Techniques and Isoquants - University of California, Berkeley
Techniques and Isoquants 1998 by Peter Berck Definitions Output Q; specific amount Q* Inputs x= (x1xn) 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 Lipows (zl) recipe.)
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 Isoquant
Let Q* be some specific output like 4 units All efficient input combinations that produce Q* are the Q*th isoquant Corn Yield in lbs. Lbs P2O5 40 80 120 160 Lbs N 80 82.3
200 88.6 106.8 116.9 122.9 Rice Milling Why mill rice at all? What is wrong with white rice from a nutritional point of view? Techniques for Milling Rice Technique Hand Pound
Investment 0 Laborers 45.83 Technique Large Mill Investment 29,675 Laborers 5.25 Notes: Small Mill 9,359 13.95 Small
Bulk 44,335 2.64 Large Bulk 77,835 1.17 Source P. Timmer Choice of Technique in Rice Milling in Java. Techniques to produce Rp 10 Million in Value added . Investment in USD. 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 Investment Costs Isoquant for Rice Milling 90000
30 Laborers 40 50 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 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? 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 + P L L
About equi-cost or outlay lines E = Pk K + P L 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 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* Investment Costs Small Rice Mill Costs Least 90000
80000 70000 60000 50000 40000 30000 20000 10000 0 Small Mill Hand 0
10 20 30 Laborers 40 50 Story:
Widows used to hand pound rice. Now SRMs are used instead. How is this bad? How is this good? 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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