Tuesday

March 31, 2015

March 31, 2015

Posted by **klynn** on Friday, October 5, 2007 at 11:18am.

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 -
**economyst**, Friday, October 5, 2007 at 1:12pmyour 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 -
**klynn**, Tuesday, October 9, 2007 at 2:37pmOk, I think I get it. Thank you so much!

**Answer this Question**

**Related Questions**

managerial economics - Can someone break down the basic components of managerial...

Managerial Economics/Math - I need help on some homework questions for an MBA-...

Managerial Economics/Math - This is an MBA-level Managerial Economics Course. I'...

Managerial Economics - Managerial Economics uses_____to help solve problems. a. ...

managerial economoics - close relationship between mnagement and economics has ...

Managerial Economics - I need help on some homework questions for an MBA-level ...

Managerial Economics/Math - I wanted to post this as a new question to make sure...

Managerial Economics - Can someone explain what is a cubic cost function? I'm ...

managerial economics - EXPLAIN 5 FUNCTIONS OF MANAGERIAL ECONOMICS WITH SUITABLE...

managerial economics - Final Project A Final Project Is Due The Last Class ...