Answer to Question #211298 in Microeconomics for hawalul

Question

(ii) Given the following Cobb Douglas Utility function u(x₁, x₂) = x₁^cx₂^d.What is Marginal Rate of Substitution MRS x₁, x₂ ?

Answer 1

Need to find-

Marginal Rate of Substitution $MRS x_1, x_2$

Given in the question-

$u(x_1, x_2) = x_1^{c}x_2^{d}$

$MRS =\frac{ MU_x1}{ MU_x2}................(1)\\ MU_x1 =\frac{\delta u(x_1, x_2)}{\delta x_1}\\ MU_x1 = \frac{\delta(x_1^{c}x_2^{d})}{\delta x_1}\\ MU_x1 = c\times(x1^{c-1})\times(x2^d )$

similarly,

$MU_x2 = \delta(x1^c)\times(x2^{d-1})$

So, from eqn."1"

$MRS = (c\times(x1^{c-1})\times(x2^{d} ))\div(\delta(x1^c)\times(x2^{d-1}))$

After simplifying 

$MRS = c(x2)\div d(x1)$