1. Intermediate Microeconomics WESS16 FIRMS AND PRODUCTION Laura Sochat

2. 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)

3. Marginal and average product

4. 12 18 24 L, 000s man hour per day, 6 0 5 10 -5 -10 Relationship between Marginal and Average product LQ 6305 12968 181629 241928 301505

5. Marginal and average product Total Product Function C 18 000s man hour per day, B A 0 18 24 000s man hour per day, 0 5 10 -5 -10 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.

6. 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 6 18 6 A B 0612182430 0000000 60515253023 L 1201548819675 1802581137162127 2403096162192150 3002375127150117

7. 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 20 50 20 50 A B

9. Special production functions: Linear and fixed proportions production functions H, High capacity computers L, Low capacity computers 10 2020 5 A B C Q, quantity of oxygen atoms H, quantity of hydrogen atoms 2 1 A 3 B C 4 6 2 (a) Map of isoquants for data storing (b) Map of isoquants for molecules of water Inputs are perfect substitutes Inputs are perfect complements

10. Special production functions: Cobb Douglas production function K, units of capital per day L, units of labor per day 10 3030 40 2020 1010 20 30 40 50

11. Returns to scale

13. 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 102030 20 10 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.

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

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

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