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”


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”



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, 


Where M=100, Px=1 and py=1

It is possible to use the technique of lagrangean, 


Solving this will give out the conditions of the first order




Solving these will give out, 


Using the method of substitution, we get


“Because X=Y”




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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