Question

The consumer has a budget of $M for the consumption of good X and Y .The price of good X is $Px and the price of good Y is $py.The consumer has a utility function given by U(X,Y)=xy.

Find the optimal consumption of the individual and the utility Obtained.

Make a graph that illustrates the solution to the problem.

Why do you use paramerters.

Answer 1

The optimal consumption of the individual occurs when:

$MUx/MUy = Px/Py$ and $Px×x + Py×y = M.$

$MUx = U'(X) = y,$

$MUy = U'(y) = x,$

y/x = Px/Py,

y = Px×x/Py or Px×x = Py×y,

2Px×x = 2Py×y = M,

y = 0.5M/Py,

x = 0.5M/Px.