Microeconomics Intertemporal choice Theory !
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Intertemporal preferences & optimization with two periods |
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- Intertemporal preferences: Our standard theory of consumer choice is perfectly adequate to describe intertemporal choice. The objects of choice-the consumption bundles will be streams of consumption over time.
- Intertemporal optimization with two periods: The method of dynamic programming, a technique for solving multi-period optimization problems by breaking them into two-period optimization problems.
The study of asset markets demands a general equilibrium approach. The equilibrium price of a given asset depends critically on how its value correlates with the values of other assets. Hence, the study of multi-asset pricing inherently involves general equilibrium considerations.
- Equilibrium with certainty
In a world of certainty, the analysis of asset markets is very simple: the price of an asset is simply the present discounted value of its stream of returns. If this were not so, there would be a possibility for riskless arbitrage.
- For example, a two-period model. We suppose that there is some asset that earns a sure total return of R0. That is, one dollar invested in asset ‘0’ today will pay R0 dollars next period for certain. If R0 is the total return on asset 0, r0= R0 - 1 is the rate of return.
There is another asset ‘ a ’ that will have a value
 next period. The equilibrium price of asset today:
- The core of an exchange economy :
A feasible allocation x is in the core of the economy if it cannot be improved upon by any coalition
- Convexity and size : The convexity assumption appears to be necessary for the existence of an equilibrium allocation since it is easy to construct
- Gross substitutes : Two goods, i and j, are gross substitutes
at a price vector p if  >0 for i≠j
- The compensation criterion:
It is often desirable to know when a government project will improve social welfare. For example, constructing a dam may have economic benefits such as decreasing the price of electric power and water. However, against these benefits we must weigh the costs of possible environmental damage and the cost of constructing the dam. In general, the benefits and cost of a project will affect different people in different ways-the increased water supply from the dam may lower water fees in some areas and raise water fees in other areas. How should these differential benefits and costs be compared? This criterion tries to extend that sort of analysis to a community of individuals, using the concepts of the Pareto criterion and the compensation criterion.
- Welfare functions:
The compensation methodology suffers from the defect that it ignores distributional considerations. An allocation that is potentially Pareto preferred to the current allocation has potentially higher welfare. But one might well argue that actual welfare is what is relevant. If one is willing to postulate some welfare function, one can incorporate distributional considerations into a cost-benefit analysis.
- Optimal taxation:
The optimal taxation problem is to maximize the consumer's utility with respect to the tax rates, subject to the constraint that the tax system raises some given amount of revenue
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