Question

In question b，it is bill spends $6 on x and $10 on y. I find a lot answer that is the bill spends $10 on x. So please help to solve this one.

3 Income Changes (6 points) Assume that there are only 2 goods, a and y. (a) Amanda spends $200 on x and $300 on y when her income is 8500. She spends S180 on and $420 on y when her income is $600. For this income change, characterize the type of each good (necessity, luxury, or infeo) 2) (b) Bill spends S6 on and 810 on y when his income is 816. He spends 88 on r and S16 on y when his income is $24. For this income change, characterize the type of each good (necessity, luxury, or inferior). (2) (c) Charles spends 83200 on r and $800 on y when his income is S4000. He spends $2800 on z and $600 on y when his income is $3400. For this income change, characterize the type of each good (necessity, luxury, or inferior). (2)

Answer 1

(a) As income increases from $500 to $600, amount spent on x decreases from $200 to $180, so it is an inferior good. As demand for inferior good decreases due to increase in income.
Amount spent on good y increases from $300 to $420 with increase in income, so it is a normal good.
Now, percentage change in amount spent on y = [(New amount-old amount)/old amount]*100 = [(420-300)/300]*100 = 40%
Percentage change in income = [(New income-old income)/old income]*100 = [(600-500)/500]*100 = 20%
So, Percentage change in amount spent on y is greater than percentage change in income. Thus, y is a luxury good and x is an inferior good.

(b) As income increases from $16 to $24, amount spent on both x and y increases. So, they are both normal goods.
Now, percentage change in amount spent on x = [(New amount-old amount)/old amount]*100 = [(8-6)/6]*100 = 33.33%
Percentage change in income = [(New income-old income)/old income]*100 = [(24-16)/16]*100 = 50%
So, Percentage change in amount spent on x is lesser than percentage change in income. Thus, x is a necessity.

Now, percentage change in amount spent on y = [(New amount-old amount)/old amount]*100 = [(16-10)/10]*100 = 60%
So, Percentage change in amount spent on y is greater than percentage change in income. Thus, y is a luxury good.

(c) As income increases from $3400 to $4000, amount spent on both x and y increases. So, they are both normal goods.
Now, percentage change in amount spent on x = [(New amount-old amount)/old amount]*100 = [(3200-2800)/2800]*100 = 14.29%
Percentage change in income = [(New income-old income)/old income]*100 = [(4000-3400)/3400]*100 = 16.65%
So, Percentage change in amount spent on x is lesser than percentage change in income. Thus, x is a necessity.

Now, percentage change in amount spent on y = [(New amount-old amount)/old amount]*100 = [(800-600)/600]*100 = 33.33%
So, Percentage change in amount spent on y is greater than percentage change in income. Thus, y is a luxury good.