17a. Cost Minimization, Production and Lagrangians

In this video, I demonstrate a mathematical method for deriving a firm's cost function from a production function. I do so by example, using the example of a constant returns to scale Cobb-Douglas production function. This video assumes familiarity with calculus. If you are unfamiliar with calculus, Lecture 17 has all of the graphical intuition that is in this video.

In the process, I demonstrate how to use the method of Lagrange multipliers. My use of the Lagrangian is operational. That is, I refrain from giving all of the technical theoretical details that justify using a Lagrangian method. In this video, I merely demonstrate how to use it to solve an expenditure minimization problem.

For a list of videos and links to all of the microeconomics videos on this channel (organized by topic), check out the Intromediate Microeconomics video web page:

http://blog.thisyoungeconomist.com/p/learn-microeconomics.html

Category:

Education

Tags:

• cost minimization
• production functions
• Cobb-Douglas example
• deriving a cost function
• cost functions
• Lagrange multiplier
• Lagrangian
• Lagrangean
• economics lectures
• microeconomics lectures
• producer behavior
• calculus and economics
• tutorial

[aewaterloo]

I've just watched a few vides and as a fellow university economics teacher, I think you're doing an amazing job. Keep up the good work!

[intromediateecon]

@aewaterloo Thanks!

[iHeartSyusuke]

quick question, why is l/k^1-alpha/k/l^alpha equal to L/K

[intromediateecon]

(L/K)^(1-alpha) / (K/L)^(alpha)

equals [by inverting and multiplying]

(L/K)^(1-alpha) * (L/K)^(alpha)

Then, you just add the exponents, when you multiply this out:

(L/K)^(1-alpha+alpha)

That equals L/K

[albertbeccu]

Thanks for the vid! Cleared some things up.

This would be exacly the same thing for a private consumers expenditure function right? But instead of C(Pl, Pk, Q0), the function would be called E(U, P1, P2) ?

And just think of the isokost as a budgetconstraint, and the isquant as a utilize "happyness" (or whatever it measures) ? :)

Regards,

[intromediateecon]

That's correct! Thanks for the comment.

[a12b3t6m]

Man you make it so intuitive and easy to understand!!! Good work! Like it

[PhilyEcono]

Don't know if you're still checking these comments but I have a question!

Would you ever consider doing the Homogenous Production Functions of Perfect Substitutes and Perfect Compliments? Cobb Douglas is easy enough to grab but I'm challenged too much when trying to describe Perfect Subs and Comps..

Thank you for the other videos! You're far clearer than my current lecturer!!

[splashchampion]

I would recommend (highly) that you state the production function in terms of A*K^(lambda)*L(1-lambda). This represents the TFP constant, which must be divided into Q0, the output level, to properly solve the optimal levels K*,L*.

[hincapie12]

This is a really good explanation, thanx! though it would be good to have a numerical example at the end :)

[mzee101]

neo classical - chicago

[Mises4theWin]

Thanks. This helped a lot on my Math Econ homework.

[TEHPenance]

if i was given a certain budget, would i work from the cost function to find the quantity and then the optimal levels of K and L?

[R2rGangstaFC]

the cobb-douglas functions are DEAD and have NO applicance is real economics. sorry