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Differential Calculus
Published in Prem K. Kythe, Elements of Concave Analysis and Applications, 2018
2.8.5 Marginal Rate of Technical Substitution (MRTS). An isoquant determines the different levels of inputs K and L that can be used to produce a specific level of output Q. One such isoquant for the output level Q=k $ Q=k $ , k constant, is defined by aK1/4L3/4=k $ a K^{1/4} L^{3/4}=k $ , and its slope dK / dL is known as MRTS. The general form of an isoquant is aKpL1-p=k $ a K^p L^{1-p}=k $ , where a is real, 0<p<1 $ 0< p< 1 $ , and k is a constant.
Demand
Published in John E. Tilton, Juan Ignacio Guzmán, Mineral Economics and Policy, 2016
John E. Tilton, Juan Ignacio Guzmán
After the firm determines its desired level of output and hence the particular isoquant curve it wants to be on, it must select the mix of steel and aluminum it will use. This involves picking the point on the relevant isoquant curve that minimizes costs. To determine this point, economic theory constructs what it calls isocost curves. The straight lines C1 and C2 in Figure 2.6a are examples. They show the various combinations of two factors—steel and aluminum—that can be acquired for a given amount of money, for example 50 million dollars. For this sum, if the price of aluminum is 2,500 dollars per ton and steel 1,000 dollars per ton, one can buy 20,000 tons of aluminum and no steel, 50,000 tons of steel and no aluminum, or various combinations of both, such as 10,000 tons of aluminum and 25,000 tons of steel. The isocost curve C1 shows all of these possible options. It intersects the steel (vertical) axis at 50,000 tons and the aluminum (horizontal) axis at 20,000 tons, and has a slope of –2.5 reflecting the negative of the ratio of the price of aluminum to the price of steel.
Plant capacity notions: review, new definitions, and existence results at firm and industry levels
Published in International Journal of Production Research, 2023
Kristiaan Kerstens, Jafar Sadeghi
The radial input efficiency measure completely characterises the input set and can be defined as follows: It is smaller than or equal to unity , with efficient production on the boundary (isoquant) of represented by unity, and it has a cost interpretation (see, e.g. Färe, Grosskopf, and Lovell 1994).