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Answer to Question #48183 in Microeconomics for mike

Question #48183
Consumer has $120 a week to spend on x and y. Price Scenario 1: x = $1, y = $2

Assume that the consumer was originally faced with price scenario 1. Now suppose that the price of x
rises to $4 and the consumer chooses 15 units of x. How many units of y would be chosen? What is
the new relative price of x? Illustrate this new choice with an indifference curve. Can you tell from
previous results how the consumer thinks of the two goods in terms of normal/inferior? [Hint: Think
about and explain the substitution and income effects.] [6]

(d) Following from part (c), suppose that income now increases to 360. Given what you know about the
consumer’s preferences, can you predict a possible equilibrium on the new budget line?
Expert's answer
c) Consumer has $120 a week to spend on x and y. Price Scenario 1: x = $1, y = $2
If the price of x rises to $4 and the consumer chooses 15 units of x, he will spend $4*15 = $60 on x and $120 - $60 = $60 on y, so he will buy $60/$2 = 30 units of y. 
The new relative price of x will be Px/Py = $4/$2 = $2. 
From the previous results we can suppose, that consumer thinks of the two goods as about normal goods, because due to the substitution effect he buys less of good x, as its price increased and buys more of good y, as it is now comparatively cheaper and because according to income effect as the income is the same, now he should consume less.
(d) If the income now increases to 360, given what we know about the consumer’s preferences, the consumer will buy the same proportion of goods, but 3 times more, so we can predict a new possible equilibrium of 45 units of x and 90 units of y.

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