¿De dónde eres tú? ¿Cuantos años tienes y a que te dedicas?
Soy de Los Angeles y tengo 21 años y estudio Economia en la universidad de Tufts.
For each of the following utility functions, find the marginal utilities (MU1 and MU2) and the marginal rate of substitution of good 1 for good 2 ( MRS12) . Also graph a typical indifference curve for the utility functions and determine whether they have a convex (smooth) indifference curve (i.e. whether MRS12 decreases as x1 increases) (a) u(x1,x2)=3x1+x2
Solution: a) u(x1,x2)= 3x1 + x^2 which is perfect substitute preference. MU1= 3, MU2=1. MRS=3 so indifference curve is linear since MRS is constant. The graph would look like this = \ on the x and y axes.
the function u(c) = (c^1 -θ)/(1-θ) where c denotes consumption of some arbitrary good and θ (the Greek letter theta) tis the parameter because its value governs how curved the utility function is and is treated as a constant. For this problem C > 0 because there is not such a thing as negative consumption. a. Plot the utility function for θ = 0. Is the utility function displaying diminishing marginal utility? Is marginal utility ever negative for this utility function?
With θ= 0 the utility function becomes the linear function u(c) = c - 1. Notice that utility may actually be negative but recall that the units of utility (utils) are completely arbitrary, so there is nothing wrong with considering negative values of utility. It does not display diminishing marginal utility because its slope is constant therefore marginal utility never becomes negative either.