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Problem Set #4 Production
300
70
350
9
360
60
1. Optimal Use of a Single Input. Julian Smyth is manages production at Taft)'
300
Apple Inc., a company that produces a variety of tafty/fiuit candies. Over the
last several10
months, he has varied then number of employees on his caran1el
410 line, and found the following relationship.
apple production
50
MRP
Labor
TP 250 MP
1
1
450
40
200
12
480
30
150
a. In the column labeled MP, calculate the mar·ginal product oflabor. (Note,
make your first entry in row 6, as the change between 5 and 6 units oflabor)
b. Suppose the apples sell tor $5 (per dozen) box. Calculate the Marginal
Revenue Product ( 1\fRP)
c. Iflabor costs $225 per day, how many laborers should the firm hire''
Number
-------------------------------------
2. Optimal Use of a Single Input. A graphical representation.
a. In the coordinate axes provided below, illustrate the general relationship
between MRP and the Price of Labor. IdentifY the equilibrium quantity of
labor to hire. (Not<:, your graph nc:ed not use the: numbc:rs in problem 3.
Just be certain to include ranges that illustrate gains from specialization
and the law of diminishing returns in your graph.
$
Q
b. Suppose that the candy workers union agrees to way concessions, that
make the price oflabor fall. In the coordinate axes below illustrate the
etlect on the equilibrium quantity of labor
$
Q
c. Finally. suppose that the price of caramel apples increases. Illustrate the
eflt:ct of this ch mge on the equilibriwn quantity oflabor c:mployed.
$
Q
3. Optimal use of multiple inputs. In his shop, Julian Valenti retrofits sunroof. into
automobiles. 1l1e process can use a combination of skilled labor and unskilled
labor. Given his current mix of employees, the marginal product of the last unit
of skilled labor is 3 sumoofs per day, and tht: marginal product of the
last unit of unskilled labor is 1 sunroof per day. CmTent market rates for skilled
and unskilled labor are $40 and $10, respectively. Is Julian using a least cost
combination of inputs? If not, which of type oflabor should he use relatively
more''
Comparison Expression:
_
Result:
_
4. Retmns to Scale. Jake's Free Runoff Bottled Water Company Produces with the
Long Run Production Function
Q = (KL)2il
a. Currentlv K = 4 and L = 4. IfJake's doubles inputs to K=8 md L=8, will it realize
increasing,
constant or
decreasmg retums to scale (circle one)''
b. As a result does Jake's enjoy
economies of scale,
diseconomies of scale, or does Jake's appear t be operating
at Efficient Scale? (circle one)
http://www.homeworkminutes.com/question/view/31052/Problem-Set-4-Production-1-Optimal-Use-of-a-Single-Input-Julian-Smyth-is-manages-production-at-Taft
Problem Set #4 Production
300
70
350
9
360
60
1. Optimal Use of a Single Input. Julian Smyth is manages production at Taft)'
300
Apple Inc., a company that produces a variety of tafty/fiuit candies. Over the
last several10
months, he has varied then number of employees on his caran1el
410 line, and found the following relationship.
apple production
50
MRP
Labor
TP 250 MP
1
1
450
40
200
12
480
30
150
a. In the column labeled MP, calculate the mar·ginal product oflabor. (Note,
make your first entry in row 6, as the change between 5 and 6 units oflabor)
b. Suppose the apples sell tor $5 (per dozen) box. Calculate the Marginal
Revenue Product ( 1\fRP)
c. Iflabor costs $225 per day, how many laborers should the firm hire''
Number
-------------------------------------
2. Optimal Use of a Single Input. A graphical representation.
a. In the coordinate axes provided below, illustrate the general relationship
between MRP and the Price of Labor. IdentifY the equilibrium quantity of
labor to hire. (Not<:, your graph nc:ed not use the: numbc:rs in problem 3.
Just be certain to include ranges that illustrate gains from specialization
and the law of diminishing returns in your graph.
$
Q
b. Suppose that the candy workers union agrees to way concessions, that
make the price oflabor fall. In the coordinate axes below illustrate the
etlect on the equilibrium quantity of labor
$
Q
c. Finally. suppose that the price of caramel apples increases. Illustrate the
eflt:ct of this ch mge on the equilibriwn quantity oflabor c:mployed.
$
Q
3. Optimal use of multiple inputs. In his shop, Julian Valenti retrofits sunroof. into
automobiles. 1l1e process can use a combination of skilled labor and unskilled
labor. Given his current mix of employees, the marginal product of the last unit
of skilled labor is 3 sumoofs per day, and tht: marginal product of the
last unit of unskilled labor is 1 sunroof per day. CmTent market rates for skilled
and unskilled labor are $40 and $10, respectively. Is Julian using a least cost
combination of inputs? If not, which of type oflabor should he use relatively
more''
Comparison Expression:
_
Result:
_
4. Retmns to Scale. Jake's Free Runoff Bottled Water Company Produces with the
Long Run Production Function
Q = (KL)2il
a. Currentlv K = 4 and L = 4. IfJake's doubles inputs to K=8 md L=8, will it realize
increasing,
constant or
decreasmg retums to scale (circle one)''
b. As a result does Jake's enjoy
economies of scale,
diseconomies of scale, or does Jake's appear t be operating
at Efficient Scale? (circle one)
