NAME 273
(a) If Flo uses no fertilizer, how many hours of talk must she devote if she
wants one happy plant? 1 hour. If she doesn’t talk to her plants
at all, how many bags of fertilizer will she need for one happy plant?
(b) If wt<w
f/2, would it be cheaper for Flo to use fertilizer or talk to
2,w
(d) Her conditional factor demand for talk is t(wf,w
t,h)= hif
wt<w
f/2and 0if wt>w
f/2.
21.8 (0) Remember T-bone Pickens, the corporate raider? Now he’s con-
cerned about his chicken farms, Pickens’s Chickens. He feeds his chickens
on a mixture of soybeans and corn, depending on the prices of each. Ac-
cording to the data submitted by his managers, when the price of soybeans
was $10 a bushel and the price of corn was $10 a bushel, they used 50
bushels of corn and 150 bushels of soybeans for each coop of chickens.
When the price of soybeans was $20 a bushel and the price of corn was
$10 a bushel, they used 300 bushels of corn and no soybeans per coop
of chickens. When the price of corn was $20 a bushel and the price of
soybeans was $10 a bushel, they used 250 bushels of soybeans and no corn
foreachcoopofchickens.
(a) Graph these three input combinations and isocost lines in the following
diagram.
0 100 200 300 400
100
200
300
400
Corn
Soybeans
125
274 COST MINIMIZATION (Ch. 21)
(b) How much money did Pickens’ managers spend per coop of chickens
(c) Is there any evidence that Pickens’s managers were not minimizing
costs? Why or why not?
(d) Pickens wonders whether there are any prices of corn and soybeans at
which his managers will use 150 bushels of corn and 50 bushels of soybeans
to produce a coop of chickens. How much would this production method
cost per coop of chickens if the prices were ps=10andpc= 10?
(e) If Pickens’s managers were always minimizing costs, can it be pos-
sible to produce a coop of chickens using 150 bushels and 50 bushels of
21.9 (0) A genealogical firm called Roots produces its output using only
one input. Its production function is f(x)=√x.
(a) Does the firm have increasing, constant, or decreasing returns to scale?
(b) How many units of input does it take to produce 10 units of output?
NAME 275
(c) How many units of input does it take to produce yunits of output?
y2.If the input costs wper unit, what does it cost to produce yunits
(d) If the input costs wper unit, what is the average cost of producing y
21.10 (0) A university cafeteria produces square meals, using only one
input and a rather remarkable production process. We are not allowed to
say what that ingredient is, but an authoritative kitchen source says that
“fungus is involved.” The cafeteria’s production function is f(x)=x2,
where xis the amount of input and f(x) is the number of square meals
produced.
(a) Does the cafeteria have increasing, constant, or decreasing returns to
(b) How many units of input does it take to produce 144 square meals?
(c) How many units of input does it take to produce ysquare meals?
√y.If the input costs wper unit, what does it cost to produce y
(d) If the input costs wper unit, what is the average cost of producing y
21.11 (0) Irma’s Handicrafts produces plastic deer for lawn ornaments.
“It’s hard work,” says Irma, “but anything to make a buck.” Her produc-
tion function is given by f(x1,x
2)=(min{x1,2x2})1/2,wherex1is the
amount of plastic used, x2is the amount of labor used, and f(x1,x
2)is
the number of deer produced.
(a) In the graph below, draw a production isoquant representing input
combinations that will produce 4 deer. Draw another production isoquant
representing input combinations that will produce 5 deer.
276 COST MINIMIZATION (Ch. 21)
0102030
40
10
20
30
40
x2
x1
x2=1
_
2x
1
Output
of 5
deer
Output
of 4
deer
(b) Does this production function exhibit increasing, decreasing, or con-
(c) If Irma faces factor prices (1,1), what is the cheapest way for her to
(d) At the factor prices (1,1), what is the cheapest way to produce 5 deer?
(e) At the factor prices (1,1), the cost of producing ydeer with this
(f) At the factor prices (w1,w
2), the cost of producing ydeer with this
21.12 (0) Al Deardwarf also makes plastic deer for lawn ornaments.
Al has found a way to automate the production process completely. He
doesn’t use any labor–only wood and plastic. Al says he likes the business
“because I need the doe.” Al’s production function is given by f(x1,x
2)=
(2x1+x2)1/2,wherex1is the amount of plastic used, x2is the amount
of wood used, and f(x1,x
2) is the number of deer produced.
NAME 277
(a) In the graph below, draw a production isoquant representing input
combinations that will produce 4 deer. Draw another production isoquant
representing input combinations that will produce 6 deer.
0102030
40
10
20
30
40
x2
x1
Output
of 4
deer
Output
of 6
deer
36
16
818
(b) Does this production function exhibit increasing, decreasing, or con-
(c) If Al faces factor prices (1,1), what is the cheapest way for him to
(d) At the factor prices (1,1), what is the cheapest way to produce 6
(e) At the factor prices (1,1), the cost of producing ydeer with this
(f) At the factor prices (3,1), the cost of producing ydeer with this
21.13 (0) Suppose that Al Deardwarf from the last problem cannot vary
the amount of wood that he uses in the short run and is stuck with using
20 units of wood. Suppose that he can change the amount of plastic that
he uses, even in the short run.
278 COST MINIMIZATION (Ch. 21)
(b) If the cost of plastic is $1 per unit and the cost of wood is $1 per unit,
(c) Write down Al’s short-run cost function at these factor prices.