Answer in Microeconomics for Imran jamil #180977
Which optimal values can be calculated from following equation? How many techniques are used to solve these equations? Give answers after solution.Q =XY…….s.t…… M=PxX+PyY
Given the budget that he/she has, the maximum amount of utility that this person can possibly receive is computed using the function of utility.
The mentioned equations are a part of the analysis of the “Utility”. This set of equations will be of help in computing how much utility a person can possibly get, given a budget that is limited.
The given equations are as follows,
“Q =XY”
“M=PxX+PyY”
In this, the first one is the equation of the utility,
Utility function is “Q =XY”
Where Q=Utility
X and Y are commodities that constitute this Utility.
Budget constraint is “M=PxX+PyY”
where,
M=Income
PX=Price of the commodity X
PY=Price of the commodity Y
Normally, in such sums, the values of the Px
, Py and M are already given.
The task here is to make sure that the utility is maximized and also to compute the quantities of these commodities X and Y.
For instance, the values given for the same function are as follows,
“100=1X+1Y”
Where M=100, Px=1 and py=1
It is possible to use the technique of lagrangean,
“L=XYu2212u03bb[100u22122Xu22122Y]”
Solving this will give out the conditions of the first order
“Yu2212u03bb=0”
“Xu2212u03bb=0”
“100-X-Y=0”
Solving these will give out,
“Y=X=u03bb”
Using the method of substitution, we get
“100u2212Xu2212Y=0”
“Because X=Y”
“100u2212Xu2212X=0”
“100=2X”
“X=50”
This “Y=50”
Thus, we have found out the units(quantities of X and Y
X and Y) of both the commodities with which this person will get the maximum amount of utility, given the budget that he/she has.
