Problem Set #4
Production



1.   Optimal Use of a Single Input.   Julian Smyth is manages production at Taft)' Apple Inc., a company that produces a variety of tafty/fiuit  candies.  Over the last several months, he has varied then number of employees on his caran1el apple production line, and found the following relationship.

Labor 	TP	MP 	MRP















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)