Chapter 4 - Production Functions and Supply Chains
We now take a look at what is behind supply-side decision-making, how corporations decide how much to produce and sell. Keep in mind that economic theory assumes that producers are profit-maximizers. This means that producers will expand output only if they expect this action will increase profit.
What is a production function?
A production function is a general statement about how a company turns inputs into output.
Inputs
In some textbooks, inputs are grouped into three categories – land, labor and capital.
Land is shorthand for land and natural resources. But land is not an economic resource until farmers use energy, tools, skills and knowledge to turn it into farmland to grow food. Natural resources are also not economic resources. Trees have to be processed to become timber and paper. Iron ore has to be mined and smelted (removed from rocks) and turned into steel. Crude oil, a polluter of water until 1859 (first oil well in the United States) has to be refined into gasoline and other fuels. Turning natural resources into economic resources takes technology (capital), energy and knowledge.
Information as an Input
Information is now recognized as another input category.
For now, we ignore who generates or sends information, the nature of information or how it is transmitted. Since information is an economic input, we are interested in who receives the information and how it affects the receiver’s behavior.
To change behavior, we assume that the information is new information for the receiver. Examples:
A stream of new orders changes production.
New cost information that changes the relative prices of inputs and then the production function – how the various factors of production are combined.
New production technology that changes how and what a company produces.
This is at the heart of the supply side of microeconomics – the effects and feedback effects of new information about the cost and price of inputs and how they are put together to produce output.
Why do I have to learn about production functions?
Because we are going to use a few general observations about production functions as the basis for talking about short-run cost curves. Cost curves, in turn, are the basis of supply decisions.
OK. Tell me about production functions.
We start with short-run production functions. Say that demand increases and the orders you receive are going up. That’s the good news. The bad news is that you have to produce more to fill the orders. How do you do that? You increase output by increasing the amount of inputs you need. So you hire more workers, make your employees work overtime, buy more raw materials, supplies, and cloud computing from other companies. The problem is that in the short-run you find out that you cannot increase all of your inputs. You can’t immediately expand the size of your plant, build new data center or distribution warehouses, hire specialized employees, install a larger computer system, install new business software like SAP or Oracle, or buy specialized machinery. All this takes time.
So in the short-run you keep adding more employees or overtime work to the same amount of plant and office space, you process more orders on the same computer system, you run your existing machinery longer hours per week. What eventually happens? You hit diminishing marginal returns.
Diminishing Marginal Returns
Sound bad. What is diminishing marginal returns?
In the short run, some inputs are fixed and some inputs are variable. Diminishing marginal returns happens when you keep adding more workers or hours worked and material (variable inputs) to a fixed amount of plant and equipment. There are capacity constraints.
The result is that output keeps going up as you add more variable inputs but the rate of increase (percent increase) slows down. Another way of saying this is that every time you add one more worker, total output goes up but by a smaller amount than when you added the prior worker.
Think about a McDonalds store. What if you continued to add workers? Total output (Happy Meals) per hour would rise but after covering the cash registers, the drive-through, the grill and the French fry machine, adding more workers wouldn’t increase output by very much.
(Paul Samuelson, in his famous textbook, says that studying economics is subject to diminishing returns. Not true! Heresy! In fact, learning specialized knowledge or a specialized skill may be subject to increasing returns, which may be one reason acquiring knowledge is important to economic development.)
Increasing Capacity and Returns to Scale
What if my orders continue to grow and I have trouble increasing output because of diminishing returns. What do I do?
Think long run. That is what strategic planning is about. In the long run, you can vary the amount and change all of your inputs. You can increase your manufacturing and information processing capacity. You can buy more and more productive machinery. You can buy better information processing systems. If you plan on doing this, however, you should be conscious of something called returns to scale. Returns to scale is what happens to unit cost when you increase your capacity (size).
Is this something good or bad?
It depends. What you would like to happen is increasing returns to scale, also known as economies of scale. This means that if you doubled the amount of all of your inputs, you would more than double the amount of output. Constant returns to scale says that doubling all inputs leads to doubling output. The bad outcome is decreasing returns to scale - doubling all inputs results in less than doubled output.
Which one can I expect?
Generally, growing companies in rapidly growing industries or industries developing or adopting new technology can expect increasing returns to scale. Expansion in mature industries with mature technology often results in constant returns to scale. Poorly managed companies that try to expand or diversify sometimes experience decreasing returns to scale. This often results in a corporate strategy we do not talk about in economics - downsizing.
Industrializing countries will usually have a number of industries exhibiting increasing returns to scale. The textbook reasons, from Adam Smith, are specialization of labor skills and machinery, and division of labor. (See my discussion of Adam Smith's famous example of a pin factory.) Another reason is that larger scale creates bottlenecks and new management control problems. Companies that solve these problems often experience increasing returns to scale and a definite competitive advantage. Innovate or fall behind.
It has also been common in the past that new product or production technology were only profitable if the new plant incorporating the new technology had substantially larger capacity than the existing plant. This was true of steel production and food processing in the late 1800s, auto production in the early 1900s and microchip production today.
All that is very interesting but why do I need to know this? In other words, why do I have to know about cost and cost curves? I thought only accountants had to know about cost.
The first objective of any organization is survival. For an economic organization, this means, in simple accounting terms, that total revenue has to be greater than total cost. This is even true of non-profit organizations like public colleges, art museums, and the Red Cross. If revenue is not greater than cost, the company has to change its strategy or face the threat of bankruptcy and liquidation. Managers will lose their jobs and owners will lose their investment.
If a company changes its strategy, such as producing more or changing its price, both total revenue and total cost will probably change. It is obviously important that total revenue increases more than total cost. What does the change in total revenue depend on? If you had changed price, it depends on the price elasticity of demand. A change in price will lead to a change in the number of units sold, and thus the number of units produced. What happens to total cost? It depends on the production function and, in the short run, probably diminishing returns.
So, what is the connection between production functions and cost curves?
Let’s start with short-run production functions and diminishing returns. First, there is this simple connection:
...the cost of fixed inputs is called fixed cost.
...the cost of variable inputs is called variable cost.
Fixed cost and variable cost are the two parts of total cost. By definition, total fixed cost stays the same as output rises. But total variable cost goes up as output rises. Why? Because you need more variable inputs (labor, raw materials, information processing) to produce more output.
Seems reasonable. So what’s the problem?
The problem is diminishing marginal returns as output rises. Say that every new employee you hire costs you $20 per hour. But every time you hire one more employee total output goes up by a smaller amount than when you hired the prior employee. You are spreading the extra $20 per hour cost over fewer extra units of output. So your variable cost per added unit of output is rising.
Here variable cost goes up by $20. What you want to know, however, is the cost per unit of added output, not the cost per added worker. The change in variable cost per added unit of output is called marginal cost.
The major conclusion from this discussion is that diminishing marginal returns is one cause of rising marginal cost. This means that after some level of output, each additional unit of output will cost you more than the prior one. How much more? Depends on how fast marginal returns are diminishing.
Marginal Cost
Are there any other reasons for rising marginal cost as output expands?
In the real world, yes. One is paying overtime. Employees do the same work at a higher hourly wage, leading to higher marginal cost. New employees may not be as productive as existing employees. The spot market price of extra raw materials may be higher than those bought under long-term contract. Machines tend to break down more often and need more maintenance when run harder and longer. Bottlenecks start to appear when systems are worked harder than normal.
Does that mean I should stop expanding output because of rising marginal cost?
Not necessarily. As long as marginal cost is less than price, expand output. Why? Because the increase in total revenue (price x quantity) will be greater than the increase in total cost (marginal cost x quantity). The difference between the two adds to total profit. This is the first version of the basic proposition of microeconomics.
If you think that orders (and marginal cost) are going to continue to rise, it is time for you to seriously think about expanding capacity and/or new capital investment to increase productivity. The goal is to reduce your average (unit) cost in the future. This is what you learn how to do when you take your finance course.
What if I don’t think that sales will keep expanding? Is there any way to reduce marginal cost in the short run?
Maybe. One possibility is to improve the productivity of your company by increasing the productivity of your employees, changing the organization structure and management procedures, and improving your internal systems. These kinds of improvements result in getting more output with the same amount of input or the same output with less input. Either way, the marginal cost curve shift down and profits go up.
Anything else I should know about cost?
Yes. A good manager knows about both accounting cost and economic (opportunity) cost. Accounting costs are important for budgeting and estimating the company’s internal cash flow. Economic cost is important for decision-making because it makes you think in terms of alternatives even when there is no explicit (accounting) cost. For example, assume your company owns its office buildings without any mortgages and are fully depreciated. Using the buildings does not generate any cash accounting costs on the income statement. But is occupying the building really free? Are there less expensive alternatives? Could you sublease or sell your office building and move to a lower-rent building? Are there any alternatives to all those offices for sales personnel who are seldom in their offices, alternatives like home offices, mobile phones and laptops?
If there is an alternative use of a resource or an alternative way to do something, there is opportunity cost. When there is opportunity cost, there is the possibility of reducing short-run marginal cost and long-run average cost.
Well, that wasn’t too bad. But supply curves seem more difficult to understand. Why does a supply curve slope up?
The main reason is that often unit costs (cost per unit of output) rise when a company tries to increase output. A company will not supply more unless it can get a higher price to cover its rising costs and make a larger total profit.
Since fixed cost per unit is going down as output goes up, this means that marginal cost (variable cost per unit when output changes) is going up. If a company’s managers believe that demand for the company’s product or service will continue to increase, they will expand capacity and invest in new capital and information technology equipment and software. Why? To produce more at a lower unit cost and increase profit.
What shifts a supply curve?
A major reason is a change in the price of inputs, which is the cost to the producer. If the price of an input goes down, a producer could lower price and make more profit by producing and selling more at the lower price. This assumes that the input price falls for all competitors and competition forces all competitors to lower price when the input price falls.
The same thing could happen if new production technology resulted in the same amount of output being produced at a lower cost. The extreme example may be computer processing. Another possibility is that management learns how to organize production and manage the company better. This could lower cost through increased productivity, which means the same output with fewer inputs.
There are macroeconomics (economy-wide) influences on the supply side. Part of total supply is imports. The cost of imports partly depends on foreign exchange rates, the ratio of the currency of one country to the currency of another country. Say the value of the Mexican peso goes down relative to the U.S. dollar. This lowers the dollar cost of Mexican imports into the U.S. Good news, bad news. The good news: This reduces the dollar cost of Mexican inputs bought by American companies in the U.S. The bad news: This reduces the dollar cost of Mexican products that compete with American-produced products. Sales of companies in Mexico go up; sales of competing companies in America go down.
What does equilibrium mean?
Equilibrium indicates that there is one price at which how much consumers want to buy equals how much producers want to supply. No one has to change their behavior; price and quantity don not change.
There are a number of assumptions behind this statement but we do not have to worry about them for a few chapters.
So why do we need both supply curves and demand curves to find equilibrium price and equilibrium output?
Remember that a demand curve or a supply curve, like a PPF curve, illustrates possible outcomes. It is only when the wishes of consumers are coordinated with the plans of producers - through changing price signals in a market - that we get equilibrium.
But what happens if a market is not in equilibrium? What if price is above the equilibrium price?
Say that at a price of $50 a barrel, crude oil producers collectively want to produce and sell more barrels of oil than oil refiners want to buy. The demand for crude oil depends on the oil refiners' forecast of demand for refined products like gasoline and aviation fuel. What happens if the refiners overestimated demand? They cut back refining production and purchases of crude oil. Excess (unsold) crude oil begins to fill up storage tanks as unwanted inventory. Drillers might decrease production or lower price to get refiners and their customers to buy more oil products in some period of time. They are assuming that a lower price of crude leads to a lower price of refined products that will lead to greater demand and sales.
At some lower price, supply equals demand. The amount oil producers pump at this price is equal to the amount refiners want to buy at this price. Nothing changes; the market is in equilibrium.
Another way of saying this is that “the market clears.” All supply is sold. So the equilibrium price is also called the “market-clearing” price.
Why do markets get out of equilibrium?
Equilibrium implies no new information.
If new information is created or received by producers or customers in a market, the adjustment period is a period of disequilibrium or disruption. Disruption may generate further new information and further disruption. If there is declining marginal disruption over time, as customers and producers absorb the new information and adjust their behavior, a market converges to a new equilibrium. Until the next change in technology or consumer preferences impact the industry.
So far the discussion has been about what happens in an isolated market producing a single product. The production possibility frontier is a general way to think about how an economy shifts inputs and production among many markets and products. (For the graph, see Production-Possibility Frontier on Wikipedia)
The production possibility frontier is an example of opportunity cost, of tradeoffs. For a given amount of inputs (workers, machinery, knowledge), the points on the PPF tell you what are the possible maximum combinations of output an economy can produce. The PPF illustrates the idea that an economy can get more of one product (drones) by giving up the production of some of another product (leaf blowers).
The PPF says more. When a society wants another one million drones, it has to give up more leaf blowers than the number it gave up to get the prior one million drones. This is an example of increasing opportunity cost (giving up more). Why do you think this happens?
The PPF is a supply-side concept. We do not know which combination of drones and leaf blowers a society will actually choose because we do not know anything about the demand side (what people want and value).
What if a society wants more of both?
Can do. Contrary to what a grumpy English reactionary said, economics is an optimistic (not dismal) social science. There are a number of ways a society can have more drones and leaf blowers. One way is to use its existing resources more efficiently, move towards the PPF. This increases productivity, getting more output from existing inputs.
Another is to trade with other countries. But countries do not trade with each other. Companies do. More and more, multinational corporations determine where to locate internal functions and where to buy inputs from other companies.
If an economy can grow (more inputs and output) and develop (new inputs and output), it can have increasing amounts of many goods and services. This has been the usual experience since the beginning of the Industrial Revolution over 200 years ago.
In the long run, the best way to have more of both is to promote economic development, which consists of producing new and better products and services through technological innovation, better organization, and a more skilled and educated workforce.
Most of an industrialized society's economic resources are owned and controlled by privately-owned business corporations. So the three growth strategies are mostly accomplished within corporations and through the interaction of corporations. Individual companies use the same growth strategies. To increase profits, corporations can use its resources more efficiently to reduce costs and increase productivity, and to develop or buy new technological or information processing inputs.
These concepts – economic development, higher productivity, economic growth – will be themes of these economics tutorials.
Applying Basic Concepts
Opportunity cost is the basic idea behind corporate financial analysis and any decision where there are alternative ways to meet an objective. Demand theory is the basis for market research and sales forecasting. Price elasticity of demand is useful when thinking about changing prices. Marginal cost is there to remind you that large and sudden increases in output often trigger rising unit cost. Economies of scale can be factored into cost and financial forecasts that are inputs into strategic planning.
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CASE STUDY
The Marginal (Opportunity) Cost of Saudi Arabian Oil
To an economist, the word “cost” implicitly has the word “opportunity” in front of it. Not knowing the difference between accounting cost and opportunity cost can lead to some serious pricing mistakes and misallocation of resources.
Saudi Arabia is one of the world’s three large crude oil producers, pumping over 10 million barrels per day. (A barrel is 42 gallons.) About 2.5 million barrels per day are refined for domestic consumption. Consumption of domestic oil has been rising rapidly.
Saudi Arabia is the world’s most inefficient user of oil. It has the world’s highest oil consumption per capita. Besides fuel, oil is used to generate electricity and desalinize water. It has been common for families to leave their air conditioning on even when going on vacation. Some offices are so cold that employees wear sweaters.
Prices to consumers are low because of low crude oil production costs and large government subsidies. Saudi Arabia is probably the world’s low cost producer of crude oil. Marginal cost is in the $5-$10 per barrel range. This low cost is passed on to refineries that produce gasoline, fuel for industry, and electricity. They, in turn, charge their customers a low price. In addition, the Saudi government spends over $10 billion/year to subsidize the cost to consumers of gasoline and diesel. Saudi drivers until 2015 paid the lowest price in the world for gasoline. The prices to consumers for electricity and water are also subsidized. The funds for these subsidies come from oil export revenue.
As domestic demand for oil products has risen, so has refining and power generating capacity. Saudi Arabia has increased production capacity by completing a $100 billion modernization and expansion of their oil infrastructure. Exports have remained constant.
For years, until 2015, the world price for crude oil was around $100/barrel. The high price of oil paid for the domestic subsidies.
For Saudi Arabia, $100/barrel was the opportunity cost of oil. Every barrel sold to domestic refineries at $10/barrel could have been sold to foreign refineries at $100/barrel. Domestic prices were based on the accounting cost of crude oil, not the opportunity cost.
If domestic prices had been based on the world price of oil, Saudi Arabia would have experienced the same effects as other countries. Growth in consumption would have been lower. There would have been an incentive to use oil more efficiently. Toyotas for Range Rovers. New technology and conservation would have appeared. Saudi Arabia is a country that could benefit from solar and wind generation of power.
The irony is that Saudi Arabia began moving in these new directions only when the opportunity cost of oil went down, when the world price of oil fell to $30-$50/barrel starting in 2015. Government revenue, over 80% dependent on export sales, fell. The government budget went from showing large surpluses to running large deficits. The government’s reserve fund was being depleted. New political leaders want to cut spending by reducing subsidies.
The government is beginning to look for alternative strategies to the burning of high (opportunity) cost oil. Investments in solar and wind have been announced. Natural gas is being substituted for oil. The prices of refined oil products and electricity are being raised. The price of gasoline, which was $0.48/gallon before an increase in 2015, rose again in 2017 to $1.35/gallon. More oil will be available to sell when the export price of oil goes up.
If you are interested about how the fall in oil prices affected the geopolitics of the Middle East and American shale production, see Saudi Arabia, Oil and Geopolitics.
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