Need some help plz

ontour

If production function q=K^0.75L^0.25, K is fixed at 50 per unit rental rate of K is r=2 while per unit wage rate is w=5. how do I calculate short run total, average (sac) and marginal (smc) cost curves. Im driving myself mad all i need is the functions plz help Im trying to work them out put have constant mcs

Flamed Diving

ontour wrote: »

If production function q=K^0.75L^0.25, K is fixed at 50 per unit rental rate of K is r=2 while per unit wage rate is w=5. how do I calculate short run total, average (sac) and marginal (smc) cost curves. Im driving myself mad all i need is the functions plz help Im trying to work them out put have constant mcs

I'm not sure what level you are at, but does the word Lagrangian sound familiar?

ontour

No I'm sorry it doesn't I'm in first year uni lost with just how to figure this one out

Flamed Diving

ontour wrote: »

No I'm sorry it doesn't I'm in first year uni lost with just how to figure this one out

[latex]
Q = K^{^3/_4}L^{^1/4_}
[/latex]

[latex]
\frac{Q^4}{K^{7/4}} = L
[/latex]

[latex]
TC = rK+wL
[/latex]

[latex]
TC = rK+w(\frac{Q^4}{K^{7/4}})
[/latex]

[latex]
K = 50, r = 2, w = 5
[/latex]

[latex]
TC = 100+\frac{Q^4}{188}
[/latex]

[latex]
VC = \frac{Q^4}{188}
[/latex]

[latex]
MC = dvc/dq = \frac{4Q^3}{188}
[/latex]

[latex]
AC = VC/Q = \frac{4Q^2}{188}
[/latex]

I'm not sure about the AC calculation, go look it up in your notes.

Économiste Monétaire

Just on the AC, I think it should be
[latex]
\displaystyle AC = \frac{TC}{Q} = \frac{100}{Q} + \frac{Q^{4}}{Q} \cdot \frac{1}{188} = \frac{100}{Q} + \frac{Q^{3}}{188}
[/latex]

ontour

Your both absolute stars thank you. Just one last question where doers the 188 come from? Thanks again to both of yis i've been pullin out my hair!

Flamed Diving

Just plug in all the values from the fifth line.

ontour

When I do that i get tc=100+5Q/500^7/4 maybe I am plugging them in wrong? Thanks again for all your help

Flamed Diving

Firstly, K = 50. Ok, so you are left with 50^7/4 = 940 (when rounded to zero decimal places).

Then you have 5Q/940 = Q/188