Butter can be bought and sold at the market at a single price. Firms produce butter and then sell it to consumers. Consumers seek to maximize the "utility" they enjoy from having wealth and consuming butter, but they can only consumer more butter by giving up some of their wealth. Firms seek to maximize profits by producing butter at a cost and then selling butter to consumers. (Firms are coincidentally also owned by consumers, whose wealth is partly dependent on the profits generated by the firms they own.)
What determines the "single price" in the market? An unspecified process known as "reaching equilibrium." If the price of butter is too high, then producers will be encouraged to produce lots of it, but then will not be able to sell all of it at this price. If the price of butter is too low, then consumers will want to buy lots of it, but producers will not produce enough to meet demand. In either of these cases, there will be "pressure" to move prices in one direction or the other. At the equilibrium price, this pressure disappears -- the market clears.
There are two questions to consider: 1) how much butter is produced and 2) how much of the produced butter is allocated to each consumer.
For consumers, more butter is better, although the gains in utility from more butter decrease as more butter is consumed ("diminishing marginal utility"). The consumer faces a tradeoff in enjoying more butter and paying for it. The first unit* of butter is likely to bring in a lot of utility, worth more than the price of butter, but as additional units of butter are consumed this eventually becomes untrue. So the consumer's consumption is determined by
Marginal Utility of Butter to Consumer = Cost of Butter to Consumer (= Market Price)
For firms, the cost of producing butter typically decreases with the initial production of a few units, due to fixed costs; it later eventually rises. Because they want to maximize profits, firms increase production until the gain from selling more butter (market price) no longer exceeds the cost of making more butter. So the firm's production is determined by
Marginal Cost of Butter to Firm = Market Price
So the market determines the total amount of butter produced, and how it is allocated to consumers.
We next compare the performance of the "free market" to the performance of an Omniscient Planner who selects how much butter is to be produced by each firm and how much butter is to be consumed by each consumer. To avoid getting too bogged down with normative comments, we only compare outcomes if one is at least as good as the other for every consumer.
1. If the planner wants to produce the same amount of butter as the market solution, it is impossible to do it cheaper than the market solution.
2. If the planner decides to produce more (less) butter than the market solution, then it is possible to select a better outcome.
3. If the planner produces the same amount of butter as the market solution, but distributes it differently, then it is possible to select a better outcome.
The basic argument is that if one consumer would prefer cash to butter, and another would prefer butter to cash, then they could each made better off at no cost to anyone else by simply trading butter for cash. This will be the case when we are not at the market equilibrium.
From this reasoning we have the two Fundamental Theorems of Welfare Economics:
1. Market equilibria are Pareto optimal.
2. All Pareto optimal outcomes can be achieved through market equilibria (and the redistribution of initial wealth).
*Being able to define butter in "units" is one of a myriad of assumptions used here. Some more important assumptions are: 1. being able to assume away the equilibrium process; 2. firms lacking any sort of market power and being easily undercut by competition; 3. consumers' utility functions are completely independent; 4. optimal outcomes are described with minimal reference to the distribution of wealth.
This post will be modified again in the future, but I need to move on now.
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