10. Suppose you are hired as a new manager of a firm producing 20 units of outpu
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10. Suppose you are hired as a new manager of a firm producing 20 units of output with 10 units of labor and 5 units of capital. Assume the price of labor is $100 and the price of capital is $100 Along the isoquant, the MRTSux is as noted in Table 1. Table 1 Between MRTS Points a and b500 b and c c and d d and e 1.00 600 750 Q20 L. 7 8 910 1 Given the above graph and table: the MC and MB of changing L) ail e wplain the optiens tor minimize cost (Hint: think about the MC and MB of changing t). units of capital. (It is possible to hire non- b. To minimize cost, you should uselaborers andu integer units of capital) c. How much total cost will you be able to save by changing the input combination? L units of output 11. A firm discovers that when it uses K units of capital and L units of labor it is able to produce K Q. a. Draw the isoquants for Q-2,3, 4 the firm produces 10 units of output with 20 units of K and 5 units of L. What is the MPL, MPK and MRTS c. On the basis of your answer in "b." is the equation MRTS MPL/MPK about right?Explanation / Answer
Ans 11/b)
Q=10; K=20 and L=5
Q=sqrt(KL)
MPL=0.5sqrt(K/L)=0.5sqrt(4)=1
MPK=0.5sqrt(L/K)=0.5sqrt(1/4)=0.25
MRS=MPL/MPK=1/0.25=4
Ans c)
yes for an equilibrium we need MRS=(MPL/MPK)
Ans d)
r=1 and K=20
10=sqrt(20L)
100=20L
L=5 units
Cost=wL+rK=1(5)+r(K)=5+20K
We know MPL=w and MPK=r=0.25
Short Cost=5+20(0.25)=10
Ans e)
In the long run
Q=sqrt(KL)
minimising cost function we get
Z=wL+rK-@(sqrt(KL)-C)
dZ/dL=w-@*0.5*sqrt(K/L)=0
dZ/dK=r-@*0.5*sqrt(L/K)=0
w/r=K/L
wL=rK
C=2rK
Q=sqrt(KL)=sqrt(KrK/w)=Ksqrt(r/w)
10=sqrt(r/w)*K=sqrt(LK)
LK=100
then L+K would be maximized when L=K
L=K=10
Long Run Cost=2rK=20r =20*MPK=20(0.5*sqrt(L/K))=20*0.5=10
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