Ann lives in Princeton, New Jersey, and commutes by train each day to her job in New York City (20 round trips per month). When the price of a round trip goes up from $10 to $20, she responds by consuming exactly the same number of trips as before, while spending $200 per month less on restaurant meals.

a. Does the fact that her quantity of train travel is completely unresponsive to the price increase imply that Ann is not a rational consumer?
b. Explain why an increase in train travel might affect the amount she spends on restaurant meals.

Answer y Explanation:

a) Ann is a rational consumer but, the train price elasticity is near zero as it is used to go to work. Annn cannot change their consumption in the short-run however if train tickects increase heavily over time Ann will shift their work location to somewhere else and stop consuming train tickets entirely.

b) The train is a cost for her and decreases their disposable income as it has to deduct from their wages the train tickets.  Thus income elasticity comes into play and other goods adjust to decrease Ann consumption. Restaurant is more like a luxury good therefore is quite sensitive to income-elasticity and Ann has experience an income drop thereofre, it consumes less of luxury good.

(a) Ann is a rational consumer because she aims at maximizing her utility. (b) Ann has a less disposable income which made her to spend less on restaurant meal

Explanation:

Ann is a rational consumer, a rational consumer chooses to spend his income on goods that will give such consumer the greatest satisfaction. A rational consumer maximizes utility where

MuX/Px = MuY/ Py

Where

MuX= Marginal utility of good x

MuY = Marginal utility of good y

Px = price of good x

Py = price of good y

Therefore in order for Ann to attain the maximum utility she simply allocate her money income so that the dollar spent on each good or service yield the same marginal utility. A rational spending would occur when the marginal utility earned per dollar is the same.

(b) The increase in the price of the train travel has reduced the disposable income of Ann as a result of these she will spend less on restaurant meal. The consumer is constraint by her income, since the income is fixed and the price of goods and services are known based on these two constraint, the consumer makes his choice to spent less on restaurant meal.

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