Chapter 2 Number 7
Solution:
a. Cigarette consumption would fall by between 4.5 and 6.0%.
b. Assuming that the prices of cigarettes were to remain constant, a 50%
increase in income would cause sales of cigarettes to increase 25%. The
weighted average of all income elasticities equals 1, so consumption of
non-cigarette items would increase by more than 50% and certainly more
than the 25% performance of cigarettes. I would not follow the broker’s
advice.
Chapter 2 Number 10
Solution:
Observation: This is a linear demand function.
a. We have the partial derivative of Q with respect to I = 4, meaning that a $1,000 increase in per capita disposable
income results in a 4-unit increase in the quantity demanded of the
product. Therefore, if per capita disposable income is expected to
increase by $5,000, then the firm’s sales will increase by 20 units per
month.
b. Now, offsetting the effect of the increase in per capita disposable income means that
the combined effects of a price increase and a per capita disposable income
increase leave quantity demanded unchanged. Hence,
-3Del(P)+4Del(I) = $6.67. That is, price should be raised by $6.67 per unit.
c. There are two possible interpretations, both leading to more elastic
demand. You could assume that the question is asking if demand is
more elastic after both the income and price have increased. Since
the partial derivative of Q with respect to P is unchanged and P/Q has increased
unchanged and P/Q has increased, the demand will be more elastic. Alternatively,
you might assume that the question is asking, as we increase the
price to choke off the anticipated increase in the quantity demanded after
income has gone up, does the demand become more or less elastic? This
is, of course, just moving up a linear demand curve, which implies an
increasingly elastic demand.
Chapter 3 Number 5:
Solution:
Chapter 3 Number 6
Solution:
If income increases to $600, the equation of the bud get line is given by
5F + 10C = 600. That indicates a parallel shift of the bud get line to the right
given the slope remains the same.
If income is $500 but the price of food increases to $10 per pound, then
the equation of the bud get line is given by 10F + 10C = 500. Slope = -1.
The previous bud get line will rotate inward or counterclockwise.
If the price of clothing increases to $20 per piece, then the equation of
the bud get line is given by 10F + 20C = 500. Equivalently, the equation is
F = 50 - 2C. Slope = -2. The original bud get line rotates clockwise.
Chapter 3 Number 8
Solution:
a.
b.
c.
d.
e.
I=$4000
X=40-Y/2
-0.5
$50
1:2 or 2:1, depending on how you look at the problem