# The production function depicts a relationship between which two variables

### Handout 6 Flashcards by Jodene Hager | Brainscape

A total-cost curve shows the relationship between the a. quantity .. (a) The production function depicts a relationship between which two variables? Also, draw. A key difference between accountants and economists is their different treatment The production function depicts a relationship between which two variables?. The production function depicts a relationship between which two variables? Also, draw a production function that exhibits diminishing marginal product.

TEAS Math Tutorial - The Relationship Between Two Variables

The output per unit of both the fixed and the variable input declines throughout this stage. At the boundary between stage 2 and stage 3, the highest possible output is being obtained from the fixed input.

Shifting a production function[ edit ] By definition, in the long run the firm can change its scale of operations by adjusting the level of inputs that are fixed in the short run, thereby shifting the production function upward as plotted against the variable input.

If fixed inputs are lumpy, adjustments to the scale of operations may be more significant than what is required to merely balance production capacity with demand. For example, you may only need to increase production by million units per year to keep up with demand, but the production equipment upgrades that are available may involve increasing productive capacity by 2 million units per year. Shifting a production function If a firm is operating at a profit-maximizing level in stage one, it might, in the long run, choose to reduce its scale of operations by selling capital equipment.

By reducing the amount of fixed capital inputs, the production function will shift down. The beginning of stage 2 shifts from B1 to B2. The unchanged profit-maximizing output level will now be in stage 2. When trying to understand the decision making process of different firms, economists assume that people think at the margin. The shape of the total cost curve is unrelated to the shape of the production function.

Diminishing marginal product exists when the total cost curve becomes flatter as outputs increases. Diminishing marginal product exists when the production function becomes flatter as inputs increase. Several related measures of cost can be derived from a firm's total cost. Fixed costs are incurred even when a firm does not produce anything. Variable costs usually change as the firm alters the quantity of output produced. Variable costs equal fixed costs when nothing is produced.

The cost of producing an additional unit of a good is not the same as the average cost of the good. Average variable cost is equal to total variable cost divided by quantity of output. The average total cost curve is unaffected by diminishing marginal product. The average total cost curve reflects the shape of both the average fixed cost and average variable cost curves. If the marginal cost curve is rising, then so is the average total cost curve.

The marginal cost curve intersects the average total cost curve at the minimum point of the average total cost curve. A second or third worker may have a higher marginal product than the first worker in certain circumstances. Assume Jack received all A's in his classes last semester. Average total cost and marginal cost are merely ways to express information that is already contained in a firm's total cost. Average total cost reveals how much total cost will change as the firm alters its level of production.

The shape of the marginal cost curve tells a producer something about the marginal product of her workers. When average total cost rises if a producer either increases or decreases production, then the firm is said to be operating at efficient scale.

Fixed costs are those costs that remain fixed no matter how long the time horizon is. Diseconomies of scale often arise because higher production levels allow specialization among workers. The fact that many inputs are fixed in the short run but variable in the long run has little impact on the firm's cost curves. In some cases, specialization allows larger factories to produce goods at a lower average cost than smaller factories.

The use of specialization to achieve economies of scale is one reason modern societies are as prosperous as they are. As a firm moves along its long-run average cost curve, it is adjusting the size of its factory to the quantity of production.

Because of the greater flexibility that firms have in the long run, all short-run cost curves lie on or above the long-run curve. There is general agreement among economists that the long-run time period exceeds one year. Adam Smith's example of the pin factory demonstrates that economies of scale result from specialization. What are opportunity costs?

How do explicit and implicit costs relate to opportunity costs? A key difference between accountants and economists is their different treatment of the cost of capital.

Does this cause an accountant's estimate of total costs to be higher or lower than an economist's estimate? The production function depicts a relationship between which two variables? Also, draw a production function that exhibits diminishing marginal product. How would a production function that exhibits decreasing marginal product affect the shape of the total cost curve? Explain or draw a graph. What effect, if any, does diminishing marginal product have on the shape of the marginal cost curve?

Bob Edwards owns a bagel shop. Bob hires an economist who assesses the shape of the bagel shop's average total cost ATC curve as a function of the number of bagels produced.

The results indicate a U-shaped average total cost curve. Bob's economist explains that ATC is U-shaped for two reasons. The first is the existence of diminishing marginal product, which causes it to rise. What would be the second reason? Assume that the marginal cost curve is linear. The second reason relates to average fixed cost 7.

If the average total cost curve is falling, what is necessarily true of the marginal cost curve? If the average total cost curve is rising, what is necessarily true of the marginal cost curve? According to the mathematical laws that govern the relationship between average total cost and marginal cost, where must these two curves intersect?

The opportunity cost of an item refers to all those things that must be forgone to acquire that item. This curve is of fundamental importance for economic analysis, for together with the demand curve for the product it determines the market price of the commodity and the amount that will be produced and purchased.

One pitfall must, however, be noted. In the demonstration of the supply curves for the firms, and hence of the industry, it was assumed that factor prices were fixed. Though this is fair enough for a single firm, the fact is that if all firms together attempt to increase their outputs in response to an increase in the price of the product, they are likely to bid up the prices of some or all of the factors of production that they use.

In that event the product supply curve as calculated will overstate the increase in output that will be elicited by an increase in price.

### Chapter 13 MC Section — The Costs of Production

A more sophisticated type of supply curve, incorporating induced changes in factor prices, is therefore necessary. Such curves are discussed in the standard literature of this subject. Marginal product It is now possible to derive the relationship between product prices and factor prices, which is the basis of the theory of income distribution.

To this end, the marginal product of a factor is defined as the amount that output would be increased if one more unit of the factor were employed, all other circumstances remaining the same.

Algebraically, it may be expressed as the difference between the product of a given amount of the factor and the product when that factor is increased by an additional unit. The marginal products are closely related to the marginal rates of substitution previously defined.

It has already been shown that the marginal rate of substitution also equals the ratio of the prices of the factors, and it therefore follows that the prices or wages of the factors are proportional to their marginal products.

This is one of the most significant theoretical findings in economics. To restate it briefly: This is not a question of social equity but merely a consequence of the efforts of businessmen to produce as cheaply as possible. Further, the marginal products of the factors are closely related to marginal costs and, therefore, to product prices.

This, also, is a fundamental theorem of income distribution and one of the most significant theorems in economics. Its logic can be perceived directly. If the equality is violated for any factor, the businessman can increase his profits either by hiring units of the factor or by laying them off until the equality is satisfied, and presumably the businessman will do so.

The theory of production decisions in the short run, as just outlined, leads to two conclusions of fundamental importance throughout the field of economics about the responses of business firms to the market prices of the commodities they produce and the factors of production they buy or hire: The first explains the supply curves of the commodities produced in an economy. Though the conclusions were deduced within the context of a firm that uses two factors of production, they are clearly applicable in general.

## Production function

Maximization of long-run profits Relationship between the short run and the long run The theory of long-run profit-maximizing behaviour rests on the short-run theory that has just been presented but is considerably more complex because of two features: It is of the essence of long-run adjustments that they take place by the addition or dismantling of fixed productive capacity by both established firms and new or recently created firms.

At any one time an established firm with an existing plant will make its short-run decisions by comparing the ruling price of its commodity with cost curves corresponding to that plant.

If the price is so high that the firm is operating on the rising leg of its short-run cost curve, its marginal costs will be high—higher than its average costs—and it will be enjoying operating profits, as shown in Figure 3. The firm will then consider whether it could increase its profits by enlarging its plant.

The effect of plant enlargement is to reduce the variable cost of producing high levels of output by reducing the strain on limited production facilities, at the expense of increasing the level of fixed costs. In response to any level of output that it expects to continue for some time, the firm will desire and eventually acquire the fixed plant for which the short-run costs of that level of output are as low as possible.

This leads to the concept of the long-run cost curve: These result from balancing the fixed costs entailed by any plant against the short-run costs of producing in that plant. The long-run costs of producing y are denoted by LRC y. The marginal long-run cost is the increase in long-run cost resulting from an increase of one unit in the level of output. It represents a combination of short-run and long-run adjustments to a slight increase in the rate of output.

It can be shown that the long-run marginal cost equals the marginal cost as previously defined when the cost-minimizing fixed plant is used. Long-run cost curves Cost curves appropriate for long-run analysis are more varied in shape than short-run cost curves and fall into three broad classes.

In constant-cost industries, average cost is about the same at all levels of output except the very lowest.

Constant costs prevail in manufacturing industries in which capacity is expanded by replicating facilities without changing the technique of production, as a cotton mill expands by increasing the number of spindles.

In decreasing-cost industries, average cost declines as the rate of output grows, at least until the plant is large enough to supply an appreciable fraction of its market.

Decreasing costs are characteristic of manufacturing in which heavy, automated machinery is economical for large volumes of output. Automobile and steel manufacturing are leading examples. Decreasing costs are inconsistent with competitive conditions, since they permit a few large firms to drive all smaller competitors out of business.

Finally, in increasing-cost industries average costs rise with the volume of output generally because the firm cannot obtain additional fixed capacity that is as efficient as the plant it already has. The most important examples are agriculture and extractive industries. Criticisms of the theory The theory of production has been subject to much criticism.