Question

Helen derives utility from consuming housing and other goods, and her preferences are described by a Cobb-Douglas utility function. She just found out that she is being transferred from New York City to Cary, and that her salary will be cut from $7,200 to $4,800 per month. When Helen tells her best friend, who is an economist, that she is devastated by such a large pay cut, her friend says she shouldn’t be! She explains that the price of housing relative to other goods is only $4 per unit in Cary compared to $9 per unit in New York City. Moreover, she knows Helen’s utility function (best friends) and calculates that Helen will have the same exact utility in Cary as she enjoyed in New York City. Assuming this is true, will Helen choose more, less or the same amount of housing in Cary as she did in New York City? Graphically illustrate your answer and analyze why using the tools of income and substitution effects.

Answer 1

in cary, helen will consume more of housing. If we believe that housing becomes relatively cheaper in Cary, the budget line will become flatter as slope decreases from 9 to 5. At the same time the income is decreasing from 7200 to 4800, and hence the budget line will shift backwards. The new budget constraint is A'B'. Hence because of fall in prices there will be a substitution effect and helen will consume more housing than other goods as housing becomes cheaper. There will also be an income effect which will reduce the consumption of both housing and other goods but because it is believed that helen has the same level of utility, it can be seen in the figure that the substitution effect will overpower income effect and helen will consume more housing in Cary than in New York