You should be sure to read the first two pages of the chapter. The production function i the rm produces one output y using n inputs x x 1,x 2. Consider the following production functions, where q is the quantity produced of the good, k is the quantity of capital used, and l is the quantity of labor used. The microeconomic foundations of aggregate production functions. Intermediate microeconomics fall 2015 problem set 7 due lecture 8 in class on paper 1. Contents 1 themarket4 2 budgetconstraint8 3 preferences10 4 utility 14 5 choice 18 6 demand 24 7 revealedpreference27. This is an exciting time to study economics, even though may not be so exciting to be part of this economy.
It is easy to show that for ces utility functions, s 1. Intermediate microeconomics mark dean homework 6 due wednesday, 30th march question 1 if a production function exhibits diminishing marginal product with respect to each input, does it have to exhibit decreasing returns to scale. To check this, form a matrix using the second derivatives of theproduction function, and see if it is negative semidefinite. Cost functions and optimal output columbia university, spring 2016 mark dean. It is recommended for students planning to apply to graduate school in economics, accounting, or finance. In one of the most indepth and detailed studies of its kind, this book captures all the existing contemporary techniques in the theoretical fields as well as the empirical applications of the. You can think of the transformation function simply as a convenient way to represent a set. Questions with parts within them give equal weight to the parts. Intermediate microeconomics demand ben van kammen, phd. Overview of mathematical tools for intermediate microeconomics christopher flinn department of economics new york university. Aims this course aims to provide students with the framework to analyse the economic behaviour of individuals in the business and public sectors, including the behaviour. Her opportunity cost are the bene ts that would be foregone if she invested in the business.
Download workoutsin intermediatemicroeconomics ebook pdf or read online books in pdf, epub. Intermediate microeconomics dirk bergemann, spring 2012 week of 122 128 1 lecture 5. Economics is the social science that studies the production and distribution of. A production function is a mathematical relationship between the quantities of inputs used and the maximum quantity of output that can be produced with those. Decompose the change in demand for good x into a substitution and an income effect. I the inputoutput relationship is captured in the production function. Our objective in this chapter is to derive a demand function from the consumers maximization problem. The output of each producer is produced using intermediate inputs and. When both inputs in a twoinput production function are variable, the production function is graphed as an isoquant map.
The short run is defined as the period of time in which at least one input is fixed. These lecture notes were prepared by xingze wang, yinghsuan lin, and frederick jao specifically for mit opencourseware. Only if the production function exhibits decreasing returns to scale 14 returns to scale and cost functions. Marek weretka problem 1 production functions a the isoquants for each of the three production functions are show below. Show that this is not true, using the production functionqkl 22, with the. Intermediate microeconomics production ben van kammen, phd. We have faced the largest nancial crisis since the great depression.
Thus a function is a rule that associates, for every value x in some set x, a unique outcome y. Advanced students willing to extend their knowledge beyond the planned limits of this book should delve into the careful bibliography supplied for each chapter. For the isoquant to be convex to theorigin, it is sufficient but not necessary that the production function is concave. On this basis production function is classified into two types. It is part of a larger category called constant elasticity of substitution ces utility functions. This beautifully presented and accessible text covers all the essential topics typically required at. Cobbdouglas preferences are easy to use and therefore commonly used. To learn these basic analytical methods, we will rely primarily on the textbook. The microeconomic foundations of aggregate production. Click download or read online button to workoutsinintermediatemicroeconomics book pdf for free now. Does production function 1 have decreasing, constant, or. Lecture notes principles of microeconomics economics.
Feb 08, 2011 the production function production refers to the transformation of inputs into outputs or products an input is a resource that a firm uses in its production process for the purpose of creating a good or service a production function indicates the highest output q that a firm can produce for every specified combinations of inputs. This section provides lecture notes from the course. Production function short run production function time when one input say, capital remains constant and an addition to output can be obtained only by using more labour. The technology of production the production function 6.
Applied microeconomics consumption, production and markets this is a microeconomic theory book designed for upperdivision undergraduate students in economics and agricultural economics. Since output goes up by the same factor as the inputs, this production function exhibits constant returns to scale. Problems with solutions, intermediate microeconomics, lecture 12. Intermediate microeconomics and its application walter nicholson amtierst college. Workoutsinintermediatemicroeconomics download workoutsinintermediatemicroeconomics ebook pdf or read online books in pdf, epub, and mobi format. The production decisions of firms are analogous to the. Cost functions of homogeneous production functions theorem suppose f x is homogeneous of degree k. Microeconomics exercises with suggested solutions 4 contents contents 1. Intermediate microeconomics with applications sciencedirect. L k2l k l f 1 f 2 f 1 microeconomics consumption, production and markets this is a microeconomic theory book designed for upperdivision undergraduate students in economics and agricultural economics. To check this, form a matrix using the second derivatives of theproduction function, and see if it is negative. Intermediate microeconomics notes and sample questions chapter 7.
Consumer theory consumers choose the best bundles of goods they can a ord. The utility function that produced the demand function x. Recall from 103 that elasticity is the ratio of two variables. The derivatives offx 1,x 2 are both positive so the technology is monotonic. Intermediate microeconomics notes and sample questions chapter 8.
The questions in part 1 should take no more than 5 minutes each to answer. Intermediate microeconomics department of economics, finance and legal studies university of alabama spring, 20 midterm ii the exam is worth 100 points. Trapper joe, the fur trader, has found that his production function in acquiring pelts is given. Econ a311f intermediate microeconomics is a fivecredit higher level course in the fulltime social sciences programme. The construction of a firms production function presumes. My intermediate microeconomics course uses a lot of calculus and algebra. For each of the following production functions, determine if the technology exhibits increasing, decreasing, or constant returns to scale. Intermediate microeconomics, 8e, chapters 2, 3 and 4 1 53. Microeconomics is the study of how individual behavior leads to social outcomes, such as an income distribution where paris hilton is rich and im not, and most pizza is made without anchovies. This video explains how the production function can be built in order to analyse it. Fixedproportions production function 207 relevance of input substitutability 208. The amount of labor a farmer uses to produce a bushel of corn is likely different than that required to produce an automobile. The lecture notes are from one of the discussion sections for the course. Different products have different production functions.
If you plug in the amount of labor, capital and other inputs the firm is using, the production function tells how much output will be produced by those inputs. Again, since production function 1 is a cobbdouglas production function we can simply add the exponents together. We have set up the firms problem converts inputs to outputs in order to maximize profit thought about how to solve the firms problem when there is. However, the aggregate production function, which does much the same thing on the production side of the economy was left largely unexamined. Appendix to chapter 1 mathematics used in microeconomics 23 al1 functions of one variable 23 ai2 graphing functions of one variable 24. Second, we will analyze some of the most important ideas in microeconomics in the last 30 years. Microeconomics 1 production theory returns to scale are easily defined for homogeneous production function. Intermediate microeconomics intermediate microeconomics. Problems with solutions, intermediate microeconomics. Production functions can have varying returns to scale, i. Intermediate microeconomics dirk bergemann, spring 2012 1 introduction 1. Production functions this chapter will introduce the idea of a production function. Consumers satisfaction there are two sides in a market for a good demand supply created by consumers created by firms.
Then the cost and conditional input demand functions are multiplicatively separable in y and w, and are given by cw,y cw,1. This chapter investigates the relationship between a production function and the cost of producing given quantities of output, assuming that a firm minimizes its. The production function for puffed rice is given by q 100kl12 where q is the number of boxes produced per hour, k is the number of puffing guns used each hour, and l is the number of workers hired each hour. For the production functions here, k and l are perfect complements and the cost minimizing combination is such that k l. Download pdf workoutsinintermediatemicroeconomics free. Mattias has quasilinear preferences and his demand function for books is b 15 0. The production function is as we have always understood it, the greater the inputs here labour by robinson. These questions use new parameters and scrambled responses so that an instructor can use them as a quiz or for more formal graded examinations. Firms in the same industry may have somewhat different production functions. Nov 20, 2018 production functions describe how output is determined by various inputs. Overview of mathematical tools for intermediate microeconomics.
A computerized version of this test bank is available at no charge to any instructor who adopts hal varians intermedi. Intermediate microeconomics and its application walter. A toolbuilding approach is a clear and concise calculusbased exposition of current microeconomic theory that is essential for students pursuing degrees in economics or business. There will be no communication with the exam proctors. Intermediate microeconomics, lecture 7 economics 352. Another way to represent production possibility sets is using a transformation function t. Demand function pdf before watching the lecture video, read the course textbook for an introduction to the material covered in this session. Jennys foregone bene ts are her salary for the year. Production functions microeconomics free download as powerpoint presentation. Production functions, noneconomic regions, interpreting marginal rate of technical substitution, perfect substitutes and perfect complements leontief production functions, and the elasticity of. A mathematical function that relates inputs to outputs.
Cost functions this chapter investigates the relationship between a production function and the cost of producing given quantities of output, assuming that a firm minimizes its costs of production. Koutsoyiannis is an extensive survey of contemporary microeconomics for undergraduates and postgraduate college students. Each question six questions on six pages is of equal value. Cardinal utility 57 constructing a utility function 58 some exam. A production function is homogeneous of degree k if where k is a constant and t is any positive real number. Production functions describe what is technically feasible when the. Calculate q 1,000 isoquant for this production function and show it on a graph. The particularly important characteristic that we stress is that there is a unique value of y associated with each. A production process uses inputs such as labor, energy, raw materials and capital to. Does production function 1 have decreasing, constant, or increasing returns to scale. If f z is concave or the production set is convex so we have nonincreasing returns to scale, f z f z, 1, then c q. The production function production refers to the transformation of inputs into outputs or products an input is a resource that a firm uses in its production process for the purpose of creating a good or service a production function indicates the highest output q that a firm can produce for every specified combinations of inputs. Feb 23, 2014 this video explains how the production function can be built in order to analyse it.