Since by the condition of the problem K=1,000 and L=100, then we have
Q=50×10000.6×1000.5=31,548
We can take the average productivity of a unit of labor as the ratio of the produced product to the amount of labor expended.
AQL=LQ=10031,548=315.48 We can take average return on assets is the ratio of output product to fixed assets.
AQK=KQ=100031,548=31.548
Marginal products characterize the effect as volume products obtained from increased resource costs.
MQL=δLδQ=L0.525K0.6
MQL=1000.525×10000.6=158
MQK=δKδQ=K0.430L0.5
MQK=10000.430×1000.5=19 A)
Q=50×200.6×250.5=1509
B)
TC=pK×K+pL×L=75×20+50×25=1500+1250=2750
C)
δL2δ2Q=−0.6
δLδKδ2Q=0.9
δK2δ2Q=−18.1
−0.6×(−18.1)−0.92=10.05 The company is located at the point of maximum.
D)
dQ=δLδQdL+δKδQdK
E)
δLδKδ2Q=0.9 The company is at the stage of growth.(0.9>0)
F)
if
K=1.15×20=23K=1.15×20=23 and
L=1.15×25=28.75L=1.15×25=28.75
then
Q=50×230.6×28.750.5=1759
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