A description of the cost of the Senate version of the stimulus:
http://cboblog.cbo.gov/?p=204
Approximately $96 billion is spent on a $500 tax credit for workers. In Neoclassical economic theory, a lump sum tax (and likewise a lump sum subsidy) has no effect on the proportion of income spent on one activity or another. An individual is no more likely to work more or less. An individual is no more likely to save more or less. This follows under the parsimonious assumption that all goods have utility functions similar to U(x, y) = -1/a(x-h)^2 - 1/b(y-k)^2 where x and y are much less than the optimal spending h and k respectively. X and y are measured in dollars as are the costs of those goods, a and b. The sign is negative to reflect optimal consumption as one reaches (h, k).
With an income constraint I = x + y or y = I - x, we can solve for the optimal consumption:
U(x, I - x) = -1/a(x - h)^2 - 1/b((I - x) - k)^2. Set marginal utility = 0 to find max.
Ux = -2/a(x - h) +2/b((I - x) - k) = 0. Multiply through by a and b. Divide by 2.
x = (h/a - k/b+I/b) (a+b)
dx/dI = (a+b)/b. Increases in Income do not affect the relative spending. (This is based on relative costs only.)
In reality, there are certain goods for which a minimum amount of consumption is necessary, and consumption in greater quantities may not be utile. That is, for example, h is on the order of magnitude of x. In a developed country like the United States, this could be "Calories". Rather than a smooth utiliy function like U(x) = -1/a(x-h)^2, a stepwise function such as U(x) = -infinity if x/a < 1000 Calories/day and the usual otherwise where h/a = 1600 Calories/day. (1 "Calorie" is 1,000 "calories".)
In this type of good, decreases in income beyond a certain point will start to affect other goods more than calories once the minimum 1000 Calories/day is reached.
"Saving" for an individual merely constitutes consumption in the future. The above model can be readily adopted by x current consumption and y future consumption with the factor b including the discount for the difference in time.
This suggests that welfare should be provided to ensure that everyone can eat. This also suggests that paying every worker $500 or cutting taxes for those already employee will have little effect on their relative spending or on saving habits. Though more will be spent/saved after the minimum consumption levels have been reached.
There is something to be said for the argument that welfare affects an individual's decision to work more or less. But we'll say it next time:
Also:
Featured on the NY Times Freakanomics Blog:
http://freakonomics.blogs.nytimes.com/2009/02/03/chicago-economists-on-the-stimulus-package/#more-3887
More once I've had a chance to watch it.
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Will post more details later, since its memorial day and I am tired. As for minimum consumption there was a video in japan about a person who had to cut back severly probably due to deflation , eating cabbage soup.
ReplyDeleteTo the OP, you had mentioned an article about the need to raise unemployment benefits and the effect of taxes on work and leisure, those wanting changes such as college education, healthcare, which avoid disease and poverty.
ReplyDeleteI would like some clarification, as the purpose of the "middle class" tax cuts was to provide or stimulate this activity. Note, however many families won't spend the money, may save it, and at tax time many people won't even get the checks anyway due to how the tax is structred, ie it adds to your agi in certain cases.
Although there are good to be consumed, it various with family - depending on the health of the individual and his/her situation, the price of food and goods can vary by location, and there are a lot of regional differences due to the person.
Healthcare comes to mind with elderly vs. older people. Also if everybody saved there would be no thrift shop for recycled goods at times.