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Economics of Input Input Combination


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Economics of Input Input Combination

  1. 1. Economics of Input input combinations Prepared By: Milan Padariya
  2. 2. Topics of Discussion Concept of isoquant curve Concept of an iso-cost line Least-cost use of inputs 2
  3. 3. Physical Relationships 3
  4. 4. Use of Multiple Inputs This lecture will refer to situations where we have multiple variable inputs Labor, machinery rental, fertilizer application, pesticide application, etc. 4
  5. 5. Use of Multiple Inputs Our general single input production function looked like the following:  Output = f(labor | capital, land, energy, etc) Variable Input Fixed Inputs Lets extend this to a two input production function  Output = f(labor, capital | land, energy, etc) Variable Inputs 5 Fixed Inputs
  6. 6. Use of Multiple Inputs Output (i.e. Corn Yield) Phos. Fert. 250 Nitrogen Fert. 6
  7. 7. Use of Multiple Inputs If we take a slice at a level of 250 output we obtain what is referred as an isoquant Similar to the indifference curve we covered when we reviewed consumer theory Shows collection of multiple inputs that generates a particular output level There is one isoquant for each output level
  8. 8. Isoquant means “equal quantity” Output is identical along an isoquant and different across isoquants Two inputs
  9. 9. Slope of an Isoquant The slope of an isoquant is referred to as the Marginal Rate of Technical Substitution (MRTS)  The value of the MRTS in our example is given by: MRTS = Capital Labor  Provides a quantitative measure of the changes in input use as one moves along a particular isoquant
  10. 10. Slope of an Isoquant The slope of an isoquant is the Capital Q=Q* Marginal Rate of Technical Substitution (MRTS)  Output remains unchanged along an isoquant  The ↓ in output from decreasing labor must be identical to the ↑ in output from adding capital as you move along an isoquant K* L* Labor
  11. 11. MRTS here is –4 1=–4
  12. 12. What is the slope over range B? MRTS here is –1 1 = –1
  13. 13. What is the slope over range C? MRTS here is –.5 1 = –.5
  14. 14. Slope of an Isoquant Since the MRTS is the slope of the isoquant, the MRTS typically changes as you move along a particular isoquant MRTS becomes less negative as shown above as you move down an isoquant
  15. 15. Introducing Input Prices
  16. 16. Plotting the Iso-Cost Line Lets assume we have the following  Wage Rate is $10/hour  Capital Rental Rate is $100/hour What are the combinations of Labor and Capital that can be purchased for $1000  Lets introduce the Iso-Cost Line
  17. 17. Plotting the Iso-Cost Line Capital Firm can afford 10 hours of capital at a rental rate of $100/hr with a budget of $1,000 10 Firm can afford 100 hour of labor at a wage rate of $10/hour for a budget of $1,000  Combination of Capital and Labor costing $1,000  Referred to as the $1,000 Iso-Cost Line 100 Labor
  18. 18. Plotting the Iso-Cost Line  How can we define the equation of this isocost line? Given a $1000 total cost we have: $1000 = PK x Capital + PL x Labor → Capital = (1000 PK) – (PL PK) x Labor  →The slope of an iso-cost in our example is given by: Slope = –PL ÷ PK (i.e., the negative of the ratio of the price of the two inputs)
  19. 19. Plotting the Iso-Cost Line Capital 2,000 PK 20 Doubling of Cost Original Cost Line Note: Parallel cost lines given constant prices 10 500 PK 5 Halving of Cost Labor 50 500 PL 200 100 2000 PL
  20. 20. Plotting the Iso-Cost Line Capital $1,000 Iso-Cost Line Iso-Cost Slope = – PK 10 PL = $10 PL = $20 50 100 PL PL = $5 200 Labor
  21. 21. Plotting the Iso-Cost Line Capital 20 $1,000 Iso-Cost Line Iso-Cost Slope = – PK PK = $50 PL 10 PK = $100 5 PK = $200 50 100 200 Labor
  22. 22. Least Cost Combination of Inputs
  23. 23. Least Cost Input Combination TVC are predefined Iso-Cost Lines Capital TVC*** > TVC** > TVC* Q* TVC*** Pt. C: Combination of inputs that cannot produce Q* Pt. A: Combination of inputs that have the highest of the two costs of producing Q* Pt. B: Least cost combination of inputs to produce Q* A TVC** B TVC* C Labor
  24. 24. Least Cost Decision Rule The least cost combination of two inputs (i.e., labor and capital) to produce a certain output level  Occurs where the iso-cost line is tangent to the isoquant  Lowest possible cost for producing that level of output represented by that isoquant  This tangency point implies the slope of the isoquant = the slope of that iso-cost curve at that combination of inputs
  25. 25. Least Cost Decision Rule When the slope of the iso-cost = slope of the isoquant and the iso-cost is just tangent to the isoquant –MPPK MPPL = Isoquant Slope – (PK PL) Iso-cost Line Slope We can rearrange this equality to the following
  26. 26. Least Cost Decision Rule MPPL PL MPP per dollar spent on labor MPPK Pk = MPP per dollar spent on capital
  27. 27. Least Cost Decision Rule The above decision rule holds for all variable inputs • For example, with 5 inputs we would have the following MPP1 P1 MPP1 per $ spent on Input 1 MPP2 P2 = MPP3 P3 MPP2 per $ spent on Input 2 MPP4 P4 =… … = MPP5 P5 MPP5 per $ spent on= Input 5
  28. 28. Least Cost Input Choice for 100 Units of Output  Point G represents 7 hrs of capital and 60 hrs of labor  Wage rate is $10/hr and rental rate is $100/hr  → at G cost is $1,300 = (100 7) + (10 60) 7 60
  29. 29. Least Cost Input Choice for 100 Units of Output   G represents a total cost of $1,300 every input combination on the iso-cost line costs $1,300 With $10 wage rate → B* represent 130 units of labor: $1,300 $10 = 130 7 60 130
  30. 30. Least Cost Input Choice for 100 Units of Output  Capital rental rate is $100/hr 13  → A* represents 13 hrs of capital, $1,300 $100 = 13 130