Question

Tom lives two periods and receives both current and future income and is neither a net lender nor a net borrower. Suppose the real interest rate increases, other things constant. Describe the effect on his current period consumption and saving as a result of this increase in the real interest rate.   

Answer 1

Tom lives two periods and receives both current and future income and is neither a net lender nor a net borrower. Suppose the real interest rate increases, other things constant. Let us consider the current consumption of Tom is C0 and the future consumption is Cf

The utility function of Tom is U = f(Co, Cf) and he will try to maximise it. So,

Max U = f(Co, Cf)

Or,      = U(Co) + ΣLU(Ct)(1+ρ)-t

Into the future this utility from consumption is discounted at some rate 'ρ' the rate of time preference for Tom. Higher values for this rate of time preference imply less satisfaction from future consumption relative to current consumption spending.

This consumption pattern is constrained by current and (expected) future levels of income Yo & E[Yf.]. In this model, the expectations of future levels of income are based on individual skills and talents, and ownership of income producing assets Wo. In addition, consumption patterns are constrained by the prevailing real interest rate 'r' which represents a payment (or reward) for foregoing current consumption.

The two- period model is developed as follows:

max U = f(Co, Cf)

subject to [Yp - Co](1+r) + Wo = Cf – Yf

Current Savings '[Yp - Co]' multiplied by an interest rate factor '(1+r)' will allow for future consumption in excess of future income of Tom. Solving for future consumption as a function of current consumption allows us to write the constraint in intercept-slope form as:

Cf = {Yp(1+r) + E[Yf] + Wo } - (1+r)Co

Here, tom is not a lender and or the borrower then the increase in interest rate will increase the income of Tom. So the budget line will sift due to change in interest rate it will indulge to sift the IC curve. If the interest rate increases then both periods consumption will increase.in the figure 1 which has been shown. As the wealth will increase from W0 to W1 and the budget line will also increase from p1p2 to p1p2’ and the IC curve will also sift from IC1 to IC2 and the consumption will also increase from c0 to c0’ and cf to cf’ as depicted by figure 1

Figure: 1