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3 years ago

12

During world war i the u.s. military developed the _____ to screen millions of recruits.

2 answers:

hichkok12 [17]3 years ago

7 0

Army Alpha and Army Beta Test

Bess [88]3 years ago

3 0

Aptitude Test. In 1918 the U.S. Military started using aptitude tests to screen prospective recruits, then called the Army Alpha and Army Beta tests. Today the U.S. Military still uses and aptitude test called the ASVAB, or the Armed Services Vocational Aptitude Battery.

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The cob Douglas production function is given by Q(K,L)=AK^1.4*L^1.6

Alexeev081 [22]

Part a) The Cob Douglas production function is given as:

$Q(K,L)=AK^{1.4} L^ {1.6 } .$

To show that this function is homogeneous with degree 3, we introduce be a parameter, t.

$Q(tK,tL)=A(tK)^{1.4} (tL)^ {1.6 } .$

Using properties of exponents, we on tinder:

$Q(tK,tL)=At^{1.4}K^{1.4} t^ {1.6 }L^ {1.6 } .$

This implies that:

$Q(tK,tL)=t^{1.4} \times t^ {1.6 }(AK^{1.4} L^ {1.6 } )$

$Q(tK,tL)=t^{1.4 + 1.6}(AK^{1.4} L^ {1.6 } )$

Simplify the exponent of t to get;

$Q(tK,tL)=t^{3}(AK^{1.4} L^ {1.6 } )$

Hence the function is homogeneous with degree, 3

Part b) To verify Euler's Theorem, we must show that:

$K\frac{\partial Q}{\partial \: K}+L\frac{\partial Q}{\partial \: L}=3AK^{1.4}L^{1.6}$

Verifying from the left:

$K\frac{\partial Q}{\partial \: K}+L\frac{\partial Q}{\partial \: L} =K(1.4AK^{0.4} L^{1.6}) + L(1.6AK^{1.4} L^{0.6})$

$K\frac{\partial Q}{\partial \: K}+L\frac{\partial Q}{\partial \: L} =1.4(AK^{1.4} L^{1.6}) + 1.6(AK^{1.4} L^{1.6})$

$K\frac{\partial Q}{\partial \: K}+L\frac{\partial Q}{\partial \: L} =(1.4 + 1.6)(AK^{1.4} L^{1.6})$

$K\frac{\partial Q}{\partial \: K}+L\frac{\partial Q}{\partial \: L} =3(AK^{1.4} L^{1.6})$

Q•E•D

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