1. Chapter 9: Input Use and Demand for Inputs

2. Key Topics 1. Derived demand for inputs 2. Revenue concepts related to input use a. Total revenue product (TRP) b. Average revenue product (ARP) c. Marginal revenue product (MRP) 3. Profit-maximizing input level a. Profit-max input rule (MRP = input P) b. Input demand curve c. Shifts in factor demand curves

3. Derived Demand The demand for resources (inputs) is dependent on (or derived from) the demand for the outputs those resources can be used to produce.

4. Input & Output Decisions Related via production function q q* L* L TP Q* = profit-maximizing q  L* = profit-maximizing L

5. Revenue Concepts that are functions of input usage Total Revenue Product (TRP) Average Revenue Product (ARP) Marginal Revenue Product (MRP)

6. Revenue Products Total Revenue Product =TRP =TP x P =paired observations on the $ value of output and physical units of a variable input

7. Revenue Products Average Revenue Product =ARP =AP x P =revenue per unit of input

8. Revenue Products Marginal Revenue Product =MRP =MP x P (= MR*) =additional revenue per unit of additional input *for competitive firm

9. Total Revenue Product ($) Average & Marginal Revenue Product ($) TP x P = TRP AP x P = ARP Input a MP x MR = MRP Input a 0 0 A B C a1a1 a2a2 a3a3 a1a1 a2a2 a3a3

10. Profit-Maximizing Input Level  Keep using an input up to the point where the additional revenue from the last additional unit equals the additional cost  MRP = input P

11. Labor Price (= w) $ P S D L $ L Mkt Firm P = w

12. Profit-Maximizing Input Level $ $ L L* TRP TC π*π* L* L MRP w ARP

13. Find D for Variable Input (e.g. L) $ ARP W3W3 W2W2 W1W1 MRP L L3L3 L2L2 L1L1

14. Increased D for Labor (examples) $  w w1w1 w2w2 MRP L L1L1 L2L2

15. Increased D for Labor (examples) $  P of Output L L1L1 L2L2 w P 2 > P 1 MRP 2 (P 2 ) MRP 1 (P 1 )

16. Increased D for Labor (examples) $  MP MP 2 > MP 1 w L MRP 2 (MP 2 ) MRP 1 (MP 1 ) L1L1 L2L2

17. Profit-Max Input Rule = Profit-Max Output Rule  MRP = MFC  MP L ∙ MR = w  MR = w / MP L  MR = MC

18. Profit Max Input Side = Profit Max Output Side TP q q* L L*

19. Profit Max Input Side = Profit Max Output Side $ w MRP L L*

20. Profit Max Input Side = Profit Max Output Side $ MC MR q q*

21. Other Input Economics Applications 1. Professional athletes (salaries) 2. Land (rent and usage)