### Create a StudySoup account

#### Be part of our community, it's free to join!

Already have a StudySoup account? Login here

# Economics Of Labor Markets ECON 65200

Purdue

GPA 3.6

### View Full Document

## 45

## 0

## Popular in Course

## Popular in Economcs

This 35 page Class Notes was uploaded by Brett Stanton on Saturday September 19, 2015. The Class Notes belongs to ECON 65200 at Purdue University taught by Staff in Fall. Since its upload, it has received 45 views. For similar materials see /class/207954/econ-65200-purdue-university in Economcs at Purdue University.

## Popular in Economcs

## Reviews for Economics Of Labor Markets

### What is Karma?

#### Karma is the currency of StudySoup.

#### You can buy or earn more Karma at anytime and redeem it for class notes, study guides, flashcards, and more!

Date Created: 09/19/15

Nonparametric Efficiency Testing I A linear programming based approach to efficiency assessment Cross section or time series inputoutput data viewed as observations from the technically feasible set Assumptions for what follows includes that each observation comes from the same technology set Modifications exist to account for technical progress Purdue University Ag Econ 652 Nonparametric Efficiency Testing cont d The easiest way to think of efficiency is by looking at a single inputsingle output system Which ofthe following observations are ef cient Observation Output Input 1 1 3 2 3 5 3 2 6 4 6 6 5 3 9 6 7 11 7 8 15 Purdue University Ag Econ 652 Nonparametric Efficiency Testing cont d Purdue University Ag Econ 652 Nonparametric Efficiency Testing cont d I What can you say about the efficiency ofthese observations I Are some observations more efficient than others Purdue University Ag Econ 652 Nonparametric Efficiency Testing cont d Purdue University Ag Econ 652 Nonparametric Efficiency Testing cont d Purdue University Ag Econ 652 Nonparametric Efficiency Testing cont d I What are you assuming about returns to scale I What happens if you change your returns to scale assumption Purdue University Ag Econ 652 Nonparametric Efficiency Testing cont d Purdue University Ag Econ 652 Nonparametric Efficiency Testing cont d I What else are you assuming I Are you assuming anything about prices Can you generalize these ideasto higher dimensions ie multiple inputs andor multiple outputs Purdue University Ag Econ 652 Nonparametric Efficiency Testing cont d I Consider a two inputone output case Which ofthe following observations are ef cient Observation Output Input 1 Input 2 1 5 1 1 5 1 3 6 1 2 4 8 1 3 5 8 2 2 6 9 3 3 7 10 4 2 Purdue University Ag Econ 652 Nonparametric Efficiency Testing cont d Which ofthe following observations are ef cient Observation Output Input 1 Input 2 1 5 1 1 2 5 2 1 Note that 2 uses more ofinput 1 the same amount of input 2 and produces no more output than 1 So 2 is inefficient Purdue University Ag Econ 652 Nonparametric Efficiency Testing cont d Which ofthe following observations are ef cient Observation Output Input 1 Input 2 1 5 1 1 3 6 1 2 4 8 1 3 Note that input use for observation 3 is the average of input use for observations 1 and 4 However the average output level for observations 1 and 4 is 65 strictly greater than observed output for 3 Hence we conclude 3 appears to be inefficient Purdue University Ag Econ 652 Nonparametric Efficiency Testing cont d Which ofthe following observations are ef cient Observation Output Input 1 Input 2 1 5 1 1 5 8 2 2 6 9 3 3 Note that the input usage for 5 is the average ofthe input usage for 1 and 6 but the output production 8 is greater than the average output 7 592 What are we assuming about returns to scale Purdue University Ag Econ 652 Nonparametric Efficiency Testing cont d I If we assume constant returns to scale CRTS what happens I Observation Output Input 1 Input 2 1 5 1 1 5 8 2 2 6 9 3 3 With CRTS we can double inputs and outputs for observation 1 So with 2 units of each input we can get 10 units ofoutput Similarly 3 units of each input we get 15 units of output 80 5 and 6 are inefficient Purdue University Ag Econ 652 Nonparametric Efficiency Testing cont d Let us formalize our assumptions Free disposability of inputs and outputs Convexity of input requirements and production possibilities I No errors in the data Purdue University Ag Econ 652 Nonparametric Efficiency Testing cont d Assume that you have a bunch of data for K different firms indexed by IF1K The output of firm k is denoted by ukand inputs are denoted by Xnk where n indexes inputs Let s not assume constant returns to scale I Considerthe set of technically feasible input combinations that produce a given amount ofoutput 0 Purdue University Ag Econ 652 Nonparametric Efficiency Testing cont d Associate a weight with each observation the single weight applies to all inputs and outputs The technically feasible set of inputs producing u0 is K u xxlxNlZuklk 2M0 k1 K xfl an n 1N k1 21k 1 1quot 2 0 k 1K k1 Purdue University Ag Econ 652 Nonparametric Efficiency Testing cont d The role ofthe M s is as weights in forming a convex combination of the inputoutput vectors The final line makes the weights nonnegative and sum to unity The first inequality defining the set ensures that At least u0 will be produced by the linear combination ofobserved inputoutput vectors Use of the inequality implies free disposal of output Purdue University Ag Econ 652 Nonparametric Efficiency Testing cont d The second set of inequalities Ensure that at least as much input as the convex combination is used I Embody free input disposal because it is an inequality Purdue University Ag Econ 652 Nonparametric Efficiency Testing cont d For the data listed above this set is 0 u xlx2l 1 2 3 4 5 6 7 0 52L 5 L 6 L 8 L 8 L 9 L 10 L 2M 1 2 3 4 5 6 7 12L 22 1 L 1 L 22 3 L 4 L 2161 1 2 3 4 5 6 7 12L 1 L 22 3 L 22 3 L 22 2162 1 2 3 4 5 6 7 k Purdue University Ag Econ 652 Nonparametric Efficiency Testing cont d Note that this set is a function of the output level u0 Ef ciency has something to do with being on the boundary of this set The technical ef ciency test asksthe question given the input vector could higher output have been produced Purdue University Ag Econ 652 Nonparametric Efficiency Testing cont d To answer this question we could solve the following problem mam39m u k k subject to u 1 214 K kk 0 x171 gxi k1 K v 211 gt0 Purdue University Ag Econ 652 Nonparametric Efficiency Testing cont d Note that X0 are the fixed input levels for firm 0 whose efficiency is being tested and whose data is included in IF1K Can you argue that there is a lower bound forthe optimal u What is that bound How should we decide if firm 0 is ef cient I What are we assuming about returns to scale Purdue University Ag Econ 652 Nonparametric Efficiency Testing cont d If we apply this test to the two input data and test for efficiency of rm 2 we solve the following problem maximizeu 1 2 3 4 5 6 7 52 52 62 82 82 92 102 2M 1 2 3 4 5 6 7 12 22 12 12 22 32 42 S2 1 2 3 4 5 6 7 12 12 22 32 22 32 22 1 1 2 3 4 5 6 7 k Purdue University Ag Econ 652 Nonparametric Efficiency Testing cont d The optimal solution forthis problem is u5 What do we conclude Does this agree with your intuition Note that this was a test oftechnical ef ciency Under what could this really be optimal Purdue University Ag Econ 652 Nonparametric Efficiency Testing cont d I What are you assuming about prices Technical efficiency Allocative efficiency Purdue University Ag Econ 652 Nonparametric Efficiency Testing cont d I Consider the following price and quantity data Output Input 1 Input 2 p61 p61 p61 5 7 3 4 2 3 4 7 4 1 3 5 4 14 2 8 3 5 3 14 2 8 16 Purdue University Ag Econ 652 Nonparametric Efficiency Testing cont d Output Input 1 Input 2 q p61 p61 7 3 4 2 3 7 4 1 3 5 Note that for the first and second observations the input mix is different but output is the same The cost of inputs for firm 1 is 3X42X318 The cost if firm 1 used rm 2 s inputs3x12x513 Hence firm 1 is inefficient Firm 2 observed cost is 4X13X519 achievable 4X43X325 So rm 2 appears to be efficient Purdue University Ag Econ 652 Nonparametric Efficiency Testing cont d Output lnput1 lnput2 Q m m 14 2 8 3 5 14 2 8 16 Now compare firms 3 and 4 Note that firm 4 is inefficient in the way that made us uncomfortable when we looked closely at technical efficiency more input same output Firm 4 observed costs2x81x622 achievable costs2x81x521 Purdue University Ag Econ 652 Nonparametric Efficiency Testing cont d Clearly we need a test that takes into account the value of inputs Now our question becomes how low could we drive costs and still produce as much as firm 0 Input levels now become variables in our testing problem and the output level is xed I When testing firm 0 we always use firm 0 prices in our measurement of costs Purdue University Ag Econ 652 Nonparametric Efficiency Testing cont d To test for cost minimization efficiency we solve N 0 K subject to 214W 2 u0 k1 K 2x5 S x k1 K 2 1 2V 2 0 k1 Purdue University Ag Econ 652 Nonparametric Efficiency Testing cont d If we apply this test to the two input data and test for efficiency of rm 1 we solve the following problem minimize 3x1 2x2 1 2 3 4 7 72 141 142 27 1 2 3 4 4 12 82 81 3x1 1 2 3 4 3 52 51 61 3x2 1 2 3 4 k Purdue University Ag Econ 652 Nonparametric Efficiency Testing cont d The optimal solution for this problem has an objective value of 13 with inputs at levels 1 and 5 Does it appearthat firm 1 is efficient I What should the objective be if rm 1 is ef cient I Can we attribute some degree of inef ciency How about noting 1OOX1813138 and saying that costs for rm 1 are 38 too high Purdue University Ag Econ 652 Nonparametric Efficiency Testing cont d If we apply this test for ef ciency to firm 2 we solve the following problem minimize 4x1 3x2 711 712 145 1414 2 7 411112 813 814 s x1 3 1 512 5 3 614 s x2 47 1 2 3 k Purdue University Ag Econ 652 Nonparametric Efficiency Testing cont d The optimal solution for this problem has an objective value of 19 with inputs at levels 1 and 5 Does it appear that firm 2 is efficient What should the objective be if rm 2 is ef cient Will we ever find hyperefficiency ie minimum feasible costs higher than observed Purdue University Ag Econ 652 Nonparametric Efficiency Testing cont d More often than not there will be a mixture of fixed and variable inputs then we solve the following I minimize waxn x1xtlllK quot1 K subject to Zuklk 2 u0 k1 K 23631quot 5xquot forlSnSt k1 Ma K xfIk 5xquot forngtt 21quot 1 11 20 k1 k Purdue University Ag Econ 652 1 Nonparametric Efficiency Testing cont d If we apply this test for firm 1 where input 1 istreated as xed we get minimize 2x2 711 712 145 1414 2 7 411 112 85 814 s 4 3 1 512 5 3 614 s x2 47 1 2 3 k Purdue University Ag Econ 652 Nonparametric Efficiency Testing cont d The optimum for this problem has an objective value of 6 Does rm 1 appearto be minimizing variable costs Remember that firm 1 was using 3 units of input 2 Recall that when both inputs were variable firm 1 appeared to be inefficient Purdue University Ag Econ 652 Nonparametric Efficiency Testing cont d Thus far we have seen tests for Technical efficiency in the production of one output I Allocative efficiency in the minimization of costs There are three other types of efficiency tests Multiple output technical efficiency Profit maximization Revenue maximization given input levels Purdue University Ag Econ 652 Nonparametric Efficiency Testing cont d Multiple output technical ef ciency test maximize I all K subject to Zuilk 2 11317 k1 K 2x32 S x2 k1 K 21quot 1 Lquot 2 0 Purdue University Ag Econ 652 Nonparametric Efficiency Testing cont d Here we are asking ifthe entire vector of outputs can be scaled up by a single factor I We are not asking whether more of any output could be produced I What will the optimal objective value be for An ef cient producer I An inef cient producer Purdue University Ag Econ 652 Nonparametric Efficiency Testing cont d Note that we are testing each output at a time for efficiency OB0A in this case k 2 Purdue University Ag Econ 652 Nonparametric Efficiency Testing cont d Here is a case where this test produces an unintuitive result t A u2 B Purdue University Ag Econ 652 Nonparametric Efficiency Testing cont d For each m we could solve the following maximize Tm TWA K subject to Zumklk 2 uia m K xflk S x2 2 1 23 2 O k1 Purdue University Ag Econ 652 Nonparametric Efficiency Testing cont d k 2 C 01 a B A 02 1 Purdue University Ag Econ 652 Nonparametric Efficiency Testing cont d Now consider our unintuitive example A uzA B 1 Purdue University Ag Econ 652 Nonparametric Efficiency Testing cont d Profit maximization looks much like cost min test M 0 0 x1 R RSl H ef EPW quot EM K k k subject to Eu 7L 2 um K kk k k Y an ltxn v1 211 gt0 Purdue University Ag Econ 652 Nonparametric Efficiency Testing cont d Notice that this is the multiple output case Notice the similarity with the cost min test How would you identify inef ciency Where is the data in the problem that is relevant to the individual firm I How does this change with fixed inputs Purdue University Ag Econ 652 Nonparametric Efficiency Testing cont d If we apply this test for firm 2 where the output price minimize 414 4x1 3x2 1 2 3 4 72 72 142 142 214 1 2 3 4 42 12 82 82 3x1 1 2 3 4 32 52 52 62 3x2 1 2 3 4 k Purdue University Ag Econ 652 Nonparametric Efficiency Testing cont d The optimal solution for this problem has an objective value of 9 Is rm 2 ef cient I Yes observed pro t was 9 How would this change if input 1 was fixed Purdue University Ag Econ 652 Nonparametric Efficiency Testing cont d Test of pro t max with input 1 fixed Firm 2 minimize 414 2x2 711 712 145 1414 2 M 4211412 8112 s1 311 512 5 3 614 s x2 1 2 3 4 k New optimal objective is 18 and firm 2 is efficient Purdue University Ag Econ 652 Nonparametric Efficiency Testing cont d Revenue maximization test i 0 maX1m1ze Ll u1uMl1lK m1pm m K subject to zumkik 2 um k1 K zxkik S x2 Elk 1 1k 2 0 k1 k1 Purdue University Ag Econ 652 Nonparametric Efficiency Testing cont d Again this is similar to cost minprofit max problems and looks as follows for rm 2 minimize 414 711 712 145 1414 2 M 4211412 8112 s1 311012 55 614 s 5 1 2 3 4 k Purdue University Ag Econ 652 Nonparametric Efficiency Testing cont d In the single output case is the revenue test strange Note that technical inef ciency implies pro t and revenue maximization inefficiency Cost minimization inef ciency implies pro t maximization inefficiency Revenue maximization inef ciency implies pro t maximization inef ciency Purdue University Ag Econ 652 Nonparametric Efficiency Testing cont d How do we add the assumption of constant returns to scale I There is a problem with the profit maximization test when all inputs are variable and we assume constant returns to scale What is it Purdue University Ag Econ 652 Nonparametric Efficiency Testing cont d Want to learn more Then read Farrell Md The Measurement of Productive Efficiency Journal of the Royal Statistical Society 1203253 290 Varian HR 1984 The Nonparametric Approach to Production Analysis Econometrica 523579597 Fare R S Grosskopf and H Lee 1990 A Nonparametric Approach to Expenditureconstrained Profit Maximization American Journal of Agricultural Economics 721574581 Purdue University Ag Econ 652 Producer Problems Complications I Incorporating additional activitiesconstraints in producer problems a question of scope What makes producer problems interesting is their interactions with the world Market interactions purchases and sales of inputs or outputs Resource transactions factor rental service hiring borrowing Purdue University Ag Econ 652 Producer Problems Complications l Regulations Prohibitions or limits on use of some inputs Prohibitions or limits on the production of some outputs Contracts with suppliers of input or demanders of outputs l Formulation of constraints and objective must re ect Producerincentives Tradeoffs available to producers Purdue University Ag Econ 652 Endogenous Price Models I In some cases price taking behavior is not the appropriate perspective eg Where producers have market power Models ofentire sectors wherein we know there is a relationship between supply and demand quantities and market prices Purdue University Ag Econ 652 Endogenous Price Models cont d The key is to know what the relationship between price and quantity is Demand QP is typically known but I What we need is inverse demand PQ so the relationship must be invertible ng QPocPs and PQQoc s Purdue University Ag Econ 652 Endogenous Price Models cont d In optimization modeling endogenous price models are often used to model partial equilibrium problems Simple example Let s say we know that demand is DP an and supply is SP cPd Purdue University Ag Econ 652 Endogenous Price Models cont d Now considerthe problem 1d b 7 d 7 maX1m1ze D1t a 119 S1ddc M SD 1b subject to D S SO I The rstorder conditions for this problem are Da 1 P 0 where P is the shadow price on the constraint So1 d P 0 and o D S 5 0 Purdue University Ag Econ 652 Endogenous Price Models cont d Notice that we can use algebra to reexpress the first order condition for D as D an And likewise for S S cPd So the shadow price on the constraint is acting like the market price and the relationships between Supply Demand and Market Price have been modeled Purdue University Ag Econ 652 Endogenous Price Models cont d l How did we do this D 15 5 141 ma uguze IO da ddJ 0SC ds subject to Dis SO 80 our objective is the integral under the inverse demand curve less the integral underthe inverse supply curve producer s plus consumer s surplus Purdue universityAg Eeerr 652 Lecture 12 Endogenous Price Models cont d Graphically here is what is going on 4 5 Demand 4 3 5 CS 339 2 5 2 PS l 5 Supply El ED 7D 0 EH SE lEIEI Purdue universityAg Eeerr 652 Lecture 12 Endogenous Price Models cont d I It is straightforward to adapt this model to analysis of spatial equilibrium problems The base is a transportation problem transhipment problem or transhipment problem with processing Demand and or supply are no longertreated as fixed but rather integrals ofthe inverse relationships are incorporated in the objective Purdue University Ag Econ 652 Endogenous Price Models cont d For example the transportation model with variable supplies and demands becomes m n D St maggigj zc Pjdjddj Pisz39dsz39 m n EECU39XU n m subject to inj ng Si vxv 300391 20 Purdue University Ag Econ 652 Endogenous Price Models cont d This formulation has the same interpretation as before producers plus consumers surplus There is an adjustment for interindustry costs Graphical illustration is no longer feasible This type of model is frequently used to study markets for a single good or a sector partial equilibrium Purdue University Ag Econ 652

### BOOM! Enjoy Your Free Notes!

We've added these Notes to your profile, click here to view them now.

### You're already Subscribed!

Looks like you've already subscribed to StudySoup, you won't need to purchase another subscription to get this material. To access this material simply click 'View Full Document'

## Why people love StudySoup

#### "Knowing I can count on the Elite Notetaker in my class allows me to focus on what the professor is saying instead of just scribbling notes the whole time and falling behind."

#### "I made $350 in just two days after posting my first study guide."

#### "There's no way I would have passed my Organic Chemistry class this semester without the notes and study guides I got from StudySoup."

#### "It's a great way for students to improve their educational experience and it seemed like a product that everybody wants, so all the people participating are winning."

### Refund Policy

#### STUDYSOUP CANCELLATION POLICY

All subscriptions to StudySoup are paid in full at the time of subscribing. To change your credit card information or to cancel your subscription, go to "Edit Settings". All credit card information will be available there. If you should decide to cancel your subscription, it will continue to be valid until the next payment period, as all payments for the current period were made in advance. For special circumstances, please email support@studysoup.com

#### STUDYSOUP REFUND POLICY

StudySoup has more than 1 million course-specific study resources to help students study smarter. If you’re having trouble finding what you’re looking for, our customer support team can help you find what you need! Feel free to contact them here: support@studysoup.com

Recurring Subscriptions: If you have canceled your recurring subscription on the day of renewal and have not downloaded any documents, you may request a refund by submitting an email to support@studysoup.com

Satisfaction Guarantee: If you’re not satisfied with your subscription, you can contact us for further help. Contact must be made within 3 business days of your subscription purchase and your refund request will be subject for review.

Please Note: Refunds can never be provided more than 30 days after the initial purchase date regardless of your activity on the site.