Question

The homeworkassignment is based on one of the ustrative test questions. Itshows how relative price changes combine with consumers'tastes to increase or decrease utility. For Parts A D, shows a oneline derivation of the answer. For Parts E and F, explain in one paragraph why Rachel is better off or worse off and explain in one paragraph why Jacob s better off or worse off CHANGES IN RELATIVE PRICES Recenty, the price of bread has risen from $4 to $6 per loaf and the price of wine has fallen from $8 to $6 perfask. Rachel's and Jacob's food budgets have stayed fixed at $48 perweek for each. The table below shows the weekdy purchases of bread by Rachel and Jacob before and after the price changes, the remaining income is spent on wine. Bvoad Purchased Batoro Priko Chang 4 loa ves 8 loa ves Anar Pnco Chango 2 loaves 5 loaves Before the price change, Rachel bought 4 loaves of bread and spent the rest of her food budgeton wine; afterthe price change, Rachel buys 2 loaves of bread and spends the rest of her food budget on wine. Before the price change, Jacob bought 8 loaves of bread and spent the restof his food budget on wine;after the price change, Jacob buys 5 loaves of bread and spends the rest of his food budget on wine. A. Howmuch wine did Rachel buy before the price change? (How much money is left in Rachels budget after buying bread, and how many fasks of wine does this buy?) B. How much wine does Rachel buy after the price change? C. How much wine did Jacob buy before the price change? D. How much wine does Jacob buy after the price change? E. Could Rachel buy the same basket of wine and bread after the price change that she bought before the price change? Since she decdes to buy something else, is she better off or worse off after the price change? F. Could Jacob have boughtthe same basket of wine and bread before the price change that he buys afterthe price change?1s hebetter off or worse off after the price change? To answer the homework questions, use the following relations: 1. The price of bread increased; both Jacob and Rachel buy less bread. 2. The price of wine has decreased; both Jacob and Rachel buy more wine. 3. Rachel likes wine; both before and after the price change, she spends more on wine than on bread 4. Jacob likes bread; both before and after the prioe change, he spends more on bread than on wine.

Answer 1

Bread Purchased

	Before	After
Rachel	4 loaves	2 loaves
Jacob	8 loaves	5 loaves

Price of Bread increased from $ 4 to $ 6.

Price of wine decreased from $ 8 to $ 6.

Budget of Rachel and Jacob $48

	Price*Bread	price*wine	Budget
Rachel	$4*4	$8*x	$ 48
Jacob	$4*8	$8*y	$48

A. Rachel

Number of wine bottles purchased, x = (48-16)/8 = 4

Jacob, no. Of wine bottles purchased,y = (48-32)/8 = 2

Before price change

	Bread ($ 4)	Wine ($ 8)
Rachel	4	4
Jacob	8	2

B. After the price change

Rachel budget line

$6*2 + $6*X = $ 48

After the price change, wine bottles purchased

= (48-12)/6 = 6 bottles

Jacob budget line

$6*5 + $6*Y = $ 48

Bottles purchased = (48-30)/6 = 3 bottles

After the price change

	Bread($6)	Wine($6)
Rachel	2 loaves	6 bottles
Jacob	5 loaves	3 bottles

E. Before the price change Rachel purchased 4 loaves of bread and 4 bottles of wine. Now after the price change the same basket will cost

$6*4 + $6*4 = $ 48

She can continue to consume the same basket even after the price change.

But in this case Rachel will be worse off since she likes Wine. As we can see before and after price change she consumes more wine. So by consuming equal quantity of bread and wine she will not be able to maximize her utility.

F. Before Jacob used to consume 8 loaves of bread and 2 bottles of wine. After the price change the same basket would cost

$6*8 + $6*2 = $ 60

No Jacob cannot continue to consume the same basket as his budget is limited to $48.

As he continues to like bread so he consumes more of bread before and after the price change.