The Firm and Production Overheads

Neoclassical firm - A neoclassical firm is an organization and earns the difference between what it receives in revenue, and what it spends on inputs (costs). Nature of the firm that controls the transformation of inputs (resources it owns or purchases) into outputs (valued products that it sells),

Business firm A business firm is an organization, owned and operated by private individuals, that specializes in production.

Production systems, goods, services and factors A production system or technology is a description of the set of outputs that can be produced by a given set of factors of production or inputs using a given method of production or production process.

Production Technologies The technology set (technology for short) for a given production process is defined as the set of all input and output combinations such that the such that the output vector y can be produced from the given set of inputs x

A factor of production (input) is a good or service that is employed in the production process. A product is a good or service that is the output of a particular production process.

Expendable factors of production are raw materials, or produced factors that are completely used up or consumed during a single production period.

Capital Capital is a stock that is not used up during a single production period, provides services over time, and retains a unique identity.

Capital services Capital services are the flow of productive services that can be obtained from a given capital stock during a production period. It is usually possible to separate the right to use services from ownership of the capital good. They arise from a specific item of capital rather than from a production process.

Revenue Revenue is the total income that comes from the sale of the output (goods and services) of a given firm or production process.

Cost Cost is the value of all factors of production used by the firm in producing a given level of output, If the input bundle used by a firm for a particular process is (x 1, x 2,... x n ), and w i is the price of the ith input, then whether a single product or multiple products.

Profit The profit from a given production plan is the revenue obtained from the plan minus the costs of the inputs used to implement it

Objectives of the firm We usually assume that firma exists to make money Given this assumption we can set up the firm level decision problem as maximizing the returns from the technologies controlled by the firm taking into account Such firms are called for-profit firms. the demand for final consumption goods, opportunities for buying and selling factors (or products) from other firms the actions of other firms in the market

In a perfectly competitive market, this means take prices as given the firm will take prices as given, and choose the levels of inputs and outputs that maximize profits Objectives of the firm

Purely competitive markets When buyer or sellers in a market are not able affect the price of a product, we say that the market is purely competitive, or just, competitive.

Why firms ? Gains from specialization One man draws out the wire, another straightens it, a third cuts it, a fourth points it, a fifth grinds it at the top for receiving the head: to make the head requires three distinct operations; to put it on is a [separate] business, to whiten the pins is another; it is even a trade by itself to put them into the paper; and the important business of making a pin is, in this manner, divided into about eighteen distinct operations, which, in some manufactories, are all performed by distinct hands.

Examples of gains from specialization Assembly lines Machines needed more than on person (2-person saw) Learning by doing and improved skills Learning by doing and economies of size

Lower transactions costs Coordination of production Lower transportation costs Lower cost of price discovery or negotiation Lower costs of making and enforcing contracts Transactions costs are the time and other costs required to carry out and enforce the terms of market exchanges (transactions) Examples Avoiding hold-up problems and opportunistic behavior

Reduced risk Larger firms may be able to reduce income risk by diversification Diversification is the process of reducing risk by spreading sources of income among different alternatives

Problems with firms Agency problems with employees Lack of market discipline Communication problems

We denote the set of all feasible input-output combinations by T We describe the technological possibilities for the firm by its technology set (technology for short) For a given level of inputs, x, we call this set the Production Possibility Set just as we denote the set of all outputs producible with a given level of inputs x, by P(x)

A particular element of the technology set is called a production plan and we write (x, y)  T Some input and output combinations (x, y) may not be elements of T Such combinations are said to be infeasible

Production Functions The production function is a function that gives the maximum output attainable from a given combination of inputs.

The production function really only makes sense with one output y1y1 y2y2 P(x)

y x P(x 1 ) x1x1 The Production Possibility Set with One Output

The Production Function y = f (x 1, x 2, x 3,... x n ) Input -x Output -y y

y (bushels) = f (land, tillage, seed, fertilizer, … ) Examples

The short run and the long run The short run and the long run have to do with what is fixed for a given decision problem The short-run is a time period brief enough that the firm vary some, but not all can vary some, but not all, of its inputs in a costless manner. The long-run is a time period long enough that the firm vary all of its inputs in a costless manner can vary all of its inputs in a costless manner If there are costs associated with varying the level of an input we say that the firm experiences adjustment costs

Fixed inputs quantity remains constant A input whose quantity remains constant, regardless of how much output is produced current decision period in the current decision period fixed input is called a fixed input Variable inputs A variable input is an input whose usage changes as the level of output changes in the current decision period

Fixed, variable, and sunk costs Fixed costs are those costs that the firm is committed to pay for factors of production, regardless of the firm's current decisions Suppose x 2 = 10 and w 2 = $50. If x 2 is fixed, then fixed cost = $500 Suppose

Example of fixed costs Output - y Cost FC

Sunk costs The portion of fixed cost that is not recoverable if the firm liquidates, is called sunk cost Example of a pizza restaurant Sub-lease of land or a building Sell off tables and chairs Specialized pizza oven Fixed cost = sunk cost + avoidable fixed cost

Variable costs Variable costs are those costs that are affected by the firm's actions in the current period Variable costs occur because of the decision purchase additional factors to purchase additional factors or factor services for use in production. n 1 is the number of variable inputs

Variable Cost Output - y Cost VC Example of variable cost

Fixed costs The bar over x denotes it is fixed Fixed costs are those costs that the firm is committed to pay for factors of production, regardless of the firm's current decisions Inputs n 1 - n are all fixed

Total costs The sum of fixed cost and variable cost is called fixed cost.

Example x 1 = cooks x 3 = brat buns x 2 = brats x 4 = grills x 5 = brat turnersx 6 = charcoal VariableCooks, brats, buns, charcoal FixedGrills, brat turners n = 6 n 1 = 4

Variable and fixed cost

Example of total cost Output - y Cost VC TC FC

Production in the short run Total (physical) product - TP (TPP) Total product (y) is the maximum quantity of output that can be produced from a given combination of inputs. It is the value of the production function y = f (x 1, x 2,..., x n )

Example numerical function

Story x 1 - number of laborers hauling hay y - bales of hay hauled per hour x 2 - number of tractor-wagon combinations

Data with 1 tractor and wagon Total Input 1Input 2Product x 1 x 2 y (TPP) laborwagonsbales

Total Product of Input 1 - x 2 = Input - x 1 Output - y y Graph of total product

Marginal (Physical) Product Marginal (physical) product is the increase in output that results from a one unit increase in a particular input In discrete terms or average terms the marginal product of the ith input is given as where y 1 and x 1 are the level of output and input after the change in the input level and y 0 and x 0 are the levels before the change in input use.

For small changes in x i, the marginal product is given by the derivative

Example calculations Change x 1 from 4 to 5 Input 1Input 2Product x 1 x 2 y (TPP) laborwagonsbales Change x 1 from 1 to 2

Using calculus

Graphical representation Marginal Product of Input 1 - x 2 = Input - x 1 Output - y MPP 1

Average (physical) product An average measure of the relationship between outputs and inputs is given by the average product, which is just the level of output divided by the level of one of the inputs

Example calculations Average product at x 1 = 5 Average product at x 1 = 2 Input 1Input 2Product x 1 x 2 y (TPP) laborwagonsbales

Graphical representation Average and Marginal Product of Input Input - x 1 Output - y MPP 1 APP 1

Discussion of marginal (physical) product Increasing returns When the marginal product rises (increases) as an input rises, we say that the marginal product of the input is increasing When there are increasing returns, an additional unit of the input causes a larger increase in output than the previous unit. When marginal product is increasing, total product is increasing at an increasing rate

Data with 1 tractor and wagon Average Total AverageMarginal Marginal Input 1Input 2Product ProductProductProduct x 1 x 2 y (TPP)APP A MPP laborwagonsbales

Graphical representation Total Product of Input Input - x 1 Output - y y Average and Marginal Product of Input Input - x 1 Output - y MPP 1 APP 1

Diminishing returns When the marginal product falls (decreases) as an input rises, we say that the marginal product of the input is diminishing When there are diminishing returns, an additional unit of the input causes a smaller (but positive) increase in output than the previous unit When marginal product is decreasing, (but positive) total product is increasing at a decreasing rate.

The law of diminishing returns The law of diminishing (marginal) returns states that as we continue to add more of any input (holding the other inputs constant), its marginal product will eventually decline. Examples fertilizer hay wagons counter workers college administrators

Negative returns When marginal product is negative, output actually falls with the addition of another unit of the input Examples fertilizer water on a plant cooks in a kitchen

Average, total and marginal product 1.When the marginal curve is positive, the total curve will be rising 2.When the marginal curve is rising, the total curve will be rising at an increasing rate (becomes steeper) 3.When the marginal curve is positive but falling, the total curve will be rising at a decreasing rate (becomes flatter) 4.When the marginal curve is greater than the average curve, the average curve is rising 5.When the marginal and average curves are equal, the average curve does not change (is usually at a maximum or minimum point) 6.When the marginal curve is less than the average curve, the average curve is falling 7.For a production function MP and AP intersect at the maximum of APP

Intuition for average-marginal relationship Cumulative GPA Average test scores

The End