Class Notes (836,153)
Canada (509,662)
Economics (1,617)
ECON 2X03 (55)
Lecture

L6E.pdf

16 Pages
94 Views
Unlock Document

Department
Economics
Course
ECON 2X03
Professor
Maxim Ivanov
Semester
Fall

Description
Lectures 6-7 Comparative Statics for Input Prices If all input prices change by the same factor a, then: 1. The cost of minimizing the input bundle for y units of output does not change. This is because the slope of the isocost line w /w will1be 2he same, thus, the equation MP /MP =w /w is unchanged. 1 2 1 2 Also, the isoquant y=F(z ,z )1is2unchanged. 2. The minimum cost of producing y units of output changes by the same factor a. This is because: TC(y,a*w ,a*1 )=a*2 *z +a*1 *1 =a*(w2*z2+w *z )1 1 2 2 =a*TC(y,a*w ,a*w ) 1 2 Econ 2G03/2X03 Oct 17, 24 Chapter 7 1/16 Comparative Statics for Input Prices ● Suppose that the cost-minimizing quantity of inputs i and j is positive, and MRTS is diminishing (in z ). positive diminishing 1 ● If w 1ncreases to aw , where a>1 and w does not,2then z* 1 1 decreases and z* incre2ses. That is, the firm partially substitutes the input that became more costly with the other input. ● This is because for new input prices, input z becomes1less productive (per dollar) compared to z : 2 MP /aw 1 and1 the quantity demanded of that input is positive, that is, z *>0, 1 then the total costs will increase: TC(y,aw ,w1) >2TC (y,w ,w ) 1 2 ● This is because the new cost-minimizing input bundle is above the initial isocost line for (z* ,z* ), that is, new input bundle is 1 2 more costly. ● See the figure below. Econ 2G03/2X03 Oct 17, 24 Chapter 7 3/16 Comparative Statics for Input Prices Econ 2G03/2X03 Oct 17, 24 Chapter 7 4/16 Comparative Statics for Level of Output ● The ooutput expansion pathshows the cost minimizing input bundles (z* 1z* 2 for all levels of output y. ● A normal input - the cost-minimizing level of that input normal input increases when output y increases. ● An iinferior input- the cost-minimizing level of that input decreases when output y increases. ● Note: the input can be normal for some level of output y , bu0 inferior for another level y . See the figure below. 1 Econ 2G03/2X03 Oct 17, 24 Chapter 7 5/16 The output expansion path Econ 2G03/2X03 Oct 17, 24 Chapter 7 6/16 Homothetic Production Functions Homothetic Production Functions ● A hhomothetic production functionis a type of function such that the MRTS is consconstantng any ray from the origin. ● A production function is homothetic if MRTS can be represented as a function of z /z : 2 1 MRTS(z ,z 1 =2f(z /z 2 1 ● Examples: if MRTS(z ,z ) = (z /z ) , then such a function is 1 2 2 1 homothetic. 3 However, if MRTS(z ,z )= 1 /2 , th2n 1uch a function is NOT homothetic. Econ 2G03/2X03 Oct 17, 24 Chapter 7 7/16 Homothetic Production Functions ● Claim: for homothetic production functions, the output expansion path
More Less

Related notes for ECON 2X03

Log In


OR

Join OneClass

Access over 10 million pages of study
documents for 1.3 million courses.

Sign up

Join to view


OR

By registering, I agree to the Terms and Privacy Policies
Already have an account?
Just a few more details

So we can recommend you notes for your school.

Reset Password

Please enter below the email address you registered with and we will send you a link to reset your password.

Add your courses

Get notes from the top students in your class.


Submit