Clean air or jobs?

[Merlin1047]

I'm no fan of government interference in the business arena.

But we already have governmental interference in the form of environmental standards. Seems to me that the government should provide assistance in order to help business defray the cost of implementing these measures.

For those who poo-pooed the notion of subsidies or outright government grants, I suggest that this is much the same as government seizing your property. Except in this case, they are telling you how you have to operate your business. Either way, if costs are incurred as a result of government mandate, then government should be responsible at least to some degree to defray those costs.

 

[Said1]

Example:

Starting with a Solow Growth model -

Y(t) = F(K(t), A(t)*L(t))

And assuming that the production has constant returns to scale and using a Cobb-Douglas production for the model...

So, what would that look like if A plus B = 1, (production function has constant returns to scale) and if L and K are increased by 15%, Y increases by 10%.

Did I ask that right.......I need serious practice. :O

 

[elephant]

So, what would that look like if A plus B = 1, (production function has constant returns to scale) and if L and K are increased by 15%, Y increases by 10%.

Did I ask that right.......I need serious practice. :O

Think about this:

Start with y(K,L), that is, output is a function of capital and labor.

y = A*K^(a)L^(b), so y is cobb douglas.

Set a + b = 1, so b = 1-a.

Thus y = A*K^(a)L^(1-a).

Now increase the inputs by a factor of t.

y(tK,tL) = A*(tK)^(a)(tL)^(1-a).
= A*t^(a)K^(a)t^(1-a)L^(1-a)
= t^(a)t^(1-a)*A*K^(a)L^(1-a), step 3
= t*A*K^(a)L^(1-a)
= t*y(K,L)
When it is constant returns to scale the production function is homogeneous of degree 1. That is, the power to which t is raised = 1. See step 3 and remember to add exponents, t^(a + (1-a)) = t^1=t.

so increasing the inputs by t results in exactly t increase in output.
Other scenarios:

If a + b > 1:

t*y(K,L) < t^(a+b)*A*K^(a)L^(b)

If a + b < 1:

t*y(K,L) > t^(a+b)*A*K^(a)L^(b)

Try substituting in numbers and see what happens.

Good luck and let me know if that helps.

 

[Said1]

Think about this:

Start with y(K,L), that is, output is a function of capital and labor.

y = A*K^(a)L^(b), so y is cobb douglas.

Set a + b = 1, so b = 1-a.

Thus y = A*K^(a)L^(1-a).

Now increase the inputs by a factor of t.

y(tK,tL) = A*(tK)^(a)(tL)^(1-a).
= A*t^(a)K^(a)t^(1-a)L^(1-a)
= t^(a)t^(1-a)*A*K^(a)L^(1-a), step 3
= t*A*K^(a)L^(1-a)
= t*y(K,L)
When it is constant returns to scale the production function is homogeneous of degree 1. That is, the power to which t is raised = 1. See step 3 and remember to add exponents, t^(a + (1-a)) = t^1=t.
so increasing the inputs by t results in exactly t increase in output.
Other scenarios:

If a + b > 1:

t*y(K,L) < t^(a+b)*A*K^(a)L^(b)

If a + b < 1:

t*y(K,L) > t^(a+b)*A*K^(a)L^(b)

Try substituting in numbers and see what happens.

Good luck and let me know if that helps.

Ok, it seems as though I did ask the question wrong, but no matter, this DOES help because I can see what I wanted above....i think.


Thanks, it appears that I'm really far from my normal (fluff) comfort zone.

 

[Said1]

Man, this is giving me a headache. No wonder Huck passed on that one.