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Allocative efficiency is a state of the economy in which production is aligned with the preferences of consumers and producers; in particular, the set of outputs is chosen so as to maximize the social welfare of society. [1] This is achieved if every produced good or service has a marginal benefit equal to the marginal cost of production.
Productive efficiency: no additional output of one good can be obtained without decreasing the output of another good, and production proceeds at the lowest possible average total cost. These definitions are not equivalent: a market or other economic system may be allocatively but not productively efficient, or productively but not allocatively ...
By doing so, it defines productive efficiency in the context of that production set: a point on the frontier indicates efficient use of the available inputs (such as points B, D and C in the graph), a point beneath the curve (such as A) indicates inefficiency, and a point beyond the curve (such as X) indicates impossibility.
In the short-run, perfectly competitive markets are not necessarily productively efficient, as output will not always occur where marginal cost is equal to average cost (MC = AC). However, in the long-run, productive efficiency occurs as new firms enter the industry. Competition reduces price and cost to the minimum of the long run average costs.
An example PPF: points B, C and D are all productively efficient, but an economy at A would not be, because D involves more production of both goods. Point X cannot be achieved. Productive efficiency occurs under competitive equilibrium at the minimum of average total cost for each good, such as the one shown here.
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Then in order to reposition society at the desired point α' it is not necessary for the government to redistribute resources in such a way that Octavio holds (α' x,α' y) and Abby holds the complement: it is sufficient to reallocate resources to take the economy to any point (say α) on the price line through α', and then leave the market to ...