Intermediate Microeconomics WESS16 FIRMS AND PRODUCTION Laura Sochat

Production functions The labor (employees) and capital (factories, robots) a firm uses are called the factors of production, or inputs. The amount of goods and services produced are called the firm's output. Given a specific combination of inputs, the firm can produce a certain amount of outputs. –The production function tells us the maximum amount the firm can produce give a particular combination of inputs. –Assuming amount of capital used is denoted as K, amount of labor used as L, and quantity of output as Q, we can write the production function as: Q=f(L,K)

Marginal and average product

L, 000s man hour per day, Relationship between Marginal and Average product LQ

Marginal and average product Total Product Function C s man hour per day, B A s man hour per day, The total product function single input production function depicting how output depends on the level of that input used, given a fixed amount of other inputs used. Law of diminishing marginal returns: Principle that as the usage of one input increases, the quantities of other inputs being held fixed, a point will be reached beyond which the marginal product of the variable input will decrease.

ISOQUANTS Isoquants enable us to represent the production function. It is a curve that shows all combinations of labor and capital that can produce a given level of output. K, 000s of machine hour a day L, 000s of machine hour a day A B L

Marginal rate of Technical substitution The marginal rate of technical substitution (of labor for capital) is the rate at which capital can be reduced for every one unit increase in labor, and keeping output constant. It is defined as the absolute value of slope of the isoquant drawn with labor on the horizontal axis, and capital on the vertical axis. K, 000s of machine hour a day L, 000s of machine hour a day A B

Special production functions: Linear and fixed proportions production functions H, High capacity computers L, Low capacity computers A B C Q, quantity of oxygen atoms H, quantity of hydrogen atoms 2 1 A 3 B C (a) Map of isoquants for data storing (b) Map of isoquants for molecules of water Inputs are perfect substitutes Inputs are perfect complements

Special production functions: Cobb Douglas production function K, units of capital per day L, units of labor per day

Returns to scale

The distinction between returns to scale and diminishing marginal returns K, units of capital per year L, units of labor per year A D E B C Returns to scale refer to the impact of an increase in all input quantities simultaneously Marginal returns refer to an increase in the quantity of a single input, such as labor holding quantities of all other inputs fixed. The figure to the left illustrates a situation where there are diminishing marginal returns to labor, but constant returns to scale.

Neutral technological progress K, units of capital per year L, units of labor per year A 0

Labor-saving technological progress K, units of capital per year L, units of labor per year A 0

Capital saving technological progress K, units of capital per year L, units of labor per year