Shutdown condition analysis

[J]

We know that 

• Q = quantity, 
• wL + rK = total costs in the long-run
  
• In the long run labor (L) and capital (K) are both variable
• wL = total variable cost in the short-run
• In the short run labor (L) is variable and capital (K) is fixed
• total cost / quantity = TC/Q = average cost
• From this we can derive:
• total variable cost / quantity = TVC/Q = average variable cost
• total fixed cost / quantity = TFC/Q = average fixed cost
• price = what you get per unit of output produced (before costs)
• PQ = price*quantity = total revenue

So the shutdown conditions in the short-run and long-run respectively are

• Short-Run
• PQ-wL<0

and

• Long-Run
• PQ-wL-rK<0

I'm trying to break it down conceptually.

Some algebra rearranges the conditions as

• Short-run
• P < wL/Q
• Long-run
• P < (wL+rK)/Q

I'm seeing this as 

• Short run
• Price < SAVC
• If price is less than average variable cost in the short-run, the firm shuts down
• Long run
• Price < LAVC
• If price is less than average variable cost in the long-run, the firm shuts down
• All inputs are variable in the long-run so really this is 
• Price < LAC
• If price is less than average cost in the long-run, the firm shuts down

Is my thinking ok here?

[Taylor Stoltzfus]

Looks great J, good analysis!

[JN]

Hi J!

Just wanted to give a huge thank you for being like my second tutor throughout this quarter :) 

I might not be able to get into the major anymore, but I wouldn't even dream of passing this class if it weren't for all your helpful posts and responses! Wish we could've been study buddies this quarter.

Thanks a bunch- you're a genius & you're gonna do awesome things in life. Good luck with everything!

[J]

Thank you JN! Your words flatter me to the core. Your response is just what I needed to get a second wind on this studying right here. I wish you luck on whatever you hope to achieve.