# 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.

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