Consider a utility function u(x1, x2) = ax1+bx2 and a budget line p1x1+p2x2=m If the absolute...

Consider a utility function u(x1, x2) = ax1+bx2 and a budget line p1x1+p2x2=m
If the absolute value of the slope of the indifference curve, a/b, is greater than the absolute value of the slope of the budget line, p1/p2 find the optimal consumption bundle

Solutions

Expert Solution

From the above utility function u(x1, x2) = ax1 + bx2 we can see it represents an equation of a straight line and it is the perfect substitutes case.

Now, We know under perfect substitute case the individual can consume only either of the two goods completely if the slope of budget line and utility function differs or it can consume any combination on the budget line if the slope is equal.

So, The optimal conditions can be mathematically represented as :-

So, We can check these conditions for the given function in question :-

As, Per the given information :

So,

So, We will consume only good 1

So,

So, Optimal Bundle is :-

Rahul Sunny answered 2 years ago

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