron, etc.

For simplicity, we study firms using L and K as inputs

The function of a firm is summarized in its production function.

q = f (L, K)

Where q is the maximum amount of output produced by using L units of

labor services and K units of labor. (Note: “Maximum” has implied that

production function is an efficient process).

7.3. Time and firms’ ability to vary inputs

Roughly, we divide a firm’s time frame into two time periods: long-run and

short-run.

Long-run: all inputs can be changed – both labor and capital.

Short-run: some inputs are not changeable – capital is fixed, labor

can change.

This is because is generally easier to hire and fire workers instead of

expand or shrink plant sizes.

Equipment is fixed but you can always hire an extra hand.

7.3.1. Short-run production

Let’s see a short-run production function (capital is fixed):

q = f(L,`K)

Production function with one variable input (L)

A few definitions first:

Marginal product of labor – the value of one extra worker

MPL = Dq/DL

Average product of labor – the value of team efforts

APL = q/L

The definition in Table 6.1.

Note that capital is fixed at 8, while labor can be varied.

The graph below shows how Total product, Marginal product, and Average

product curve look like.

Figure 6.1

Facts:

TP (Total Product)

1. Initially, TP increases faster and faster as L increases.

This is because specialization can increase productivity.

2. After the benefit of specialization is fully utilized, the increase in TP

will slow down until an extra worker contributes negatively.

 

MP (Marginal Product) by definition, it is the slope of TP.

1. MP increases.

2. MP decreases but is still positive

3. MP is negative.

 

As production increases, it will enter the range of “diminishing marginal

returns.” This is called the “law of diminishing marginal returns.”

This means the extra benefit from an extra worker decreases as the

number of workers increases.

 

AP is the slope of the line from the origin to (L, q).

Its relationship with MP:

1. MP > AP à AP increases

2. MP < AP à AP decreases

3. MP = AP (crossing point) à AP at maximum

  Why?

When L is 4, we have AP=14, which means that in average, each worker

can produce 14 units of output. If we increase 1 more unit of labor, this

extra labor will generate 19 units of output. If he can only generate 14

units of output, then AP will not be changed. But now 19>14, so this extra

unit bids up the average product.

Exercises

1. Suppose a chair manufacturer is producing in the short run when

equipment is fixed. The manufacturer knows that as the number of

laborers used in the production process increases from 1 to 7, the

number of chairs produced changes as follows: 10, 17, 22, 25, 26,

25, and 23.

a. Calculate the marginal and average product of labor for this

production function.

Answer: The average product of labor, APL, is equal to Q/L. The marginal product of

labor, MPL, is equal to DQ/ DL, the change in output divided by the change in labor input.

For this production process we have:

b. Does this production function exhibit diminishing returns to labor?

Explain.

Answer: This production process exhibits diminishing returns to labor. The marginal

product of labor, the extra output produced by each additional worker, diminishes as

workers are added, and is actually negative for the sixth and seventh workers.

c. Explain intuitively what might cause the marginal product of labor to

become

negative.

Answer: Labor’s negative marginal product for L > 5 may arise from congestion in the

chair manufacturer’s factory. Since more laborers are using the same, fixed amount of

capital, it is possible that they could get in each other’s way, decreasing efficiency and

the amount of output.

2. The marginal product of labor is known to be greater than the

average product of labor at a given level of employment. Is the

average product increasing or decreasing? Explain.

Answer: If the marginal product of labor, MPL, is greater than the average product

of labor, APL, then each additional unit of labor is more productive than the average of

the previous units. Therefore, by adding the last unit, the overall average increases. If

MPL is greater than APL, then APL is increasing. If the MPL is lower than the APL,

then the last unit reduces the average. The APL is at a maximum when the productivity

of the last unit is equal to the average of the previous units (i.e., when MPL = APL).