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Chapter 9:

Chapter 9:. Input Use and Demand for Inputs. Key Topics. Derived demand for inputs Revenue concepts related to input use Total revenue product (TRP) Average revenue product (ARP) Marginal revenue product (MRP) Profit-maximizing input level Profit-max input rule (MRP = input P)

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Chapter 9:

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  1. Chapter 9: Input Use and Demand for Inputs

  2. Key Topics • Derived demand for inputs • Revenue concepts related to input use • Total revenue product (TRP) • Average revenue product (ARP) • Marginal revenue product (MRP) • Profit-maximizing input level • Profit-max input rule (MRP = input P) • Input demand curve • 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 TP q* Q* = profit-maximizing q  L* = profit-maximizing L L 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 ($) TP x P = TRP C B A 0 a1 a2 a3 Input a Average & Marginal Revenue Product ($) AP x P = ARP Input a 0 a1 a2 a3 MP x MR = MRP

  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) $ $ S P P = w D L L Firm Mkt

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

  13. Find D for Variable Input (e.g. L) $ ARP W3 W2 W1 MRP L L3 L2 L1

  14. Increased D for Labor (examples) $  w w1 w2 MRP L L1 L2

  15. Increased D for Labor (examples) $ • P of Output w P2 > P1 MRP2 (P2) MRP1 (P1) L L1 L2

  16. Increased D for Labor (examples) $  MP MP2 > MP1 w MRP2 (MP2) MRP1 (MP1) L L1 L2

  17. Profit-Max Input Rule = Profit-Max Output Rule • MRP = MFC • MPL∙ MR = w • MR = w / MPL • MR = MC

  18. Profit Max Input Side = Profit Max Output Side q TP 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 • Professional athletes (salaries) • Land (rent and usage)

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