Assignment:
1. ??(??, ??) = ?? ????????
a) Write down the utility maximization problem.
b) Find the MRS if ?? is 24, ?? is 16, ?? is 3, ?? is 2 and ?? is 1. How would you interpret this value?
c) Does the utility function represent convex preference? (Assume ?? and ?? are positive)
d) Find out the optimal demand of good ?? and ?? in terms of prices, ??, ?? and ??.
e) Show how the changes of prices and income affect the demand for good ?? and ??. (Assume ?? and ?? are positive)
f) Write down the lagrangian for the utility optimization problem.
g) Write down the first order conditions (F.O.C.s).
h) Solve the system of equations in part i) to find the optimal ??, ?? and ??.
i) Find the value of ?? when ?? = 200, ?? = 2, ?? = 3, ?? = 1 and ???? = 8, ???? = 12. How would you interpret the value of ???
j) Write down the indirect utility function in terms of ????, ???? and ??.
k) Now set up the cost minimization problem.
l) Write down the lagrangian for the cost minimization problem.
m) Write down the first order conditions.
n) Find the solution of the cost minimization problem.
o) Write down the expenditure function in terms of prices and utility.