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Techniques and Isoquants

Techniques and Isoquants. © 1998 by Peter Berck. Definitions. Output Q; specific amount Q* Inputs x= (x 1 …x n ) If using inputs x results in output Q*, then x is a technique to make Q*.

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Techniques and Isoquants

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  1. Techniques and Isoquants © 1998 by Peter Berck

  2. Definitions • Output Q; specific amount Q* • Inputs x= (x1…xn) • If using inputs x results in output Q*, then x is a technique to make Q*. • 1 brisket, 1 pan, 3 hours of oven services at 375, 1 large sheet foil, 4 coarsely sliced onions, salt, pepper, paprika are a technique for making pot roast. (Esther Lipow’s (z’’l) recipe.)

  3. Efficient • If x is less than or equal to y in every dimension and x and y both produce Q*, then y is not efficient. • xi yi for every i y input 2 x input 1

  4. Isoquant • Let Q* be some specific output like 4 units • All efficient input combinations that produce Q* are the Q*thisoquant

  5. Corn Yield in lbs.

  6. Rice Milling • Why mill rice at all? • What is wrong with white rice from a nutritional point of view?

  7. Techniques for Milling Rice Notes: Source P. Timmer Choice of Technique in Rice Milling in Java. Techniques to produce Rp 10 Million in Value added . Investment in USD.

  8. Milling • Why is this in value added rather than tons? • VA = Revenue – Cost of materials • How do you convert capital costs into a yearly equivalent? • interest • depreciation

  9. Isoquant for Rice Milling

  10. What Technique Minimizes Cost • Need prices for labor and investment • Price of investment is 1. Plant is assumed to last 50 years with no maintenance (urrg.) • Price of 50 years worth of labor is calculated as the size of bank account (with 24% interest) that would pay a laborer $200 per year for 50 years. It is $833 per laborer

  11. Interest Rates • Is 24% per year a high interest rate for a developing country? • Are there investment clubs in the US that charge their members 2.5% per month?

  12. Outlay or Isocost Line • All input combinations of K, investment, and L, laborers, that cost amount E, an unknown, are given by • E = K + $833 L • More generally: • E = Pk K + PL L

  13. About equi-cost or outlay lines • E = Pk K + PL L • K = E/Pk - L PL/PK • So varying E (which is not known) gives a family of parallel equi-outlay lines • The cost of every input bundle on the line is the vertical intercept times PK. • When PK conveniently equals one, the vertical intercept is the cost of every bundle on the line

  14. Which line? • The least cost way of producing output Q* is found by finding the equi-cost line tangent to the Q*th isoquant. • C(Q*) is the cost of any input bundle on that line • The input bundle (or technique) at the tangency is the least cost way to produce Q*

  15. Small Rice Mill Costs Least Small Mill Hand

  16. Story: • Widows used to hand pound rice. • Now SRM’s are used instead. • How is this bad? • How is this good?

  17. Technology Transfer • In US, build small dam with tractors, backhoes, dump trucks, very few workers • In India, the same dam would be built by using many many laborers and hand tools. • These are two efficient techniques for building a dam. • Why would we say that the US technique, if used in India was inappropriate tech. transfer?

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