Answer to Question #212329 in Microeconomics for hawalul

Question #212329

(ii)              Given the following Cobb Douglas Utility function u(x1, x2) = x1cx2d.What is Marginal Rate of Substitution MRS x1, x2 ?



1
Expert's answer
2021-07-01T05:05:19-0400

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)\\\\\n\nMU_x1 =\\frac{\\delta u(x_1, x_2)}{\\delta x_1}\\\\\n\nMU_x1 = \\frac{\\delta(x_1^{c}x_2^{d})}{\\delta x_1}\\\\\n\nMU_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)"


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