If Veronica Vaughn spends all of her daily income on cigarettes
and Yoo-Hoo, she can afford 10 packs of cigarettes and 10 bottles of Yoo-Hoo.
She can also afford 6 packs of cigarettes and 22 bottles of Yoo-Hoo.
(a) What is the relative price of cigarettes in terms of bottles of Yoo-Hoo (what is the ratio of prices)?
(B) Exactly how much income does Veronica earn in one week if the price if
cigarettes are $6? Write a budget equation for Veronica that is a function
of the packs of cigarettes, C, and the number of bottles of Yoo-Hoo, Y.
(c) Draw Veronica’s daily budget set with packs of cigarettes on the x-axis
and bottles of Yoo-Hoo on the y-axis.
(d) Now suppose the price of cigarettes falls by $1 and the price of Yoo-Hoo
rises by $1. If Veronica was consuming 5 packs of cigarettes and 30
bottles of Yoo-Hoo prior to the price changes, how much must her income
rise under the new prices in order for her to just afford the old bundle,
(5,30)? Draw this new budget line.
(a) I = PxX + PyY
Where: I = Income
Px = Price of cigarettes
Py = Price of Yoo Hoo
X = Cigarettes
Y = Yoo Hoo
I = 10Px + 10Py
I= 6Px + 22Py
Relative prices of cigarettes to Yoo Hoo
"10Px+10Py=6Px+22Py"
"10Px-6Px=22Py-10Py"
"4Px=12Py"
"\\frac {Px}{Py}=\\frac {4}{12}"
Ratio = 1:3
(b) (i)Earning in one week if Px=$6
I = 10Px + 10Py
"substitute \\ 6 \\ in \\ I = 10(6) + 10Py"
Income in one day "=60+10Py"
"Income\\ in\\ one\\ week=7(60+10Py)"
=$(420+70Py)
b(ii) budget equation for Veronica that is a function of the packs of cigarettes, C
I = PxX + PyY
Where: I = Income
Px = Price of cigarettes
Py = Price of Yoo Hoo
C = Cigarettes
Y = Yoo Hoo
Answer Px(C) = I - Py(Y)
(c) Daily Budget
(d) I = PxX + PyY
Where: M = Income
Px = Price of cigarettes
Py = Price of Yoo Hoo
X = Cigarettes
Y = Yoo Hoo
I = 10Px + 10Py
I= 6Px + 22Py
I/10 = Px
I/10 = Py
Assume I = 120
Px = "\\frac{120}{10} = 12"
Py = "\\frac{120}{10} = 12"
New price of cigarettes = 12 – 1 = 11
New price of Yoo Hoo = 12 + 1 = 13
New income = (5 "\\times" 11) + (30 "\\times" 13) = 55 + 390 = 445
New Budget line
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