1 Introduction To Inputs And Production Functions

2 Inputs/Factors Of Production: Resources such as labor, capital equipment, and raw materials, that are combined to produce finished goods. Output: The amount of a good or service produced by firm.

3 Production function: A mathematical representation that shows the maximum quantity of output a firm can produce given the quantities of inputs that it might employ. Q = f (L, K) Q = quantity of output L = quantity of labor used K = quantity of capital employed

4 Production Function With Single Input Total Production Function Figure 6.2. Page 187 LQ

5 Marginal And Average Product Average Product Of Labor (APl): APl = (Total Product)/(Quantity Of Labor) = Q/L

6 Marginal And Average Product (continued) LQAPl

7 Figure 6.3. Page 189 Average and marginal Product Function MPl = (change in total product)/(change in quantity of labor) = delta Q / delta L

8 Figure 6.4. Page 190 Relationship among Total, Average, and Marginal Product Function “Law Of Diminishing Marginal Returns”

9 Relationship Between Marginal And Average Product If APl increases in L, then MPl > APl If APl decreases in L, then MPl < APl When APl neither increases nor decreases in L, then MPl = APl

10 Isoquant Isoquant: a curve that shows all of the combination of labor and capital that can produce a given level of output. Figure 6.8. Page 196 Isoquant

11 Problem: Production function Q = (KL) 1/2 What the isoquant when Q=20? Answer: Q = (KL) 1/2 20 = (KL) 1/2 (20) 2 = (KL) 1/ = KL K = 400/L………..The Isoquant

12 Return To Scale Return To Scale: the concept that tell us the percentage by which output will increase when all inputs are increased by a given percentage.

13 Increasing Return To Scale A proportionate increase in all input quantities resulting in a greater than proportionate increase in output.

14 Constant Return To Scale A proportionate increase in all input quantities resulting the same proportionate increase in output.

15 Decreasing Return To Scale A proportionate increase in all input quantities resulting in a less than proportionate increase in output.

16 Problem: Q = 2L 0.5 K 0.7 Exhibit increasing return to scale?

17 Problem: Q = 6L 2 – L 3 How much the firm should produce so that: a. Average product is maximized b. Marginal Product is maximized c. Total Product is maximized

18 Problem: What can you say about the returns to scale of the linear production: Q = aK + bL where a and b are positive constant.