Consider the utility function u(x1, x2) = 4(x1)^0.5 + x2 (a) What type of utilit
ID: 1215291 • Letter: C
Question
Consider the utility function u(x1, x2) = 4(x1)^0.5 + x2
(a) What type of utility function is this? If x1 was fixed (thus you can think of it as a constant), what type of function is this utility function in terms of x2?
(b) Derive the marginal utility for good 1, MU1. (as always remember to show your work!)
(c) Derive the marginal utility for good 2, MU2.
(d) Derive the marginal rate of substitution MRS (write out any formulas you use).
(e) Evaluate the MRS at the following bundles: (9, 10) and (9, 20) (ie give a numerical answer).
Explanation / Answer
Quasilinear function its a convex function (linear in one term and deacreasing in other) and if x1 is constant then its linear function.
u(x1, x2) = 4(x1)^0.5 + x2
dU(X1, X2)/dX1 = 2(X1)^(-0.5)
dU/dX2 = 1
MRSxy = dux/duy = 2(X1)^(-0.5)