Utility Maximizing Consumption Bundle: Cobb-Douglas

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Jun 9, 2023, 7:35:47 PM

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Jul 6, 2016, 2:51:18 PM

u (x, y) = x ⋆, y ⋆ = \frac{a \cdot y}{(a + b) \cdot p x}, \frac{b \cdot y}{(a + b) \cdot p y}

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

(a) utility exponent for good x

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

(b) utility exponent for good y

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

(p x) Price of Good x

$(px)"Price of Good x"$

(p y) Price of Good y

$(py)"Price of Good y"$

(y) Consumer Income Level

$(y)"Consumer Income Level"$

x* $= \frac{a \cdot y}{(a + b) \cdot p x}$ $= (a*y)/((a+b)*px)$

y* $= \frac{b \cdot y}{(a + b) \cdot p y}$ $= (b*y)/((a+b)*py)$

where:

$x^{α} y^{β} : : : P_{x} x + P_{y} y = Y$ $x^alphay^beta::: P_x\x + P_y\y = Y$

This equation, Utility Maximizing Consumption Bundle: Cobb-Douglas, is used in 2 pages

• Production Function, Cost Optimization by AustinS

• Utility Maximization & Analysis by AustinS

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