You are
not
expected to absorb this sequence of equations immediately. They are here
for two main reasons: for future reference, and to illustrate yet another way in which
keeping track of the units can assist in understanding theoretical relations.
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View Full Document2. Exercises
1. The demand curve in each period for Novoplacebo, the new miracle drug which
doesn’t really
do
anything but is very attractively packaged, is given by the equation
P
= 60 –
Q
D
, where
P
is in $/kg and
Q
D
is in kg.
(a) Calculate Total Revenue, in $, when
P
= $36/kg.
(b) Rewrite the equation for this demand curve when: (i)
P
is measured in cents/kg
and
Q
is in kg; (ii)
P
is in cents/kg and
Q
is in grams; (iii)
P
is in cents/gram and
Q
is in grams; (iv)
P
is in cents/gram and
Q
is in kg; (v)
P
is in $/pound and
Q
is in pounds (using the conversion factor 1 kg = 2.2 lbs.).
(c) Calculate Total Revenue, in both $ and in cents, for
each
demand curve in (b) at
the
same
position as in (a).
2. (a) The weekly supply curve for Doggy Yums Kanine Kibble is given by the equa
tion
P
= 4 + 0.26
Q
S
, where
P
is in $/kg and
Q
S
is in kg/week. Assuming that
there are 52 weeks in a year, give the supply equation when
P
is in $/kg and
Q
S
is in kg/year.
(b) The daily demand curve for Doggy Yums is given by the equation
P
= 40 – 4
Q
D
,
where
P
is in $/kg and
Q
D
is in kg/day. (i) Give the demand curve for February,
2003, with
P
in $/kg. (ii) Give the demand curve for the year 2003, with
P
in
$/kg.
3. You are given the model in Example 8, except that now the units for the de±ned
period are as follows:
X
is measured in tonnes,
L
in labourhours,
P
X
in $/tonne, and
P
L
in $/labourhour.
(a) Give the correct units for the following: MFC
L
; Total Revenue; MC; MP
L
; MRP
L
;
and MR.
(b) Identify which of the following equations are
incorrect
(de±nitionally or as prof
itmaximization conditions) for a ±rm that is a perfect competitor in the
input
market: (i) MRP
L
/MR = MP
L
; (ii)
P
L
/MP
L
= MRP
L
; (iii) MP
L
= MFC
L
/MC;
(iv)
P
L
/MP
L
= MC; (v) MP
L
= MFC
L
/
P
L
; (vi) MRP
L
/MFC
L
= 1; (vii)
P
X
≥
MRP
L
/MP
L
.
4. In this period, the price of output
P
X
is a constant $2.50/kg, the wage rate (
P
L
) is a
constant $40/labourday, and the equation for the MP
L
curve is MP
L
= 40 –
L
, with
MP
L
in kg/labourday and
L
in labourdays.
(a) What is the pro±tmaximizing number of labourdays to hire this period?
(b) If
P
X
and
P
L
both double, how many labourdays should be hired?
(c) If
P
X
doubles with
P
L
constant, what is the pro±tmaximizing level of
L
?
(d) If
P
L
doubles with
P
X
constant, how many labourdays should be hired?
M48
MATH MODULE 4: USING ECONOMIC UNITS
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 Fall '12
 Danvo
 Supply And Demand, Orders of magnitude, Qd, Kilometre, economic units

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