p.p1 of a), moving from point A

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When the interest rate increases, saving is more attractive as it is relatively more rewarding to save out of current income to fund consumption tomorrow. Thus, the saver will tend to substitute away (substitution effect – the effect on consumption when there’s a change of interest rates, assuming the same level of income) from current consumption as seen in figure 2.2. The saver will consume less (b instead of a), moving from point A to point B. However, assuming that future and current consumption are both normal goods, higher interest rates will increase relative income (Income effect – the effect on consumption when there’s a change in real disposable income) as seen in figure 2.3. The saver’s income payments and net savings are now worth more. The saver is better off. Thus, for a net-saver, this increase in relative income will induce him to increase his current consumption, moving from point B to C and consuming more (c instead of b). Therefore, overall (substitution + income effect), the saver reduces his current consumption slightly from A to C, nullifying the statement. 

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This is because in this case, the substitution effect is greater than the income effect. The individual is highly responsive to an increase in the price of current consumption which leads to a decrease in a current consumption and an increase in savings. Had the saver reacted more strongly to the increase in purchasing power, the overall effect to his current consumption would be positive. Instead, his current consumption would increase whilst his savings would decrease. Thus, the statement is false, an increase in the interest rate does not always lead a saver to reduce current consumption. Every saver is different and has different tendencies. Some will increase their current spending, reacting strongly to the increase in their purchasing power, whilst others won’t. Likewise, other factors such as the perceptions of the economy in the future can play a role in the effect that an increase in interest rates will have on savers. For example, if savers believe that in the future, the prices of goods will fall, savers won’t react as strongly at having a higher purchasing power due to the higher interest rates, instead, they will cut current consumption and increase their savings in order to consume in the future (consuming becomes cheaper in the future).