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Chapter 6 Firms and Productions 6 The Ownership and Management of Firms Firm. An organization that converts inputs such as labor, materials, energy and capital into outputs, the goods and services that it sells. Private, Public and Nonprofit Firms Gross Domestic Product (GDP). GDP is a measure of a ...

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Chapter 6 Firms and Productions 6.1

The Ownership and Management of Firms

Firm. An organization that converts inputs such as labor, materials, energy and capital into outputs, the goods and services that it sells.

Private, Public and Nonprofit Firms Gross Domestic Product (GDP). GDP is a measure of a country’s total output, i.e. the gods and services that it sells. Organizations that pursue economic activity fit into three broad categories: Private Sector Sometimes referred to as the for-profit private sector, consists of firms owned by individuals or other non-governmental entities and whose owners try to earn a profit. In almost every country, this sector contributes the most to the GDP Public Sector Consists of firms and organizations that are owned by governments or government agencies. For example, the National Railroad Passenger Corporation (Amtrak) is owned primarily by the US government. The government produces less than one-fifth (51) of the total GDP in most developed countries. 1

However, government’s share is higher in some developed countries that provide many government services or maintain a relatively large army. The government’s share varies substantially in less developed countries, ranging from very low levels to very high. Strikingly, a number of former communist countries now have public sectors of comparable relative size to developed countries and hence must rely primarily on the private sector for economic activity. Nonprofit or Not-for-profit Sector Consists of organizations that neither government-owned nor intended to earn a profit. According to U.S. Census Bureau’s 2009 U.S. Statistical Abstract, the private sector created 77% of the U.S. GDP, the government sector was responsible for 11%, and nonprofits and households contributed the remaining 12%.

The Ownership of Fort-Profit Firms The legal structure of firms determines who is liable for its debts. Within the private sector, there are three primary legal forms of organization: • A sole proprietorship • A general partnership • A corporation Sole proprietorships Firms owned by a single individual who is personally liable for the firm’s debts General Partnerships Often called partnerships are businesses jointly owned and controlled by two or more people who are personally liable for the firm’s debts. The owners operate under a partnership agreement. In most legal jurisdictions, if

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any partner leaves, the partnership agreement ends and a new partnership agreement is created if the firm is to continue operations. Corporation Owned by shareholders in proportion to the number of shares or amount of stock they hold. The shareholders elect a board of directors to represent them. In turn, the board of directors usually hires managers to oversee the firm’s operations. Some corporations are very small and have a single shareholder; others are very large and have thousands of shareholders. A fundamental characteristic of corporations is that the owners are not personally liable for the firm’s debts; they have limited liability. Limited Liability. A condition whereby the personal assets of the owners of the corporation cannot be taken to pay a corporation’s debts if it goes into bankruptcy. Because corporations have limited liability, the most that shareholders can lost is the amount they paid for their stock, which typically becomes worthless if the corporation declares bankruptcy. The purpose of limiting liability was to allow firms to raise funds and grow beyond what was possible when owners risked personal assets on any firm in which they invested. According to the 2010 U.S. Statistical Abstract, U.S. corporations are responsible for 83% of business receipts and 67% of net business income, although they comprise only 19% of all nonfarm firms. Nonfarm sole proprietorships are 72% of all firms but receive only 4% of sales and earn 10% of net income. Partnerships comprise 10% of firms, account for 13% of receipts, and earn 23% of net income. These statistics show that larger firms tend to be corporations, whereas smaller firms are often sole proprietorships.

The Management of Firms In a small firm, the owner usually manages the firm’s operations. In larger firms, typically corporations and larger partnerships, a manager or a management team usually runs the company. In such firms, owners, managers and lower-level supervisors are all decision makers. What is in the best interest of the owners may not be in the best interest of managers or other employees. For example, a manager may want a fancy 3

office, a company car, a corporate jet, and other perks, but an owner would likely oppose those drains on profit. The owner replaces the manager if the manager pursues personal objectives rather than the firm’s objectives. In a corporation, the board of directors is responsible for ensuring that the manager stays on track. If the manager and the board of directors are ineffective, the shareholders can fire both or change certain policies through votes at the corporation’s annual shareholders’ meeting. For now, we’ll ignore potential conflict between managers and owners and assume that the owner is the manager of the firm and makes all the decisions.

What Owners Want π = R−C Where profit, π, is the difference between revenue R = pq and its cost, C. Efficient Production or Technological Efficiency. Situation in which the current level of output cannot be produced with fewer inputs, given existing knowledge about technology and the organization of production. If a firm does not produce efficiently, it cannot be profit maximizing - so efficient production is a necessary condition for profit maximization. However, efficient production alone is not a sufficient condition to ensure that a firm’s profit is maximized.

6.2

Production

Firms uses many types of inputs, most of which can be grouped into three broad categories: Capital (K) Long-lived inputs such as land, buildings (factories, stores), and equipment (machines, trucks) Labor (L) human services such as those provided by managers, skilled workers (architects, economists, engineers) and less skilled workers (custodians, construction laborers) Materials (M) Raw goods (oil, water, wheat) and processed products (aluminium, plastic, paper) The output can be a service. 4

Production Functions The various ways inputs can be transformed into output are summarized in the production function. Production Function. The relationship between the quantities of inputs used and the maximum quantity of output that can be produced, given current knowledge about technology and organization. The production function for a firm that uses only labor and capital is q = f (L, K),

(6.1)

where q units of output are produced using L units of labor services and K units of capital. The production function only shows maximum amount of output that can be produced, because it includes only efficient production processes.

Time and the Variability of Inputs A firm can more easily adjust its input in the long run than in the short run. the more time a firm has to adjust its input, the more factors of production it can alter. Short Run A period of time so brief that at least one factor of production cannot be varied practically fixed input A factor that cannot be varied practically in a short run variable input A factor of production whose quantity can be changed readily by the firm during the relevant time period. Long Run A lengthy enough period of time that all inputs can be varied (all factors of productions are variable inputs) How long it takes for all inputs to be variable depends on the factors a firm uses. For many firms, materials and often labor are variable inputs over a month. However, labor is not always a variable input. Similarly, capital may be a variable or fixed input.

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6.3

Short-Run Production: One Variable and One Fixed Input

In the short run, the firm’s production function is ¯ q = f (L, K)

(6.2)

¯ is the fixed number of units of capital. where q is output, L is workers, and K We can show how extra workers affect the total product by using two additional concepts: the marginal product of labor and the average product of labor.

Total Product The exact relationship between output or totalproduct and labor can be illustrated by a particular function, Equation 6.2.

Marginal Product of Labor Marginal Product of Labor (MPL ). The change in total output, ∆q , resulting from using an extra unit of labor, ∆L, holding other factors constant. MPL =

∆q ∆L

Average Product of Labor Average Product of Labor (APL ). The ratio of output, q, to the number of workers L, used to produce that output. APL =

q L

Graphing the Product Curves Effect of Extra Labor In most production processes, the average product of labor first rises and then falls as labor increases. Output may initially rise because output increases more than in proportion to labor, so the average product of labor rises. 6

As the number of workers rises further, however, output may not increase by as much per worker as they have to wait to use a particular piece of equipment or get in each other’s way. Relationship of the Product Curves The three curves are geometrically related. The average product of labor for L workers equals the slope of a straight line from the origin to a point on the total product curve for L workers. The marginal product of labor also has a geometric interpretation in terms of the total product curve. The slope of the total product curve at a given point, δq , equals the marginal product of labor. that is, the marginal product of δL labor equals the slope of a straight line that is tangent to the total output curve at a given point.

Law of Diminishing Marginal Returns Next to supply equals demand, probably the most commonly used phrase of economic jargon is the law of diminishing marginal returns. This law determines the shapes of the total product and marginal product of labor curves as the firm uses more and more labor. Law of Diminishing Marginal Returns. If a firm keeps increasing an input, holding all other inputs and technology constant, the corresponding increases in output will become smaller eventually. That is, if only one input is increased, the marginal product of that input will diminish eventually. Note that this is not the same thing as diminishing returns, which many people mistake it with. The two phrases have different meanings. Where there are diminishing marginal returns, the MPL curve is falling, but it may be positive. With diminishing returns, extra labor causes output to fall. Thus saying there are diminishing returns is much stronger than saying there are diminishing marginal returns. We often observe firms producing where there are diminishing marginal returns to labor, but we rarely see firms operating where there are diminishing total returns. Only a firm that is willing to lose money would operate so inefficiently that it has diminishing returns. Such a firm could produce more output by using fewer inputs.

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A second misconception of this law is to claim that marginal products must fall as we increase an input without requiring that technology and other inputs stay constant. If we increase labor while simultaneously increasing other factors or adopting superior technologies, the marginal product of labor may rise indefinitely. See page 162 for Thomas Malthus’ example of this fallacy.

6.4

Long-Run Production: Two Variable Inputs

In the long run, both inputs are variable. With both factors variable, a firm can usually produce a given level of output by using: • a great deal of labor and very little capital, • a great deal of capital and very little labor, • moderate amounts of both That is, the firm can substitute one input for another while continuing to produce the same level of output, in much the same way that a consumer can maintain a given level of utility by substituting one good for another. Typically, a firm can produce in a number of different ways, some of which require more labor than others. For example, a lumberyard can produce 200 planks an hour with 10 workers using hand saws, with 4 workers using handheld power saws, or with 2 workers using bench power saws.

Isoquants Isoquant. A curve that shows the efficient combinations of labor and capital that can produce a single (iso) level of output (quantity ) If the production function is q = f (L, K), then the equation for an isoquant where output is held constant at q¯ is q¯ = f (L, K ). An isoquant shows the flexibility that a firm has in producing a given level of output. We can use these isoquants to illustrate what happens in the short run when capital is fixed and only labor varies. 8

Thus, if the firm holds one factor constant and varies another factor, it moves from one isoquant to another. In contrast, if the firm increases one input while lowering the other appropriately, the firm stays on a single isoquant. Properties of Isoquants Isoquants have most of the same properties as indifferent curves. The biggest difference between indifference curves and isoquants is that an isoquant holds quantity constant, whereas an indifference curve holds utility constant. There are three (3) major properties of isoquants. Most of these properties result from firms’ producing efficiently. First, the farther an isoquant is from the origin, the greater the level of output. That is, the more inputs a firm uses, the more output it gets if it produces efficiently. Second, isoquants do not cross. Such intersections are inconsistent with the requirement that the firm always produces efficiently. Thus, efficiency requires that isoquants do not cross. Third, isoquants slope downward. If an isoquant sloped upward, the firm could produce the same level of output with relatively few inputs or relatively many inputs. Consequently, because isoquants show only efficient production, an upward-sloping isoquant is impossible. Virtually the same argument can be showed to show that isoquants must be thin. Shape of Isoquants The curvature of an isoquant shows how readily a firm can substitute one input for another. The two extreme cases are production processes in which inputs are perfect substitutes or in which they cannot be substituted for each other. If the inputs are perfect substitutes, each isoquant is a straight line. Suppose either potatoes from Maine, x, or potatoes from Idaho, y, both of which are measured in pounds per day, can be used to produce potato salad, q, measured in pounds. The production function is q = x + y. Sometimes it is impossible to substitute one input for the other: Inputs must be used in fixed proportions. Such a production is called a fixedproportions production function. Dashed lines show that the isoquant 9

would be right angles if isoquants would include inefficient production processes Other production processes allow imperfect substitution between inputs. The isoquants are convex (so the middle of the isoquant is closer to the origin that it would be if the isoquant were a straight line). They do not have the same slope at every point, unlike the straight-line isoquants. Most isoquants are smooth, slope downward, curve away from the origin, and lie between the extreme cases of straight lines (perfect substitutes) and right angles (non substitutes).

Substituting Inputs The slope of an isoquant shows the ability of a firm to replace one input with another while holding output constant. Figure 6.4 shows this substitution. The isoquant shows various combinations of L and K that the firm can use to produce 10 units of output. The firm can produce 10 units of output using the combination of inputs at a or b. At point a, the firm uses 2 workers and 16 units of capital. The 10

firm could produce the same amount of output using ∆K = −6 fewer units of capital if it used one more worker, ∆L = 1, point b. If we drew a straight = −6. Thus, the slope tells us how line from a to b, its slope would be ∆K ∆L many fewer units of capital (6) the firm can save if it hires one more worker.

The slope of an isoquant is called the marginal rate of technical substitution (MRTS): Marginal rate of technical substitution. The number of extra units of one input needed to replace one unit of another input that enables a firm to keep the amount of output it produces constant. MRT S =

change in capital ∆K = change in labor ∆L

Because isoquants slope downward, the MRTS is negative. That is, the firm can produce a given level of output by substituting more capital for less labor (or vice versa). Substitutability of Inputs Varies Along an Isoquant The marginal rate of technical substitution varies along a curved isoquant, as in Figure 6.4 for the printing firm. If the firm is initially at point a and it 11

hires one more worker, the firm gives up 6 units of capital and yet remains on the same isoquant as point b, so the MRT S is -6. If the firm hires another worker, the firm can reduce its capital by 3 units and yet stay on the same isoquant, moving from b to c, so the MRT S is -3, ad nauseam. This decline in the absolute value of the MRT S along an isoquant as the firm increases labor illustrates diminishing marginal rate of technical substitution. The curvature of the isoquant away from the origin reflects diminishing marginal rates of technical substitution. The more labor the firm has, the harder it is to replace the remaining capital with labor, so the MRT S falls as the isoquant becomes flatter. In the special case in which isoquants are straight lines, isos do not exhibit diminishing marginal rates of tech sub. because neither input becomes more valuable in the production process: The inputs remain perfect substitutes. Substitutability of Inputs and Marginal Products The marginal rate of tech. subst. – the degree to which inputs can be sub’d for each other – equals the ratio of the marginal product of labor to the marginal product of capital, as we now show. The MRTS tells us how much a firm can increase one input and lower the other value while still staying on the same iso. Knowing the MPL (labor) and MPK (capital), we can determine how much one input must increase to offset a reduction in the other. ∆q ∆K ∆q Because the MPL = δL is the increase in output per extra unit of labor, if the firm hires ∆L more workers its output increases by MPL ∗ ∆L. For example, if MPL is 2 and the firm hires one extra worker, its output rises by 2 units. A decrease in capital alone causes output to fall by MPK ∗ ∆K, where ∆q MPK = δK is the output the firm loses from decreasing capital by one unit, holding all other factors fixed. To keep output constant, ∆q = 0, this fall in output from reducing capital must exactly equal the increase in output from increasing labor: (MPL ∗ ∆L) + (MPK ∗ ∆K) = 0 MPK =

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Rearranging, we find: −

∆K MPL = = MRT S. ∆L MPK

(6.3)

That is, the MRT S which is the change in capital relative to the change in labor, equals the ratio of the marginal products. We can use Equation 6.3 to explain why MRT S diminish as we move to the right along the iso in Figure 6.4. As we replace capital with labor (shift downward and to the right along the iso), the MPK increases – when there are few pieces of equipment per worker, each remaining piece is more useful – and the MPL falls, so the M PL MRT S = − M falls in absolute value. PK

6.5

Returns to Scale

We now turn to the question of how much output changes if a firm increases all its inputs proportionately. The answer helps a firm determine its scale or size in the long run. In the long run, a firm can increase its output by building a second plant and staffing it with the same number of workers as in the first one. Whether the firm chooses to do so depends in part on whether its output increases less than in proportion...