Recap on last week

• Elasticities matter, as they dictate how surpluses are distributed in a market.

• It is important also for the government.

• Demand elasticity varies depending on preference and the state of the good

  • substitute vs complement, luxury vs normal, etc
  • usually hard to change market preferences.
  • preference can be estimated but it is beyond the cover of this course.

Today's cover

• Supply curve is a bit different:

  • Cost can be easier to guess.
  • Easier to make framework.
  • Has an important implication to the market.

• What we will learn today is:

  • The production function.
  • Types of cost.
  • Implication to the supply curve and the market.

The production function

• A firm is an organization that produces goods and services.

• To produce, it uses inputs and transform them into a final product and then sell it to the market.

• This relationship:

$$input \xrightarrow{magic!} output$$

         is called production function

Reminder: What is a function?

• Function is a mathematical expression to show a relationship between two or more variables.

• Let $X$ be input and $Y$ be output, a production function is:

$$Y=f(X)$$

• How labor makes rice is sometimes not the main emphasize for economist.

• We care more on how much $X$ is needed to make $Y$.

The production function

• Let there be a hypothetical rice farmer named Kensi.

• Kensi own a hectare of land. In the short run, Kensi can't increase his number of land.

• However, Kensi can hire a labour to work at his farm.

• In this case, the inputs are land and labour, while the output is rice.

Fixed and variable input

• We call land a fixed input, an input which can't be changed.

• We call labour a variable input because Kensi can hire or fire labour anytime.

• It is important to distinguish the two, because a producer can adjust variable input to adjust demand.

  • In good times, hire more labour. In bad times, fires.

Short and long run

• Fixed input won't probably be fixed for long.

  • buying and selling new land may take time, but it is doable.
  • However, when there's a quick shock to demand, it is not easy to adjust it.

• For example, the price for surgical mask at one point rose to 150k IDR a box, but it is now settled back to around 30k IDR a box.

  • In the short run, fixed input can't keep up.

• TSMC and Samsung need time to build new factories.

Short and long run

• How long is 'long run'? depends on how quickly the fixed input can adjust.

• In the case of masks, it catched up to the demand shock in less than a year. Hand sanitizer is even faster.

• In the case of chip, the new capacity for TSMC will operate somewhere in 2022, while Samsung needs even longer time.

• Knowing how long is the demand shock is also important.

  • forecasting demand is a useful skill to have.

The hypothetical farmer

• Kensi can't change his arable land, but can change how much labour he employs.

Marginal product

• In general, marginal product of an input is the additional quantity of output produced by using one more additional unit of that input.

• In our case, we have MPL of every one more additional worker. But if that data is not possible, we can just use the formula in general

• for example, if Kensi have only two data points: one where he work alone and one when he hire 7 workers.

Marginal product

$$MPL=\frac{\Delta Q}{\Delta L}=\frac{96-19}{8-1}=11$$

• In our case, MPL decreases as the number of worker increases:
  • it is better to have a smooth data point.
  • We call this a diminishing return to labour

Marginal product curve

Diminishing return to an input

• When you have 1 hectare of land, 1 worker can only work so much before he gets tired.

• It is sensible to hire one more person to work on a larger area. This will lead to a huge gain in harvest.

• If the land area is fixed, as we introduce more people, each person will have to work in a smaller area.

• Too much people become inefficient.

• In an office setting: imagine if you add workers without adding the number of computers.

Marginal product and the fixed input

• If Kensi would like to scale up production, increasing only labour will be inefficient.

• Kensi can start planning to increase its land to 2 hectare by buying or renting his neighbour's land, for example.

• Suppose it takes one year for Kensi to buy one more hectare of land, what's his TP and MPL would look like one year later?

TP shifts up with additional land

MPL is still diminishing, but higher

Marginal product

• The crucial point of the diminishing marginal product concept is ceteris paribus.

  • if you increase labour AND land, then MPL will look like it goes up.

• Hence, when we measure MP of an input, it must be the case that everything else is held fixed.

• Production function can be a bit more complex.

  1 programmer in 12 months $\not\rightarrow$ 12 programmers in 1 month.

From production function to profit

• Kensi understand how his farm work. He would like to profit from his farm.

• If Kensi can't control the selling price (rice is competitive), he needs to know how to control his own cost.

• He has to know at least two things:

  • fixed cost (FC), the cost of his land, and
  • variable cost (VC), the cost of labour.

Kensi's hypothetical cost

• Suppose Kensi's land's rent price is 200 k IDR, while the wage rate in his neighbourhood is 100k IDR.

Total cost curve for Kensi's farm

Total product curve vs total cost curve

• Both are upward sloping

• however, as production increase, TP is getting flatter, while TC is increasingly steeper.

• Using more labour increases additional TC but decreases additional TP.

Marginal cost

• Marginal cost (MC) is the change in total cost generated by producing one additional unit of output.

$$MC = \frac{\text{Change in }TC}{\text{change in }Q}=\frac{\Delta TC}{\Delta Q}$$

• Let's add MC on Liv's fancy footwear cost structure

Liv' fancy footwear cost structure

Liv's fancy footwear

Liv's fancy footwear

Average Total Cost (ATC)

• There is also average total cost, or simply Average Cost

$$ATC=\frac{TC}{Q}$$

• ATC is important because it tells the cost of each fancy footwear given the current state of production.

• Be careful, $ATC \neq MC$

• Which one would Liv use to set the price?

Liv's fancy footwear cost structure

Liv's cost structure

Liv's fancy footwear Average Total Cost Curve

MC and ATC

• It is probably best to produce at the lowest ATC. Q=3 is the minimum-cost output.

• Note that:

  • at $Q=3$, $ATC=MC$;
  • at $Q<3$, $ATC<MC$;
  • at $Q>3$, $ATC>MC$.

• Works like your GPA: At GPA=3.0, an additional A will increase your GPA, a C will decrease your GPA, while a B doesn't change your GPA.

Cost Curves

Cost curves

• Note that in our graph, ATC is not exactly equals to MC.

• This is because MC is an incremental cost from Q:

  • for example, a marginal cost from Q=1 to Q=2 should be plotted somewhere between Q=1 and Q=2, not exactly at Q=2.

• It easier to understand the logic when we use function.

• The logic remains: a Q where cost is lowest is when MC=ATC

Short run and long run

• In the long run, Liv can upgrade (or downgrade) her capacity by changing her fixed cost.

• Higher fixed cost leads to higher overall cost, but typically can reduces variable cost at a higher Q.

• If Liv's client is just 3 people, buying a automated sewing machine might be an overkill.

• If Liv's business is forecasted to grow in the future, she can prepare for an upgrade.

High capacity vs low capacity

High capacity vs low capacity

• Upgrading is only worth it if Liv sell at least 5 pairs of shoes.

• If upgraded, the minimum-cost output is $Q=6$

• In the long run, fixed cost can be changed (hence become variable to some extent)

• The most important is to know:

  • How the different capacity ATC looks like;
  • How easy each input can be changed;
  • whether changes in the market is long lasting or not.

High capacity vs low capacity

Long run cost curves

• Long run average cost (LRAC) is an average total cost which treat the fixed cost as a variable cost.

• Calculating LRAC requires many curves corresponding with different level of fixed cost.

• In fact, with so many other costs, using graph may no longer be practical.

• We won't cover it in this course, but it is useful to know that LRAC exists and can be useful for you in the future.

Returns to scale

• Upgrading makes sense if the industry is having an increasing returns to scale.

• Increasing returns to scale happens when scaing up leads to lower LRAC.

  • in liv's case, she scaling up leads to lower cost overall, which may lower the price.
  • this is also the case for many industries, where big firms are able to offer their products at a lower price.

• When increasing scale leads to higher cost, we say decreasing returns to scale. Happens when a firm is too big, coordination gets costly.

Perfect competition

• We learned in the perfect competition, producer takes price as given.

• This is called price-taking producers (and price-taking consumers)

• essentially means nobody can affect prices.

• How much should Liv produce? Depends on the revenue.

• For now, let's assume that the fancy footwear a highly competitive industry, where P=$100

Liv's cost, revenue and profit (Total)

Liv's cost, revenue and profit (total)

Liv's cost, revenue and profit (per unit)

Profit under perfect market

• The necessary condition for profit maximisation is as close as possible with:

$$MR = MC$$

• MR is short for Marginal Revenue, how much additional revenue you get from selling one more good.

$$MR = \frac{\Delta TR}{\Delta Q}$$

• It is like marginal cost, but revenue.

• This is why marginal cost is important.

Marginal Revenue & Marginal Cost

MR, MC and AC in action

MR & MC

• Profit is equals to margin times quantity sold

$$\pi=(P-ATC) \times Q$$

• hence the red area on the previous 2 graphs.

• When $MR < MC$, the additional Q that we produce reduces profit.

• When $MR > MC$, the additional Q that we produce increases profit.

• That is why at $MR = MC$, we have profit-maximizing output.

MR & MC

• In Liv's case, she doesn't have any point where $MR=MC$

• In this case, she produce as close as possible with $MR=MC$, but still $MR>MC$

  • profit is starting to go down when $MR<MC$

• In a bigger firm with more Q and more continuous data point, $MR=MC$ is very useful and approachable.

Perfect market

• In the perfect market, producers are price-taking (pasrah).

• That is why $MR=P$

  • no matter how much (or less) a producer produce, the price will always be the same

• We will see next week how the market will look like when producer's action can change prices.