1. Techniques, Isoquants, and Cost Curves © 2010 Peter Berck

2. 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*. – 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. – x i  y i for every i input 1 input 2 y x

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

5. Find points on same isoquant for 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. Laborers is the number of workers each and every year.

8. Milling Does a rice mill and hand pounding produce the same white rice product? Which would you rather buy? Why is this in value added rather than tons? – VA = Revenue – Cost of materials

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 = P k K + P L L

13. About equi-cost or outlay lines E = P k K + P L L K = E/P k - L P L /P K – 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 P K. – When P K 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 Hand Small Mill

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

17. Isoquant and Production Function The Q* isoquant: { x | x is an efficient technique and x produces Q*} Production function: Q = F(x). Output as function of (efficient) input bundles – {x| F(x) = Q*, x efficient} is also isoquant – Isoquant is level curve of production function – see the physical model

18. Cost function is the Minimum amount of money necessary to buy the inputs that will produce output Q. – Answer is amount of money as function of Q Isocost line, I: {x | I = p 1 x 1 + p 2 x 2 } – Straight line Intercept I/p 2 Slope - p 1 /p 2

19. Pollution in an isoquant world Two goods – Other stuff – Clean Air Services negative of pollution air has 1 ppm of gunk –polluton air has 99 ppm of non-gunk – cleanth

20. Cost Min Technique Price of “Other Stuff” = 2 Equations for 3 lines. Cost of Chosen bundle?

21. Isocost Lines: Price of “Other Stuff” = 2 Blue Isocost: slope -2=- p 1 /p 2 ; p 1 = 4; I = 80*2=160; 160 =4 Air + 2 OS Green Isocost: 200 = 4 Air + 2 OS. Red Isocost: 120 = 4 Air + 2 OS

22. C(Q*) = 160 Price of “Other Stuff” = 2 cost 200 cost 160 Chosen (24,32)

23. C(Q 1 )=120, C(Q*)=160, C(Q 2 )=200

24. C(Q) Plot Q 1, Q 2,Q 3 against 120,160,200. That is your cost curve. You can choose any set of increasing Q’s given the information you have been given.

25. Pollution Control

26. Technology Standard Technology is a way to do something (see above) Technology Standard – Must use a specific technology Building codes-one stud every 18” (done) Safety codes: must wear your goggles in lab. One could choose a technology standard to reduce emissions – One could (but doesn’t) require catalytic converters

27. Effluent Standard Effluent (or emissions) Standard – Can emit no more than X tons per (choose one) megawatt hour (output) Grams Nox per 100 km driven (output) per year (absolute!) per ton of coal burned (per input) – Obviously get very different results depending on what you choose

28. Calif Effluent standards cars: Table 1LEV Emission Standards for Light-Duty Vehicles, FTP-75, g/mi Categor y 50,000 miles/5 years100,000 miles/10 years NMOG a CONOxPMHCHONMOG a CONOxPMHCHO Passenger cars Tier 10.253.40.40.08-0.314.20.6-- TLEV0.1253.40.4-0.0150.1564.20.60.080.018 LEV0.0753.40.2-0.0150.0904.20.30.080.018 ULEV0.0401.70.2-0.0080.0552.10.30.040.011 LDT1, LVW <3,750 lbs Tier 10.253.40.40.08-0.314.20.6-- TLEV0.1253.40.4-0.0150.1564.20.60.080.018 LEV0.0753.40.2-0.0150.0904.20.30.080.018 ULEV0.0401.70.2-0.0080.0552.10.30.040.011 LDT2, LVW >3,750 lbs Tier 10.324.40.70.08-0.405.50.97-- TLEV0.1604.40.7-0.0180.2005.50.90.100.023 LEV0.1004.40.4-0.0180.1305.50.50.100.023 ULEV0.0502.20.4-0.0090.0702.80.50.050.013 a - NMHC for all Tier 1 standards Abbreviations: LVW - loaded vehicle weight (curb weight + 300 lbs) LDT - light-duty truck NMOG - non-methane organic gases HCHO - formaldehyde

29. Calif has an Effluent Standard Manufacturers meet that standard by choosing a technology: – Catalytic Converters – Also tuning engines, better burn, etc THERE IS NO requirement to choose a particular technology.

30. Technology Based Effluent Standard (TBES) – First find a technology that reduces emissions at a reasonable cost – Find out how much emissions would go down – Then set an emissions (or effluent) standard for that amount. – Used in both Clean Air Act and Clean Water Act

31. TBES Price of “Other Stuff” = 2

32. The Regulation: When you make Q*, you may use no more than 20 units of clean air services. You may use the technique the regulatory engineers have discovered (20,100) or any other technique that uses no more than 20 units of air and has output Q*

33. Why this way? Regulator knows that it can be done Regulator has upper bound on cost Regulator is assured of cleaning up the air.

34. Response to TBES Technique (20,50) costs 180 and is least cost way to make Q* using 20 units of air Technique (20,80), the basis for the regulation, costs 240 and makes Q*.

35. Back Door Economics Best Practicable Technology – used for water pre 1977 – means known technology at reasonable cost Best Available Technology – used for water post 1983 – means any technology; but in practice is limited by cost Intent: Cleaner water under BAT.

36. What to read Chapter 8 in BH. Example is agricultural pollution. – Isoquant = equal output – Isopleth = equal pollution

37. An exercise Let Q = k x, where x is an input and k is a positive number. Let w be the price of the input x. For a given x how many ways are there of making Q? What is the least cost way of making Q? What is C(Q)?

38. Conditional Factor Demand How much of an input will be used as a function of output required and prices of inputs? X(Q,p) How could changing the price of clean air result in the same usage of clean air / unit output as the TBES regulations?

39. Our Assumption Firm’s need to dispose of waste gas, which they vent to the air. It is never free to vent the gas--it requires fans to push it out. Firm’s can dispose of less gas and make the same output by using more of another input. For instance, by buying capital in the form of an afterburner.

40. Air as a function of price Price of “Other Stuff” = 2 I= 200*2=400 P1 = 400/25=8

41. Conditional Factor Demand In this chart the output is held constant at Q*.

42. Using Prices Slope on High Price line is -100/15 = -p 1 /2 so p = 13.3. A price for air of 13.3 achieves the same level of clean air as the TBES of 20 units of air.

43. Using Prices Pollution charge of 13.3- 4 = 9.3 adds $465 to cost Before pollution charge, it already cost $4/unit to use the air to dispose of waste

44. Summary Both a TBES and a pollution charge can produce the same level of use of clean air services and pollution. A TBES does not cost the firm, so C(Q; TBES) < C(Q; pollution charge) when the TBES and charge result in the same use of air