So I am kinda stuck on this question. The question goes as follows: Consider a multiperiod firm, selling q1 units of a product in period t=1 at spot price P1 and q2 units in period t=2 at spot price P2. It uses three factors in production: capital K, which is acquired for price Pk at t=0 and last two periods, and labor in each period, L1 and L2, with respective spot prices PL1 and PL2; the firm acquires L1 at t=0 and L2 at t=1. The firms product is perishable, so it cannot carry inventory from one period to another.
Assume prices are as follows: P1=40, P2=50, PK=20, PL1=10, PL2=15. the interest rate is r=10%. Set up the firms profit maximization problem, in t=0 present value terms.
So our definition of spot price: spot price = price * (1+r)^t. What I have at the moment is
max 44q1 + 60.5q2 - 10L1 - 16.5L2
max 36.36q1 + 41.32q2 - 10L1 - 13.63L2
I'm not sure what do about capital (K), since its acquired in t=0 and last two periods and is not noted to be a spot price.
EDIT: since PK=20, but the price isn't a spot price and its acquired in 3 different periods, does that mean it should just be 60*K in regards to the max problem?
EDIT 2: Could also be the formula PV = FV * (1/(1+r)^t). Where PV is present value and FV is future value (spot price).