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why isn't this just dependent on using a willingness to pay definition that is perhaps unnecessarily and rigidly ex-post? think about a normal partial equilibrium ppd case in an industry where the consumption comes first and the labor second, like a for profit university. do we say that first degree price discrimination fails here because firms will charge a price that causes all students to work less tomorrow and buy less education? or can wtp mean the firms explicitly consider the leisure/labor trade off in their ppd price setting? what does the wtp foresight embedded in ppd even mean in general equilibrium if everyone could do it and everyone knew everyone could do it?

dlr: suppose there were some exogenous individual-specific characteristic E that perfectly predicted the cross-section distribution of wage income in equilibrium. If PPD firms made prices contingent on E, rather than on observed income Y, there wouldn't be any distortion. Just like if the government put a 99.99% tax on E instead of Y there wouldn't be any distortion. Yes.

But notice that the government, being a large player, has an incentive to make taxes contingent on E rather than Y. An individual monopolist, being a small part of the whole economy, has no such incentive, because its choosing Y rather than E will have only a very small effect on the wage it pays in equilibrium. And even then, actual governments sets taxes contingent on Y not E, because E is hard to observe.

makes sense, thank you.

dlr: if it makes sense to you, then I'm more confident than I was that it really does make sense!

I've thought about this some more and at first I thought it depended on your definition of willingness to pay (similar to dlr's comment above). In partial equilibrium, willingness to pay should include all the information about what could have been purchased in every other market. For example, if each apple gives me 2 units of utility and each banana gives me 3 and they are the same price, isn't my marginal benefit of buying an apple actually negative (because I lose the 3 units of utility from the banana)? In the same sense, we could think of leisure as just another good and so consumer surplus should actually be (utility from the good - disutility from working long enough to buy it) and that is really what should be set to zero.

But I think your comment above explains why this intuition doesn't work. I can't make decisions about how much to buy and how much to work at the same time. Once I have earned the income, I can't then buy back my leisure time back so my only option is to buy one of the goods which have perfect price discrimination and so I can't get any of the utility I lost from working back. Therefore total expected consumer surplus ex ante will always be negative. If consumers could somehow write a contract to lock in a price before they made a decision on how much to work we could reach the efficient outcome, but without that nobody would have any incentive to work at all.

Is that right?

Chris: I *think* that's right. But notice it all works differently if we barter labour for apples. Then we would easily escape my PPD equilibrium where nobody works: the firm would offer one household just enough apples to persuade them to accept a take-it-or-leave-it offer of apples for labour to produce those apples plus maximum apple profits leftover for the firm.

I can't fully wrap my head around it, but even in barter it seems like there could be inefficiency if people want to consume more than one good. Unless they are working for each type of firm and getting paid in goods at each one, it seems like we would run into the same problem. I would have no incentive to get paid apples to trade for bananas because the price of bananas in terms of apples would be pushed so that my surplus was still zero. So I would work, but I would never work longer than my desired consumption of whatever good I am being paid in.

But then it gets tricky because I'm not sure what happens to the apple profits. I have to think more.

Chris: you could get efficiency if either:

1. Each household works for each of the n firms, and gets wages paid in kind, so there are n exchanges, each with 2 agents (firm and household). That's barter.

2. There's one big central Walrasian market where each household meets with all n firms at the same time, and the n+1 parties to the exchange.

The trouble with micro is that they are a bit sloppy about specifying how many markets there are, and what gets swapped by who in each market. (Macro aren't much better).

But even with working at each of the n firms, is it always efficient? What if workers have different productive abilities. So one guy is really good at producing apples but would also like to consume bananas. Workers should produce according to comparative advantages, but if the only way to get a good is to produce it and get paid those wages then it seems like this specialization wouldn't happen.

Chris: I think you're right on that. With differing types of labour, they would need to use some sort of medium of exchange.

This is the progressive tax model, you first buy one progressively priced unit of government good then go shopping for regular stuff.

So, the government agent stands outside of WalMart, and they make you buy your quota of government good before you enter the store. But, you need twice as many government agents as you have Walmart clerks, because the government agents need a complete sample of customers queues before they measure the income adjusted price. They have to process customers at least twice the rate as Walmart clerks.

Another option is to have everyone buy a government good in January, then they are free of government for 11 months. That solution will cycle, the government agents cannot keep up.

The third option is TBTF banking. Any agent can maintain a triple entry accounting system, and bank directly with the central bank. Because they agree to cover the government share, they get low rates on overnight money. This third option gets you a stable split between high powered money and retail money.

Have you ever tried a mangosteen before? I vaguely remember trying one a while back and really liking it. Problem is that they are relatively rare here in California. Personally, I'd be willing to pay a lot more for a mangosteen than for an apple. What would happen if everybody paid their max WTP for mangosteens? Mangosteen farmers would sure be happy. Except, this would mean more mangosteen farmers, and more mangosteens. As they became more common, people's max WTP for them would decrease accordingly.

Buying mangosteens has an inherent contradiction. On the one hand, I want to pay the smallest amount possible (maximize consumer surplus)... but on the other hand, I also want the supply to be optimal. These two desires are mutually exclusive. The better the deal that I get, the less accurate the signal that my payment sends.

A good way to bump the intuition is to eliminate the buying aspect entirely. Imagine if Netflix subscribers could decide for themselves how they divide their subscription dollars among all the content. They'd still have unlimited access to the content. In this case, the subscribers aren't buying the content. They are simply and solely using their subscription dollars to direct society's resources. If you perceive that there's a shortage of nature shows, then you'd spend more of your subscription dollars on nature shows. The amount that you spent would accurately signal your perception of the size of the shortage. There'd be absolutely no point in trying to get a deal. It's not like you'd have the option to spend your subscription dollars outside of Netflix.

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