# Utility function is given as U(x1, x2) = 10x 0.5 1 + 5x2

Given a utility function $$U= {10x^{0.5}} + 5y$$, calculate the MRS and explain its economic meaning.

The MRS I calculated is $$\frac{1}{\sqrt{x_1}}$$, but I can't really understand it's economic meaning or how to derive its indifference curve. Some help please?

The MRS represents the rate of exchange between goods x and y that would leave the agent indifferent to trading the two. It is the slope of the indifference curve for a given value of utility U.

To derive the indifference map (the set of indifference curves), take U constant in the utility function, and solve for y in terms of x. You can check if your MRS calculation is correct by taking the first derivative of your indifference map function.

1) To draw indifference curves. Assume some value of U on the LHS, assume some values of x and calculate corresponding values of y. for e.g. assume U=10.

assuming
x=0,0.01, 0.04, 0.09, 0.16, 0.25, 0.36, 0.49, 0.64, 0.81, 1 you get
y=2, 1.8, 1.6 ,  1.4,  1.2, 1,    0.8,  0.6,  0.4,  0.2,  0.


Join these (x,y) coordinates to get indifference curve for U=10. Repeat for other values of U. What does this curve mean? It means any (x,y) on this curve gives you the same utility U=10. Therefore you are indifferent between all points (x,y) on this curve.

2) MRS

What you did is right mathematically.

The MRS is the slope of the indifference curve. It is the rate at which you must substitute y for x to remain on the same utility curve. i.e. suppose you are currently consuming a bundle (1,0) . You now want to consume some y, how much x must you substitute out to get to consume 1 unit of y at this point? That's the question the MRS answers.