Topic on Production and Cost Functions and Their Estimation

Production function A table, graph, or equation showing the maximum output rate of the product that can be achieved from any specified set of usage rates of inputs

Production function Thomas Machine Company

Law of diminishing marginal returns If equal increments of an input are added to a production process, and the quantities of other inputs are held constant, eventually the marginal product of the input will diminish Note: 1) This is an empirical generalization. 2) Technology remains fixed. 3) The quantity of at least one input is held fixed.

Marginal revenue product The amount that an additional unit of the variable input adds to the firm’s total revenue MRP Y = D TR/ D Y

Marginal expenditure The amount that an additional unit of the variable input adds to the firm’s total costs. ME Y =  TC /  Y

Optimal level of input use MRP Y = ME Y

Production functions with two variable inputs

Q = f (labor, machine Tools)

Isoquant A curve showing all possible (efficient) combinations of inputs that are capable of producing a certain quantity of output Iso quant same quantity

Labor Capital 0 K2K K1K1 L2L2 L1L1

Marginal rate of technical substitution Shows the rate at which one input can be substituted for another input, if output remains constant. (Slope of the isoquant.) Given Q = f(X 1, X 2 ) MRTS = -  X 2 /  X 1 = -MP 1 / MP 2

Isocost curves Various combinations of inputs that a firm can buy with the same level of expenditure P L L + P K K = M where M is a given money outlay.

Labor Capital 0 M/P K M/P L Slope = -P K /P L

Maximization of output for given cost Labor Capital R

MP L /P L = MP K /P K Labor Capital R

Optimal Lot Size To consider the size of inventory Find the relationship between size of lot and total annual cost.

What Toyota Taught the World? Lower the cost per setup Reduce the optimal lot size Just-in-time production system

Returns to scale If the firm increases the amount of all inputs by the same proportion: Increasing returns means that output increases by a larger proportion Decreasing returns means that output increases by a smaller proportion Constant returns means that output increases by the same proportion

Output elasticity The percentage change in output resulting from 1 percent increase in all inputs.  > 1 ==> increasing returns e decreasing returns e = 1 ==> constant returns

Example: Xerox Sending out teams of engineers and technicians to visit other firms to obtain information concerning best-practice methods and procedures. Competitive Benchmarking

Measurement of Production Functions Three types of statistical analysis Time series data Cross section data Technical information

The Analysis of Costs

Opportunity costs The value of the other products that the resources used in production could have produced at their next best alternative

Historical costs The amount the firm actually paid for a particular input

Explicit vs. implicit costs Explicit costs include the ordinary items that an accountant would include as the firms expenses Implicit costs include opportunity costs of resources owned and used by the firm’s owner

Short run A period of time so short that the firm cannot alter the quantity of some of its inputs Typically plant and equipment are fixed inputs in the short run Fixed inputs determine the scale of the firm’s operation

Three concepts of total costs Total fixed costs = FC Total variable costs = VC Total costs = FC + VC

Fixed, variable, and total costs Media Corp.

Fixed, Variable, and Total Costs -- Media Corp.

Average and marginal costs Media Corp.

Long-run cost functions Often considered to be the firm’s planning horizon Describes alternative scales of operation when all inputs are variable Quantity of output Average cost

Long-run average cost function Shows the minimum cost per unit of producing each output level when any scale of operation is available Quantity of output Average cost SR average cost functions LR average cost

Key steps: Cost estimation process ¶Definition of costs · Correction for price level changes ¸ Relating cost to output ¹ Matching time periods º Controlling product, technology, and plant » Length of period and sample size

Minimum efficient scale The smallest output at which long-run average cost is a minimum. Quantity of output Average cost Q mes

The survivor technique Classify the firms in an industry by size and compute the percentage of industry output coming from each size class at various times If the share of one class diminishes over time, it is assumed to be inefficient These firms are then operating below minimum efficient scale

Economies of scope Exist when the cost of producing two (or more) products jointly is less than the cost of producing each one alone. S = C(Q 1 ) + C(Q 2 ) - C(Q 1 + Q 2 ) C(Q 1 + Q 2 )

Break-even analysis Quantity of output Dollars Total Revenue Total Cost Loss Profit