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.

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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*. l 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. x i y i for every i input 1 input 2 y x

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.

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

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.

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

Isoquant for Rice Milling

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 = P k K + P L L

About equi-cost or outlay lines §E = P k K + P L L §K = E/P k - L P L /P K l So varying E (which is not known) gives a family of parallel equi-outlay lines l The cost of every input bundle on the line is the vertical intercept times P K. l When P K 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*

Small Rice Mill Costs Least Hand Small Mill

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. l These are two efficient techniques for building a dam. l Why would we say that the US technique, if used in India was inappropriate tech. transfer?

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