Question

U = 4x11/2 + 2x2. The Marginal Rate of Substitution at (1,2) is?

Answer 1

Marginal Rate of Substitution, MRS = Marginal utility of x1/Marginal utility of x2

Marginal utility of x1 = $\frac{\partial U}{\partial x1} = 4(\frac{1}{2})x_{1}^{\frac{1}{2}-1} = 2x_{1}^{\frac{-1}{2}}$

Marginal utility of x2 = $\frac{\partial U}{\partial x2} = 2$

So, MRS = $\frac{2x_{1}^{-1/2}}{2} = x_{1}^{-1/2} = \frac{1}{x_{1}^{1/2}}$

At (1,2), MRS = $\frac{1}{1^{1/2}} = 1$

The Marginal Rate of Substitution at (1,2) is 1.