# Firm's profit max problem, in present value terms

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

or

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).

• Question doesn't seem complete to me. Where is the production function? – Amit May 24 '18 at 11:01
• Theres no production function giving. imgur.com/CU0u0Di is all the information that is given. – statman May 24 '18 at 11:15
• Technology/Production function is given very clearly in the image you provided, this means you haven't read the question carefully. I suggest you read the question and try it again yourself. – Amit May 24 '18 at 12:17
• Do you mean that I should add the technology contraints to the max problem? – statman May 24 '18 at 12:40