Cobb Douglas Function – Demand Theory

In the past installments from DiscussEconomics on demand theory, now we’re venturing into the graphical and mathematical expressions of the Cobb Douglas demand function.
cobb douglas

Graphically expressed (utility maximizing) with the assumption well-behaved preferences.
cobb douglas graph
The interior solution characterized by two statements (the equals sign is really supposed to be three lines thus ‘is equal to):

1. p1x1* + p2x2* = m
2. MRS (x1*, x2*) = p1/p2 (Left side is the slope of the indifference curve; right side is the slope of the budget line)

When combined describe consumer equilibrium conditions. When the indifference curves are smooth, and when quantities demanded are positive, the utility maximizing bundle is on the budget line at the point where relative price is equal to MRS (marginal rate of substitution).

To solve for X1 and X2, simultaneously solve equation 1 and 2 for (x1*, x2*).

cobb douglas
cobb douglas

Here is an extended example for your review.

cobb douglas eqn
cobb douglas example

[tags]Cobb Douglas, Demand Theory[/tags]