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Utility Maximizing Consumption Bundle: Cobb-Douglas

$u(x, y) = xstar,ystar = (a*y)/((a+b)*px) , (b*y)/((a+b)*py)$

$(a)"utility exponent for good x"$

$(b)"utility exponent for good y"$

$(px)"Price of Good x"$

$(py)"Price of Good y"$

$(y)"Consumer Income Level"$

Tags

The Cobb-Douglas Utility Maximizing Consumption Bundle calculator computes the x and y value for the maximized consumption based on the utility exponents for two goods, the price of the two goods and the consumer income level.

INSTRUCTIONS: Choose units and enter the following:

(a) Utility exponent for good x
(b) Utility exponent for good y
(px) Price of good x
(py) Price of good y
(y) Consumer Income Level

Utility Maximizing Consumption Bundle ( x*, y*): The calculator returns the maximized bundle.

The Math / Science

The formula for the Cobb-Douglas Utility Maximizing Consumption Bundle is:

x* $= (a*y)/((a+b)*px)$

y* $= (b*y)/((a+b)*py)$

where:

x*,y* = Utility Maximizing Consumption Bundle
a = Utility exponent for good X
b = Utility exponent for good Y
px = Price of good X
py = Price of good Y
y = Consumer Income Level

$x^alphay^beta::: P_x\x + P_y\y = Y$

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