Allocative and Productive efficiency in PC

This is related to my previous post on perfect competition.

Remember the definition of both allocative and productive efficiency.

Allocative efficiency is when P = MC. Wikipedia has a definition available here. Productive efficiency is when ATC is minimized. Wikipedia has a definition of productive efficiency here. But I want to explain how we get there in perfect competition. What I want to get across is that Allocative and productive efficiency flows from the very assumptions of Perfect Competition

1) The individual firm cannot influence price because it is a very small player in a very big market. Thus its demand curve is flat. (perfectly elastic)
a) Since its demand curve is flat, it can only have one Price.
b) Since it only has one price, its Marginal Revenue Curve (MR) will also be flat. Further it is the same as its demand curve. Why? Because the demand curve is flat (say price = $5). It will not go lower nor higher than $5 due to the explanation I offered in the previous post. Since it is at $5, each additional unit sold will bring in $5 of marginal revenue. Think about it. If I sell one good rather than 0 I earn $5 instead of 0. Thus my marginal revenue is $5. If I sell 2 instead of 1 I earn $10 instead of $5. So my marginal revenue for 2 goods is 10-5 = 5. Get it?

2) The firm should produce until Marginal Revenue = Marginal Cost. No more or no less (see previous post.)
a) If this is the case, then the firm will produce until Marginal Cost = $5. Why? Because if Marginal Cost is $4 dollars then the firm SHOULD produce more because Marginal Revenue is $5. By producing the good the firm banks an extra $1 in profit. So you see that the firm has to produce until Marginal Cost = $5.

So now we can see why we have allocative efficiency. The very definition of allocative efficiency is that P = MC. In a perfectly competitive environment, the firm produces until MR=MC. Since we have PC, MR = P (look at graph above). Thus, we have achieved allocative efficiency. The market is producing the right goods for the right people at the right price.

3) In perfect Competition, the ATC will be minimized.
Note that this is the definition of productive efficiency (ATC minimized). Why is this the case in perfect competition? Well, if a firm is not producing at the lowest possible unit cost (ATC = $5), another firm will enter the market and undercut them. The firm goes out of business. In other words, competition ensures that every single firm in the industry produces at the least possible ATC per unit. In other words, if Firm A and Firm B are in the same industry--and that industry is perfectly competitive---you only need to find one ATC. If you found one you've found them all. If Firm A's ATC is $5, then Firm B's is $5 as well.

Read on if you want the policy implications of this. (What is below will not be a multiple choice or part 2 problem on the test, but reading it may help illuminate the above).

What I have described above is the best possible outcome for markets. Under the assumptions of perfect competition, we have achieved what is called "pareto efficiency."

That fancy and scary name is really a technical way of saying the following. If a situation exists where I can make one person better off without making anyone else worse off, we a pareto efficient opportunity. Steven Landsburg in his book "The Armchair Economist" gave an example in nature to illustrate this concept. Say you have a flock of birds. The female birds in the flock are attracted to male birds that have "large tails" (you students of Freud are left to make the connection). However, large tails hurt a birds flight as they increase wind resistance. How can we make a pareto efficient outcome out of this. Well, what we can do is take all the male birds and cut their tales off by 2 inches. Therefore, every single bird in the flock has a smaller tale but the ones with the big tales still have a their relatively large tail in comparison with the other birds intact. Every bird can now fly faster and we did not have to disadvantage any of the birds in the process.

This is what perfect competition does with regards to allocative and productive efficiency. The market has created a situation where the most efficient allocation and production of resources has occurred. Nothing can be done to improve efficiency without harming someone at the expense of someone else. Perfect competition has consumers trying to maximize their utility and producers trying to maximize their profits. Market forces ensure that we reach an equilibrium where we maximize the gains to everyone.