<p>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.</p>

<p>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.</p>

<p>So our definition of spot price: spot price = price * (1+r)^t.
What I have at the moment is </p>

<p>max 44q1 + 60.5q2 - 10L1 - 16.5L2 </p>

<p>or</p>

<p>max 36.36q1 + 41.32q2 - 10L1 - 13.63L2</p>

<p>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.</p>

<p>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?</p>

<p>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).</p>

CC BY-SA 4.0
2018-05-24T11:01:16.560Z
Question doesn't seem complete to me. Where is the production function?
Amit
CC BY-SA 4.0
2018-05-24T11:15:35.107Z
Theres no production function giving. https://imgur.com/CU0u0Di is all the information that is given.
statman
CC BY-SA 4.0
2018-05-24T12:17:53.180Z
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
CC BY-SA 4.0
2018-05-24T12:40:10.090Z
Do you mean that I should add the technology contraints to the max problem?
statman
<microeconomics><mathematical-economics><profit-maximization>
Firm's profit max problem, in present value terms
statman
# Firm's profit max problem, in present value terms

(Asked by: username_0 on 2018-05-23)

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).

**Tags:** microeconomics, mathematical-economics, profit-maximization

> **Comments:**
> **username_1**: Question doesn't seem complete to me. Where is the production function?  
> **username_0**: Theres no production function giving. https://imgur.com/CU0u0Di is all the information that is given.  
> **username_1**: 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.  
> **username_0**: Do you mean that I should add the technology contraints to the max problem?  

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## 0 answers

