Praxis

February 3, 2008

Equilibrium Analysis and Deadweight Loss

Filed under: Economics — duncan @ 5:46 pm

[Apologies for the shonky graphs here – I used Paintbrush, badly. Does anybody know any good free graph-making software, perhaps?]

So here’s your supply and demand curves for some product, say petrol. This market is operating, we’re assuming, without taxation. The quantity supplied is Q1, the market price is P1.
graph-02.jpg
And now the government imposes an excise tax on petrol.
graph-03.jpg
The quantity of petrol supplied is reduced – moving to Q2. We can calculate government revenues from this tax by calculating the area of the rectangle A. Revenue = Q2(P3 – P2). Right? The deadweight loss from this tax is the area of the triangle B. Yes? There is a net loss of value from the imposition of the tax – there is less value in the economy after the tax that there was before, because government revenues are smaller than the total loss in consumer and producer surpluses (i.e. the area of A and B combined). This will always be the case. The smaller the elasticity of supply and demand, the smaller the deadweight loss – but there will always be a deadweight loss when taxation moves a market away from equilibrium. Taxation always creates economic inefficiency.

I’m glossing my textbook (Krugman, Wells and Graddy, 2007). But as far as I can tell, my textbook makes little sense. My response to the above is basically: WTF?! [Calculate the area of that triangle…]

Why are we here seeing the imposition of a tax as generating a movement away from equilibrium? Why aren’t we seeing a change in the supply and demand curves, as a result of the changing costs of producing/supplying/purchasing the product? Surely the new quantity of petrol supplied is the product of a new market equilibrium?

But no mention is made of a new market equilibrium in my textbook – rather, the situation post-taxation is presented as a deviation from equilibrium; a bad-news deviation from the optimal scenario of voluntary free exchange.

“Deadweight loss triangles are produced not only by excise taxes, but by other types of taxation. They are also produced by other kinds of distortions of markets, such as monopoly.” (p. 157.) “As a result [of taxation] some mutually beneficial trades between producers and consumers do not take place.” (p. 156).

But no. From the point of view of both consumers and producers, taxes are a cost like any other [well, not necessarily like any other – but they’re a cost]. You could re-run this entire scenario with some other cost instead of an excise tax – and this cost would also produce a ‘deadweight loss’ as it brought the market away from the equilibrium we’d see if there were no such cost. That doesn’t mean that we’re here (or anywhere) moving away from an efficient (equilibrium) market to an inefficient (distorted) one: it means only that the factors determining the supply and demand curves, and thus market equilibrium, have changed.

Why is taxation [and, later in the textbook, monopoly] singled out for special treatment? Why is this cost treated as external to and separable from movements of the supply and demand curves, while some other cost (an increase in the price of oil, say), is accepted as part of the normal functioning of the market?

‘Deadweight loss’ is everywhere. The supply and demand curves are created by deadweight loss.

Or am I getting everything wrong? (More than likely.)

2 Comments

  1. Hi,

    I’m trying to teach myself economics too, and stumbled across this
    blog while Googling for ‘Poverty and Famine’. Nice blog.

    My understanding of ‘deadweight loss’ follows.

    An unstated assumption of the capitalist system is ‘more trade the
    better’. That is, trade is always beneficial to both the parties
    involved, and the wealth of a society increases in proportion to the
    amount of trade.

    Taxation establishes a new market equilibrium in which the quantity of
    goods traded is lower. By the above assumption, we conclude that
    taxation is a bad thing, since it has decreased the amount of trade
    and hence (presumably) decreased the society’s wealth.

    How is taxation different from an increase in the supply cost due to
    any other reason? The difference is that a tax, unlike a free market
    commercial transaction, involves a third-party, the government. The
    government by imposing a tax has interfered with the market and
    reduced the society’s wealth. It can only redeem itself if it puts the
    tax money to good use (building roads, paying police officers) such
    that it offsets the deadweight loss of the tax.

    Well, these are just the thoughts that come to my mind right now.
    I need to think about this more.

    Apropos graph-making software, you could try Inkscape (http://www.inkscape.org/) or Open Office
    Draw (http://www.openoffice.org/product/draw.html). Both are quite adequate for drawing not-too-complex diagrams.

    Comment by Vikas Gorur — February 15, 2008 @ 8:18 pm

  2. Vikas, thanks for the comment. Glad you like the blog!

    “An unstated assumption of the capitalist system is ‘more trade the better’.” Definitely. W/r/t deadweight loss, it seems to me that the loss the economists mourn isn’t so much the quantity of trade per se as the value of the trade – but this is the same thing, in most respects. “The difference is that a tax, unlike a free market commercial transaction, involves a third-party, the government.” Yeah, that sounds right to me. I mean, the price of petrol could be increased, by ‘price-gouging’ say – but if this increase were intentional (the result of monopoly or oligopoly) then I guess economists would also call this a deadweight loss. If we follow this reasoning, we’re only dealing with true equilibrium (without deadweight loss) if prices aren’t increased intentionally, through ‘perversion’ of the market, but through ‘natural’ forces – say, running short of oil, or higher transportation costs.

    But I’m not really satisfied with this explanation of the distinction between deadweight loss and true market equilibrium for two reasons.

    1) It seems to me that almost any transaction involves a deliberate increase in prices over and above that which is necessary for the transaction to take place – such increases are, after all, the source of profits, without which you’ve got no capitalism. Why isn’t the increase in the price of petrol which the petrol-station owner imposes in order to make a profit also counted as a deadweight loss?

    2) I’m not altogether clear by what means the distinction is drawn between intentional and non-intentional increases in costs. To put this in the strongest terms: in what contexts is it legitimate to distinguish between trade, on the one hand, and the appropriation of natural resources (without any form of exchange), on the other? If I invest money in order to get oil out of the ground, couldn’t this, on some super-abstract level, be considered as exactly equivalent to an exchange, in which I pay the earth for oil? How does the concept of ‘intention’ function here? But that’s an almost completely different issue, only of interest to people like me who’ve spent too much time reading philosophy. 🙂

    Sorry if this is gibberish, I’m typing at speed. I hope I haven’t misunderstood or misrepresented you…

    And thanks for the graph software tips, I’ll check them out!

    Comment by praxisblog — February 16, 2008 @ 9:54 pm


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