Producer theory. Lecture note 3

Transcription

1 Producer theory Lecture note 3

2 Goals 1. Decision to be analysed (1) Firm input and output decisions Why Prediction Prescription 2. Formulate model 3. Derive testable predictions 4. Evaluate them 5. Apply model

3 2. Assumption I: action set (p353) N inputs Examples

4 2. Assumption I (p322) Interlude for production technology Definition of production function N inputs 2 inputs Examples

5 2. Assumption I Positive marginal returns 2-good diagram

6 2. Assumption I Isoquants N-dimensional definition 2-input diagram Implication of positive marginal returns

7 2. Assumption I IQs in three dimensions Quarter-hemisphere Why are we using IQs? To be able to solve in 2D (otherwise useless)

8 2. Assumption I Moving along an IQ What does this represent TRS Definition (mathematical; non-limiting) Definition (mathematical; limiting)

9 2. Assumption I Perfect complements and perfect substitutes in a diagram

10 2. Assumption I Convexity assumption N-dimensional definition 2-good diagram

11 2. Assumption I Technology vs. utility Cardinality vs. ordinality Not invariant to PMTs Assumptions on strategic space vs. maximand Observability / estimability

12 2. Assumption I Back to the action set Select any combination of inputs Subject to minimum output being produced 2-input diagram

13 2. Assumption II Firms want to minimise cost Definition of cost Price-taking on inputs

14 Assumption II Comparing costs in a diagram 2-inputs Drawing lines with [slope = relative input cost]

15 3. Determining behaviour (p354) State cost-minimisation problem mathematically N-input case 2-input case

16 3. Determining behaviour Diagrammatic representation of problem Pick point bounded by isoquant that corresponds to lowest cost

17 3. Determining behaviour Necessary condition 1: Being on the isoquant Q: which assumption implies this?

18 3. Determining behaviour Necessary condition 2: Slope of IQ = relative price of factor inputs Relative prices = TRS Q: what assumption implies this?

19 3. Determining behaviour The assumptions yield what are known as conditional factor input demands They also define a cost function

20 3. Determining behaviour Familiar concepts Average cost Marginal cost

21 Recap What is the decision to be analysed? What assumptions have been made? What have we determined? What is the next step?

22 4. Testable predictions If we know the production function and factor prices, we can predict behaviour In principle, unlike utility, we can observe the production function Realistically, though, we have very little information about it Mainly because we can t even observe many of the important inputs The only parameters we can manipulate are relative factor prices

23 4. Testable predictions What happens when the price of a factor increases? Diagrammatic analysis

24 4. Testable predictions Cost-minimisation analogue to law of demand Unfortunately, that s it Actually, there are lots more things that you can say about substitutability, but they get very technical and are beyond this course

25 5. Empirical testing As things stand, the model only tells us how, given the desire to produce a given level of output, how to select the inputs To complete the story, we need a model of output So we go back to the assumptions and adjust the model

26 2. Assumption I The action set will be selecting a positive level of output

27 2. Assumption II Firms are profit maximisers Definition of profit Note the cost function from before Price-taking assumption What does it mean? Is it realistic? What are the alternatives? What will make us want to change the assn? Q: what is the relationship between cost minimisation and profit maximisation?

28 3. Determining behaviour (p334) Firm s problem mathematically: In reduced form In primitive form

29 3. Determining behaviour Diagrammatic analysis: When MC is increasing MC=MR=p

30 3. Determining behaviour Diagrammatic analysis: When MC is decreasing

31 3. Determining behaviour Diagrammatic analysis: When MC is constant

32 3. Determining behaviour So there are three possible solutions Depend on whether MC is increasing/constant/decreasing What determines whether MC is increasing/decreasing?

33 3. Determining behaviour (p330) Take a step back and return to the production function Recap Q: what does the production fn tell us?

34 3. Determining behaviour (p358) When we double all inputs, if output more than doubles, what does that imply for MC? What does this imply for AC? IRS

35 3. Determining behaviour If doubling inputs leads to an exact doubling of output, what does this imply for MC? And for AC? CRS

36 3. Determining behaviour If doubling inputs leads to less than a doubling of output, what does this imply for MC? And for AC? DRS

37 3. Determining behaviour Does DRS really make sense? Replication argument Implication: must actually be holding one factor constant Examples

38 3. Determining behaviour Back to firm s problem If price-taking, then: Under DRS (or fixed-factor) Under CRS Under IRS

39 4. Testable predictions Things that we can observe for sure: Price of output Factor prices Things that we may be able to observe: Returns to scale in production function Fixed factors Unit costs Things that we d love to able to see but are unlikely to see MC Exact production function

40 4. Testable predictions Predictions based on these different pieces of information

41 5. Empirical evidence Most of the predictions are very difficult to test convincingly However, one thing that casual observation tells us is that infinite output doesn t happen Maybe that s because DRS always kicks in Or maybe that s because the pricing model is wrong

42 5. Empirical testing We will not cover these here, but there are alternative models of pricing Monopoly Oligopoly Monopolistic competition Require theoretical machinery not to be covered (game theory) here However Ilia will cover this in Econ 612

43 6. Usefulness of model Though we have not covered them, there are some interesting testable hypotheses Especially when we refine the model to allow for more sophisticated pricing Ilia will cover this From a framework perspective Allows us to analyse implications of taxes/legislation on profits If we collect enough data Example: British privatisation