This question is on consumption and the real interest rate.

Consider the consumer who lives for two periods and the diagram illustrating the budget line (budget constraint). What happens to the budget line if the real interest rate is decreased?

Select one or more:

a. The budget line pivots clockwise around the point corresponding to the incomes in the two periods

b. The budget line shifts down

c. The budget line pivots counter-clockwise around the point corresponding to the incomes in the two periods

d. The budget line shifts up

 

A decrease in real interest rate will pivot the budget line counter-clockwise around the point corresponding to the income in the two periods and will experience a parallel shift downwards.  

Step-by-step explanation

A decrease in real interest rate will have income and substitution effects in an intertemporal choice model.  

Initially, the budget line is given by line AB and the interest rate is r. We take first period consumption on x-axis and second period consumption on y-axis. The income is given by I.  

A decrease in real interest rate will pivot the budget line around point I anticlockwise as the interest rate has decreased from r to r'. This will make the budget line flatter and the budget line will have a slope of -(1+r'). The new budget line due to substitution effect will be CD. This will occur because future consumption has become cheaper than before. This is known as substitution effect. This will imply that the consumer will consume more in period 1 and less in period 2.  

The next effect will be the income effect. The budget line will shift parallel downwards from CD to EF. This will occur because there is a decrease in lifetime resources as a result of decrease in income. This is known as income effect. With a decrease in real interest rate, the real income of the consumer decreases which causes this parallel downward shift. This will cause the consumption to fall in both the periods. Now, the final consumption in the first period will depend on the magnitude of income effect and substitution effect as both the effect cause opposite movements. For the second period, consumption will definitely fall. Assuming that the income effect and the substitution effect are equal to each other, the final consumption in period 1 will be C1' and the final consumption in the second period will be C2''.  

Thus, a decrease in real interest rate will pivot the budget line counter-clockwise around the point corresponding to the income in the two periods and will experience a parallel shift downwards.  

Please see the attached file for the complete solution