The Firm and Optimal Input Use Overheads

1. The Firm and Optimal Input Use Overheads

2. Nature of the firm A neoclassical firm is an organization that controls the transformation of inputs (resources it controls) into outputs (valued products that it sells), and earns the difference between what it receives in revenue, and what it spends on inputs.

3. Profit Profit = Revenue - Cost

4. Objectives of the firm We assume that firms exist to make money, so they maximize profits by choosing the optimal levels of inputs and output

5. Technology and the firm • Thetechnologyfor a given production process is the setofall input and output combinationssuch that theoutput y can be produced fromthe given set ofinputs x

6. The Producible Output Set P(x) The producible output set P(x) is the set of all combinations of outputs that are obtainable from a fixed level of inputs

7. Production Functions The production function is a function that gives the maximum output attainable from a given combination of inputs

8. Example production function

9. Production and factor costs in the short run Total (physical) product - TPP Total product (y) is the maximum quantity of output that can be produced from a given combination of inputs It is the value of the production function y = f (x1, x2 , . . . , xn )

11. Marginal (Physical) Product (MPP) Marginal (physical) product is the increase in output that results from a one unit increase in a particular input

12. Marginal Revenue Product (MRP) The marginal revenue product of an input is the increase in output that results from a one unit increase in that particular input

13. Marginal Revenue Product (MRP) is given by For a competitive firm, MRP is given by

14. x y DMPP MRP MFC 0.0 0.00 10.0 1.0 14.50 14.50 72.50 10.0 2.0 28.00 13.50 67.50 10.0 3.0 40.50 12.50 62.50 10.0 4.0 52.00 11.50 57.50 10.0 5.0 62.50 10.50 52.50 10.0 6.0 72.00 9.50 47.50 10.0 7.0 80.50 8.50 42.50 10.0 8.0 88.00 7.50 37.50 10.0 9.0 94.50 6.50 32.50 10.0 10.0 100.00 5.5 27.50 10.0 11.0 104.50 4.5 22.50 10.0 12.0 108.00 3.5 17.50 10.0 13.0 110.50 2.5 12.50 10.0 14.0 112.00 1.5 7.50 10.0 15.0 112.50 0.5 2.50 10.0

15. 80 70 60 DMPP 50 MRP 40 30 20 10 0 0 2 4 6 8 10 12 14 16 Input Marginal Product & Marginal Revenue Product

16. Marginal Factor Cost (MFC) The additional amount that the firm has to pay for a factor when it hires one more unit of the factor is called marginal factor cost For a firm that is a price taker in the input market, marginal factor cost is equal to factor price MFCi = wi

17. The Profit Maximizing Output Level The marginal approach to profit maximization says that the firm should take any action that adds more to revenue than to cost

18. The Profit Maximizing Rule The firm should use another unit of the ith input as long as the marginal revenue product of the input is larger than the marginal factor cost of the input

19. 80 70 60 50 MRP 40 MFC 30 x opt 20 10 0 0 2 4 6 8 10 12 14 16 Input Marginal Product & Marginal Factor Cost

20. Demand for a variable input (single input) When the firm only uses one variable input, the downward sloping portion of the marginal revenue product curve is the input demand curve The input demand curve tells us how many units of the input the firm will chose to employ at various prices

21. w x MRP 72.5 1.0 72.50 67.5 2.0 67.50 62.50 3.0 62.50 57.50 4.0 57.50 52.50 5.0 52.50 47.50 6.0 47.50 42.50 7.0 42.50 37.50 8.0 37.50 32.50 9.0 32.50 27.50 10.0 27.50 22.50 11.0 22.50 17.50 12.0 17.50 12.50 13.0 12.50 7.50 14.0 7.50 2.50 15.0 2.50

22. 80 $ MRP 70 60 MFC 50 MFC 1 40 MFC 2 30 MFC 3 20 10 0 0 2 4 6 8 10 12 14 16 18 20 22 Input Input Demand

23. Summary of results on the firm Profit Maximization p × MPPi = wi, i = 1, 2, … , n

24. The End