Question

a) What is his marginal rate of substitution between X =3 and Y=4? If A=1, a = 0.4 and b = 0.5.

Answer 1

Using given values, utility function is

U = AXaBy

U = X0.4Y0.5

$\text{MU}_{x}=\dfrac{\delta U}{\delta X}=\dfrac{0.4 \times 0.5Y}{0.6X}$

$\text{MU}_{y}=\dfrac{\delta U}{\delta X}=\dfrac{0.5 \times 0.4X}{0.5Y}$

$\text{Marginal rate of substitution} = \dfrac{- MUx }{ MUy}$

$=\dfrac{\dfrac{(0.4 x Y0.5) }{ X0.6}}{\dfrac{(0.5 x X0.4)}{ Y0.5}}$

$\dfrac{- (0.4)}{0.5} \times\dfrac{Y}{X}$

$\dfrac{ -4}{5} \times \dfrac{4}{3}$

$\dfrac{-16}{15}$

$\text{Marginal rate of substitution}= - 1.0667$