Ever more kinked…

I have just revised oligopolies in theory of the firm (ToF) for HL students in IB2. I introduced the kinked demand curve a bit differently this time: I outlined the premises carefully, drew the market equilibrium point in a diagram and then asked the students to carefully obey the PED conditions of ‘…if I lower my price and the other firms follow…’ in drawing the demand curve. This gave an entirely different outcome than most textbooks!

I also played a game of ‘Find the flaw’ by Googling pictures of kinked demand curves. Try it here. How many of the diagrams on your screen are flawed or simply erroneous?! Play this game again after you’ve read to the end of this post.

So why is it that in following the premises to a ‘t’, my students and I get a different kinked demand curve than most textbooks? Because if PED < |1| when an oligopolist lowers the price then it is impossible for any portion of the marginal revenue (MR) curve relating to this section of the demand curve to be positive!

Let’s reiterate the basic assumptions and outline of the model. We have a non-collusive oligopoly with a high degree of interdependence among firms (we leave out the question of product homogeneity!) and the initial equilibrium price and quantity have been set. (No, the model does not explain how this initial equilibrium is set – it’s one of several weaknesses.) The model then seeks to explain what one frequently sees in oligopoly markets, namely broad price rigidity over time with resulting non-price competition.

Looking only at the price rigidity issue, the model posits the following for a single oligopoly firm: raising the price means losing customers to competitors and lowering the price means that competitors fear losing their customers. Thus, the individual oligopoly firm is faced with the question “…if I raise my price I go it alone since competitors will gain from me losing my customers…and if I lower my price they will have to follow suit to hinder me from stealing their customers…” Thus a rise in price will result in a large loss of customers and highly elastic demand. A price decrease will result in other firms matching the price cut and so far less an increase in sales for the individual oligopolist than if the firm had been able to act without reciprocation.

So, the basic idea is that PED > |1| when raising the price but PED < |1| when lowering the price. Again, this is from the viewpoint of the individual oligopoly firm. This gives us a demand curve like this:

Olig 1

Now, here’s the discussion I was forced to have with my students in order to underpin why textbook diagrams are simply erroneous. Recall the basic PED law that elasticity will go from infinite (on P-intercept) to zero (Q-intercept) with unitary PED ‘halfway’ (between zero price and the P-intercept or zero quantity and the Q-intercept):

Olig 2

Now assigning a degree of market power to the oligopolist, i.e. approximating the oligopoly by using a marginal revenue (MR) curve for the monopoly:

Olig 3

In our diagram, when PED = |1| then MR = 0. This is an important point to make and is basically what my entire argument pivots on. If PED < |1| then MR must be NEGATIVE. There can be no portion of the MR curve above the Q-axis over the range where PED < |1| !

For our kinked demand curve, still assuming “…high price sensitivity in raising my price….low price sensitivity in lowering my price…”, we get the following:

Olig 4

And this illustrates my argument in a nutshell: if PED < |1| when the oligopolist lowers the price, there can NOT BE ANY PORTION OF THE MR CURVE THAT IS POSITIVE! In syllogistic form:

  1. In lowering the price, the oligopolist faces a PED < |1|
  2. When PED < |1|, MR is negative
  3. There can be no positive portion of MR in lowering the price

In other words:

Olig 5

So, back to Googling. I stuck in the search string “kinked demand curve” (here) and you can check out the results. You tell me whether this diagram is correct – or even possible! Or this one. Or this….

Of the first 20 images on the search page, at least 15 are simply erroneous and out of the remaining five four a questionable and ONE is correct. When one stops to thing that this is how the majority of our students conduct research, well, food for thought.

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