The Cobb-Douglas utility function

1. The utility function formula: U = a^.X^Bx ^.Y^By, where X and Y are variables, and a, Bx and By are positive parameters (often Bx+By=1).

Bx^.a^.X^Bx.Y^By MUx=Bx^.a^.X^Bx-1.Y^By= -------------- => X MUx = Bx^.U/X		By^.a^.X^Bx.Y^By MUy=By^.a^.X^Bx.Y^By-1= --------------- => Y MUy = By^.U/X
	Bx^.U/X So MRS = ---------- => By^.U/Y Bx Y MRS = ---- ^. --- By X

3. How MRS behaves for a Cobb-Douglas utility function:

    Consider moving down a single indifference curve. Decide whether each of the following rises, falls or remains the same:
        Bx/By: ____________
        Y/X: ____________
        MRS: ____________

4. Example:

U = X^0.6.Y^0.4

MRS formula: ____________

Value for MRS if X=30 and Y=90: ____________

In the diagram to the right, illustrate the indifference curve passing through the point X=30, Y=90, and label the MRS value and where it shows shows up in the diagram.