Managerial Economics/Math

posted by .

I'm working on some HW for my MBA Managerial Economics class. I've got one problem down to the end, but I'm stuck. Any help would be greatly appreciated. And, of course, if you could check my work on a & b, that would be excellent. Thanks! :)

1.) The mathematics of consumer equilibrium can be demonstrated using the following logic:

A consumer will spend or save his/her entire income, so that:

I = P1X1 + P2X2 + .......... PnXn
Where I = consumer income

X1X2,..............Xn = quantities of n commodities, one of which is saving

P1P2,.............Pn = respective prices of the n commodities (the implied price of saving would be 1)

The consumer wants to maximize his/her total utility, TU, where:

TU = f(X1,X2,..........Xn)

subject to the above income constraint.

a.) Set up the Lagrangian expression that is to be maximized.

I think (?) the answer to this is:

Ltu = TU + lamba(I - P1X1 - P2X2......PnXn)

b.) Show the partial derivative equations whose solution gives optimal values for X1,X2,.........Xn. Note that the partial derivative of TU with respect to X1 is designated as MUx1.

According to my math, these are the partial derivatives:

dLtu/x1 = dTU/dX1 - lambdaP1

This one would be the marginal utility of x1, I think?

dLtu/xn = dTU/dXn - lambdaPn

And, this one shoul dbe the marginal utility of Xn.


c) Show that consumer equilibrium requires the following relationship:

MUx1/P1 = MUx2/P2 = ....... = MUn/Pn

Interpret the economic meaning of the above relationship.

On this one, I'm completely stuck. I've used the Lagrangian Multipler Technique dozens of times, but it's always had actual figures in it. Without actual numbers, I don't even know where to start. :(

  • Managerial Economics/Math -

    your a) and b) look correct.

    For c) you are almost there.
    You have Ln = dTUn/dXn - LambdaPn
    The first term to the right of = is MUn. Also, at a maxima, the whole term is zero. So you have MUn - LambdaPn=0.
    Thus, MUn = LambdaPn. This is true for all goods. So, MUx1=LambdaPx1
    Thus MUn/MUx1 = LambdaPn/LambdaPx1
    The Lambdas cancel. So MUn/MUx1=Pn/Px1
    which can be re-written as MUn/Pn = MUx1/Px1

  • Managerial Economics/Math -

    Ok, I think I get it. Thank you so much!

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Managerial Economics/Math

    I need help on some homework questions for an MBA-level Managerial Economics class. Here is the first question. 1. JALT, Inc. is a new firm offering investment consultant services to the rich. Harvey Milkemnow, having had experience …
  2. Managerial Economics

    Managerial Economics uses_____to help solve problems. a. mathematical programming b. Statistics c. decision sciences d. microeconomics e. all of the above
  3. Managerial Economics/Math

    This is an MBA-level Managerial Economics Course. I'm working on some HW and just want to double-check my answers. 1. Jimbo's is a new company producing exploding cigars. Jimbo's company has the following demand curve for the cigars: …
  4. Managerial Economics/Math

    I wanted to post this as a new question to make sure you saw it. Thanks! :) Posted by klynn on Wednesday, October 3, 2007 at 11:29am. This is an MBA-level Managerial Economics Course. I'm working on some HW and just want to double-check …
  5. managerial economics

    EXPLAIN 5 FUNCTIONS OF MANAGERIAL ECONOMICS WITH SUITABLE EXAMPLE.
  6. managerial economics

    Can someone break down the basic components of managerial economics to me. I have having a really tough time with this class. H-E-L-P.
  7. Managerial Economics

    I need help on some homework questions for an MBA-level Managerial Economics class. The total operating revenues of a public transportation authority are $100M while its total operatiing costs are $120M. The price per ride is $1, and …
  8. Managerial Economics

    Can someone explain what is a cubic cost function?
  9. managerial economoics

    close relationship between mnagement and economics has led to the development of managerial economics
  10. managerial economics

    Final Project A Final Project Is Due The Last Class Session. In Your Final Project, Describe And Answer In Economic Terms A Managerial Decision You Have Knowledge About (For Example One That Has To Be Made At Your Place Of Employment). …

More Similar Questions