In: Economics
In the Mankiw's Principles of Economics Ch.21 Consumer Theory regarding budget constraints and indifference curve.
There are two applications; wages and labor supply & Interest Rates and Saving.
What are the slope of the budget constraint curve and indifference curve in both cases?
Please tell me the meaning and the mathematical form of optimization of both.
In the wages and labor supply
the Budget constraint is the tradeoff between consumption and leisure. The total number of hours a person has is constant so the sum of hours spent working and leisure is constant leading to a downward sloping line. The relative price of an hour of leisure is the amount of consumption foregone that is could have bought with the hour's wages
The indifference curve in this case is the curve with the set of points of combinations of leisure and work where the person is equally satisfied and is thus indifferent between being on any of those points.
In the interest rate and savings
The Budget is the total amount consumed when young and old where the amount left to consume when older is subject to interest rates. The budget constrant shifts according to the interest rate.Higher interest rate changes the slope in favor of consumption when old.
The indifference curve is the curve along which the person is indifferent between the amount consumed in present and when old
Optimization is the process of having maximum satisfaction(best or most north-eastern indifference curve) within the given budget constraints. In the mathematical form,the optimum level is point of intersection of the most indifference curve that touches the budget constraint(making the budget constraint a tangent of the curve)