Question

Assume inverse demand is linear, and that marginal costs are linear but increasing. Show that DWWL = (PmQm )K/2ε, where K = (Qc - Qm )/Qm, and that K < 1.

Answer 1

Answer:

Given that,

Assume inverse demand is linear, and that marginal costs are linear but increasing.

Show that DWWL = (PmQm)K/2ɛ, where K= (Qc - Qm )/Qm, and that K<1.

MARGINAL COST :

Marginal Cost is the increase in cost caused by producing one more unit of the good.

The Marginal Cost curve is U shaped because initially when a firm increases its output, total costs, as well as variable costs, start to increase at a diminishing rate. ... Then as output rises, the marginal cost increases.

Marginal cost is not the cost of producing the "next" or "last" unit.The cost of the last unit is the same as the cost of the first unit and every other unit. In the short run, increasing production requires using more of the variable input — conventionally assumed to be labor. Adding more labor to a fixed capital stock reduces the marginal product of labor because of the diminishing marginal returns. This reduction in productivity is not limited to the additional labor needed to produce the marginal unit – the productivity of every unit of labor is reduced.

Thus the cost of producing the marginal unit of output has two components: the cost associated with producing the marginal unit and the increase in average costs for all units produced due to the "damage" to the entire productive process. The first component is the per-unit or average cost. The second component is the small increase in cost due to the law of diminishing marginal returns which increases the costs of all units sold.

Since the wage rate is assumed constant, marginal cost and marginal product of labor have an inverse relationship—if the marginal product of labor is decreasing (or, increasing), then marginal cost is increasing (decreasing), and AVC = VC/Q=wL/Q = w/(Q/L) = w/APL

Private versus social marginal cost :

Of great importance in the theory of marginal cost is the distinction between the marginal private and social costs.Externalities are costs (or benefits) that are not borne by the parties to the economic transaction.

A producer may, for example, pollute the environment, and others may bear those costs. A consumer may consume a good which produces benefits for society, such as education; because the individual does not receive all of the benefits, he may consume less than efficiency would suggest. Alternatively, an individual may be a smoker or alcoholic and impose costs on others. In these cases, production or consumption of the good in question may differ from the optimum level.

Device that converts work into thermal E. (Qc).

During the cycle,

Heat (Qc) is absorbed from a source at low T (e.g. outside air or food) by a circulating fluid.

Work is done on the engine by a compressor.

Heat (Qh) is expelled to a source at higher T (e.g. room).

Since it is a cyclic process, ∆U = 0. Thus, W = Qtotal  W = Qh – Qc

K = coefficient of performance = ratio of heat transferred to work required to transfer the heat.

K = Qc / W = Qc / (Qh – Qc)

K can be much larger than 100% (denominator < 1).

A perfect refrigerator would transfer heat from a colder body to a hotter body without doing any work. From 2nd law of thermo, this is impossible.

E.g. K of a refrigerator = 5 or 6

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