
Costs question
I am given two equations:
Min 5K + 15L
and the constraint: 10=$\displaystyle L^{.5}K^{.5}$
given that K=4 (then L=25)
and am asked to find the:
1. short run average cost
2. short run variable cost
3. shortrun marginal cost
And I'm a bit confused. What is the 10 actually represent in constraint? Is it total quantity produced?
Is the answer to question 1 suppose to be:
5(4) + 15(25)= 20+ 375= 395
395/10 = 39.5?
2. seems to be the cost of labor (wL), or in this case 15L, or w=15.
3. I know that SRMC should be the change in SRTC/ change in quantity. I just don't understand where your find those values.

1. fine
2. Not clear if you mean "short run total variable cost" or "short run average variable cost".
SRTVC = 15L
SRAVC = 15L / 10
3.
Compute the amount of labour needed to produce X units of output given that K is fixed at 4.
Compute the SRTC = 15L + 4*5 [[note: it will be a function of x!!]]
Differenciate SRTC with respect to X to obtain the SRMC
