The decrease in the price of air-conditioning (AC) leads to a negative income effect which overpowers the positive substitution effect, leading to a negative overall price effect, in turn leading to a paradoxical decrease in the demand for air-conditioning.
Let the travel package be the Good A(the quantity demanded of which is QA, taken along the y-axis) and Air-conditioning (AC) be the Good B(the quantity demanded of which is QB, taken along the x-axis) The current income of the consumer puts him on the budget line BL1 and EA is the optimum, where the consumer consumes QA’ and QB’ quantities of the vacation and AC respectively.
Now consider a fall in the price of AC. It leaves the consumer with more income to spend, which can be taken as an increase in the real income or the purchasing power of the consumer. Thus, the consumer now moves to the budget-line BL2 (the price of the travel package remaining the same)
With the fall in the price of Air-conditioning, the consumer is left with more income (shown by BL2). But paradoxically, the quantity demanded of AC decreases in spite of the price fall. The consumer chooses to use the extra income to invest more into his annual vacation fund to a cold place (perhaps to Australia in the Southern hemisphere, experiencing winter!) The net negative price effect is illustrated as a combination of a negative income effect and a positive substitution effect, which leads to air-conditioning being inferior to the travel package and arising to be a Giffen good.
With fall in the price of AC, the consumer’s real income/purchasing power increases. However, the consumer chooses to spend the extra money on his vacation by pooling into his vacation fund, rather than on more AC i). Just because AC is cheaper, it cannot be limitlessly used beyond the optimal, comfortable (indoor liveable) temperatures; this leads to ii). AC being shut-down for the duration of the vacation = less usage = cheaper bills.
The Income and Substitution effects giving rise to AC being a Giffen good can be explained as follows.
A). The Income Effect: The increase in the real income of the consumer has a negative effect on the quantity of AC demanded as the consumer chooses to spend more on his vacation in a cold place. As a result, the demand for AC=QB falls from QB’ to QB” and consequently, the quantity demanded of the vacation (which might be the number of days on vacation, leave from work, vacation budget, etc.) increases. Thus, the income effect is negative and AC can be considered as being inferior to