Chapter 7 Production Theory

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

Production Function Thomas Machine Company

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.

Law of Diminishing Returns Law of Diminishing Returns: as more units of a variable resource are applied to a fixed resource, output will eventually increase by a smaller and smaller amount.

Product Curves Total Product: total output of a good associated with different levels of a variable input. Marginal Product: the change in total product due to a one unit increase in variable input. Average Product: Total product divided by the number units of the variable input.

Law of Diminishing Returns As units of variable input (labor) are added to a fixed input, total product will increase . . . Law of Diminishing Returns Total Product Total Product First at an increasing rate . . . 80 Then at a declining rate . . . Note that the Total Product curve is smooth, indicating that labor can be increased by amounts of less than a single unit (it is a continuous function). 70 60 Units of Variable Resource Total Product (Output) Marginal Product Average Product 50 40 1 8 2 20 30 3 34 4 46 5 56 20 6 64 7 70 10 8 74 9 75 1 2 3 4 5 6 7 8 9 10 10 73 Quantity of Labor

Law of Diminishing Returns The Marginal Product curve will initially increase (when TPC is increasing at an increasing rate), reach a maximum, and then decrease (as TPC increases at a decreasing rate). Law of Diminishing Returns Average and/or Marginal Product 16 Marginal Product The Average Product curve will have the same general form except that its maximum point will be at a higher output level. 12 Average Product Units of Variable Resource Total Product (Output) Important Note : MP always crosses AP at its maximum point. Marginal Product Average Product ----- ----- 8 1 8 8 8 2 20 12 10 3 34 14 11.3 4 46 12 11.5 4 5 56 10 11.2 6 64 8 10.7 7 70 6 10 8 74 4 9.3 9 75 1 8.3 1 2 3 4 5 6 7 8 9 10 10 73 - 2 7.3 Quantity of Labor

Law of Diminishing Returns Graphed together, one can see the relationship between the TP, MP, and AP curves more clearly. Law of Diminishing Returns Average Product Marginal Product AP & MP Quantity of Labor 5 4 3 2 1 8 12 16 6 7 9 10 Total Product TP 20 30 40 50 60 70 80

Marginal Revenue Product The amount that an additional unit of the variable input adds to the firm’s total revenue MRPY = DTR/DY

Marginal Expenditure MEY = DTC/DY The amount that an additional unit of the variable input adds to the firm’s total costs. MEY = DTC/DY

Optimal Level of Input Use MRPY = MEY

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

Capital K2 300 K1 200 100 Labor L2 L1

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(X1, X2) MRTS = -dX2 / dX1 = -MP1 / MP2

Isocost Curves Various combinations of inputs that a firm can buy with the same level of expenditure PLL + PKK = M where M is a given money outlay.

Capital M/PK Slope = -PK /PL Labor M/PL

Maximization of Output for Given Cost Capital R 300 200 100 Labor

MPL/PL = MPK/PK Labor Capital 100 200 300 R

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. e > 1 ==> increasing returns e < 1 ==> decreasing returns e = 1 ==> constant returns

Three Types of Statistical Analysis Time series data Cross section data Technical information