{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

19_CostFunctions_ToPost-1

19_CostFunctions_ToPost-1 - , run HenryDavidThoreau ECON...

Info icon This preview shows pages 1–13. Sign up to view the full content.

View Full Document Right Arrow Icon
“The cost of a thing is the amount of what I will call life which  is required to be exchanged for it, immediately or in the long  run.” –Henry David Thoreau ECON 410 Cost Functions
Image of page 1

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
2 Class 19 - Cost Functions
Image of page 2
3 Class 19 - Cost Functions
Image of page 3

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
4 Mathematical Analogy 1 2 ( , ) f x x Of the bundles that can produce q, which is cost minimizing? 1 1 2 2 1 2 ( , ) ( ) w x w x q f x x λ = + + - L 2 1 1 2 f f w w = Class 19 - Cost Functions
Image of page 4
5 Class 19 - Cost Functions
Image of page 5

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
6 Class 19 - Cost Functions Individual Demand Curve An Individual Demand Curve is the graphical relationship between a Good’s price and the amount of the Good an individual will select when optimizing over her changing budget set.
Image of page 6
7 Class 19 - Cost Functions Factor Demand Function A Factor Demand Function specifies the relationship between the prices of input goods, the quantity of output produced, and the amount of an input good a firm will select when minimizing its costs.
Image of page 7

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
8 Class 19 - Cost Functions Steps to Analytically Solve for a Firm’s Factor Demand Functions 1. Create the Lagrange equation with the specified production function, but leave q, w1, and w2 as parameters. 2. Take the FOC’s and solve for x1 and x2. Your results will be as a function of q, w1, and w2 (or some combination of the three). x1 and x2 will be your Factor Demand Functions.
Image of page 8
9 Class 19 - Cost Functions Assume a firm has a Cobb- Douglas production function of the form f(x1, x2)=x11/2x21/2. Find the firm’s factor demand functions 1. Create the Lagrange equation with the specified production function, but leave q, w1, and w2 as parameters. 1/ 2 1/ 2 1 2 1 1 2 2 [ ] w x w q x x x λ + + - L 1/ 2 1/ 2 1 2 2 1 2 1 [ ] x w q x x x w λ + + - L Cost Functio n Output Constraint
Image of page 9

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
10 Class 19 - Cost Functions 2. Take the FOC’s and solve for x1 and x2. Your results will be as a function of q, w1, and w2 (or some combination of the three). x1 and x2 will be your Factor Demand Functions. 1 0 x = L 1/ 2 1/ 2 1 1 2 2 0 1 x w x λ - - = 1/ 2 1/ 2 2 1 2 0 1 2 x x w λ - - = 2 0 x = L 0 λ = L 1/ 2 1/ 2 1 2 0 q x x - = 1/ 2 1/ 2 1 2 1 2 1 2 [ ] x w w q x x x λ + + - L Assume a firm has a Cobb- Douglas production function of the form f(x1, x2)=x11/2x21/2. Find the firm’s factor demand functions
Image of page 10
11 Class 19 - Cost Functions 1/ 2 1/ 2 1 1 2 2 0 1 x w x λ - - = 1/ 2 1/ 2 2 1 2 0 1 2 x x w λ - - = 1/ 2 1/ 2 1 2 0 q x x - = 1 1/ 2 1/ 2 1 2 2 x w x λ - = 2 1/ 2 1/ 2 1 2 2 w x x λ - = 2. Take the FOC’s and solve for x1 and x2. Your results will be as a function of q, w1, and w2 (or some combination of the three). x1 and x2 will be your Factor Demand Functions. Assume a firm has a Cobb- Douglas production function of the form f(x1, x2)=x11/2x21/2. Find the firm’s factor demand functions
Image of page 11

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
12 Class 19 - Cost Functions 2 1 1/ 2 1/ 2 1/ 2 1/ 2 1 2 1 2 2 2 w x x x x w - - = 1/ 2 1/ 2 1 1 2 2 0 1 x w x λ - - = 1/ 2 1/ 2 2 1 2 0 1 2 x x w λ - - = 1/ 2 1/ 2 1 2 0 q x x - = 1 1/ 2 1/ 2 1 2 2 x w x λ - = 2 1/ 2 1/ 2 1 2 2 w x x λ - = 2.
Image of page 12
Image of page 13
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern