Economics of Input Input Combination

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  • 1. Economics of Input input combinations Prepared By: Milan Padariya
  • 2. Topics of Discussion Concept of isoquant curve Concept of an iso-cost line Least-cost use of inputs 2
  • 3. Physical Relationships 3
  • 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. 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. Use of Multiple Inputs Output (i.e. Corn Yield) Phos. Fert. 250 Nitrogen Fert. 6
  • 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. Isoquant means “equal quantity” Output is identical along an isoquant and different across isoquants Two inputs
  • 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. 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. MRTS here is –4 1=–4
  • 12. What is the slope over range B? MRTS here is –1 1 = –1
  • 13. What is the slope over range C? MRTS here is –.5 1 = –.5
  • 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. Introducing Input Prices
  • 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. 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. 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. 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. 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. 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. Least Cost Combination of Inputs
  • 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. 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. 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. Least Cost Decision Rule MPPL PL MPP per dollar spent on labor MPPK Pk = MPP per dollar spent on capital
  • 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. 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. 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. 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