Question

Discuss the production and cost functions of a typical firm.

Answer 1

The production function relates the maximum amount of output that can be obtained from a given number of inputs.

In economics, a production function relates physical output of a production process to physical inputs or factors of production. It is a mathematical function that relates the maximum amount of output that can be obtained from a given number of inputs – generally capital and labor. The production function, therefore, describes a boundary or frontier representing the limit of output obtainable from each feasible combination of inputs.

Firms use the production function to determine how much output they should produce given the price of a good, and what combination of inputs they should use to produce given the price of capital and labor. When firms are deciding how much to produce they typically find that at high levels of production, their marginal costs begin increasing. This is also known as diminishing returns to scale – increasing the quantity of inputs creates a less-than-proportional increase in the quantity of output. If it weren’t for diminishing returns to scale, supply could expand without limits without increasing the price of a good.

The law of diminishing returns states that adding more of one factor of production will at some point yield lower per-unit returns.

In economics, diminishing returns (also called diminishing marginal returns) is the decrease in the marginal output of a production process as the amount of a single factor of production is increased, while the amounts of all other factors of production stay constant. The law of diminishing returns states that in all productive processes, adding more of one factor of production, while holding all others constant (“ceteris paribus”), will at some point yield lower per-unit returns. The law of diminishing returns does not imply that adding more of a factor will decrease the total production, a condition known as negative returns, though in fact this is common.

For example, the use of fertilizer improves crop production on farms and in gardens; but at some point, adding more and more fertilizer improves the yield less per unit of fertilizer, and excessive quantities can even reduce the yield. A common sort of example is adding more workers to a job, such as assembling a car on a factory floor. At some point, adding more workers causes problems such as workers getting in each other’s way or frequently finding themselves waiting for access to a part. In all of these processes, producing one more unit of output will eventually cost increasingly more, due to inputs being used less and less effectively.

This increase in the marginal cost of output as production increases can be graphed as the marginal cost curve, with quantity of output on the x axis and marginal cost on the y axis. For many firms, the marginal cost curve will initially be downward sloping, representing added efficiency as production increases. If the law of diminishing returns holds, however, the marginal cost curve will eventually slope upward and continue to rise, representing the higher and higher marginal costs associated with additional output.

In the short run, a firm has a set amount of capital and can only increase or decrease production by hiring more or less labor. The fixed costs of capital are high, but the variable costs of labor are low, so costs increase more slowly than output as production increases. As long as the marginal cost of production is lower than the average total cost of production, the average cost is decreasing. However, as marginal costs increase due to the law of diminishing returns, the marginal cost of production will eventually be higher than the average total cost and the average cost will begin to increase.

A production function relates the input of factors of production to the output of goods. In the basic production function inputs are typically capital and labor, though more expansive and complex production functions may include other variables such as land or natural resources. Output may be any consumer good produced by a firm. Cars, clothing, sandwiches, and toys are all examples of output.

Capital refers to the material objects necessary for production. Machinery, factory space, and tools are all types of capital. In the short run, economists assume that the level of capital is fixed – firms can’t sell machinery the moment it’s no longer needed, nor can they build a new factory and start producing goods there immediately. When looking at the production function in the short run, therefore, capital will be a constant rather than a variable. Although in reality a firm may own the capital that it uses, economists typically refer to the ongoing cost of employing capital as the rental rate because the opportunity cost of employing capital is the income that a firm could receive by renting it out. Thus, the price of capital is the rental rate.

Labor refers to the human work that goes into production. Typically economists assume that labor is a variable factor of production; it can be increased or decreased in the short run in order to produce more or less output. The price of labor is the prevailing wage rate, since wages are the cost of hiring an additional unit of capital.

• One consequence of the law of diminishing returns is that producing one more unit of output will eventually cost increasingly more, due to inputs being used less and less effectively.
• The marginal cost curve will initially be downward sloping, representing added efficiency as production increases. If the law of diminishing returns holds, however, the marginal cost curve will eventually slope upward and continue to rise.
• The SRAC is typically U-shaped with its minimum at the point where it intersect the marginal cost curve. This is caused by the first increasing, and then decreasing, marginal returns to labor.
• The typical LRAC curve is also U-shaped, reflecting increasing returns of scale where negatively-sloped, constant returns to scale where horizontal and decreasing returns where positively sloped.