# 5. Production Theory
###### tags: `microEconomics`

- Utility Function -> Production Function
- Goal: Maximize Profits $\pi = Return - Cost$
- Q = Market's production function
- q = Firm's production function = $f(Labour, Kapital)$
- Factors of production: Labour aka Workers, Kapital (machines + buildings)
- Variable/Fixed inputs - short VS long run
- variable: hours of work
- fixed: size of production plant
- Short term: $L, \overline K$ - days/weeks/months
- Long term: $L, K$ - years (however long it takes for them to be variable lmao)

## Short Run Production
$q = f(L, \overline K)$

only think about L then. Hours, numbers etc

- Marginal Product of Labour: $MP_L$ = change in output for next unit of labour
- $MP_L = \Delta q/\Delta L$
- Diminishing $MP_L$: next worker is not as productive the current one
- Why? Limited Capital!

## Long Run Production
$q = f(L, K) = \sqrt{LK}$

- isoquants: what combination of capital and labour gives the same output
- isoquants are tanglible unlike utility function
- Perfectly substitible: $q = L + K$ => linear isoquants (try drawing!)
- Perfectly unsubstitible: $q = min(L, K)$ => Leontiff production function (try drawing!)
- slope = MRTS = marginal rate of technical substitution
- $\Delta L MP_L + \Delta K MP_K = 0$
- $\Delta K/\Delta L = MRTS$

Q: WTF does one unit of Kapital mean??

## Return to Scale
- Constant Returns to Scale function: $CRS = f(2L, 2K) = 2 f(L, K)$
- Increase returns to scale $IRS = f(2L, 2K) \ge 2 f(L, K)$
- Decrease returns to scale $DRS = f(2L, 2K) \le 2 f(L, K)$
- think about the signs

## Productivity
people innovate
$q = A_t \times f(L, K)$

rate of productivity improvement: $r(t) = \frac{dA/dt}{A}$

however, if time is seen from a discrete view, we have: $r(t)=\frac{A_{t+1}-A_t}{A_t}$

determines the standards of living (A, K)

Q: Why did IT gainz slow down after 2005, when they only started mid 1990s?
A: we do more shit. but we also watch more porn. so there you go.

Q: What to do with them gainz?
A: work even harder OR chill out

Q: Who *actually* gains?
A: I think we all know that already