Anindita P. answered • 02/05/21

Economics Tutor for Introductory, Intermediate, and AP Courses

An utility function that exhibits increasing MRS_{x,y} is **U(x,y) = Ax**^{2}** + By**^{2}**. **

MRS_{x,y} = MU_{x}/MU_{y} where MU_{x} is the marginal utility of good x and MU_{y} is the marginal utility of good y.

For U(x,y) = Ax^{2} + By^{2}, MU_{x} = 2Ax, MU_{y} = 2By.

So,** MRS**_{x,y}** = 2Ax/2By = Ax/By, **which increases as the consumer increases consumption of x and reduces the consumption of y along an indifference curve. Thus, this utility function exhibits increasing marginal rate of substitution. The indifference curves corresponding to this utility function are concave to the origin.