Online Tutoring Microeconomics Technology & Specification
Online Assignments help of Microeconomics Technology,Specification,Cobb-Douglas,Leontief Technology and Profit Maximization
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The simplest and most common way to describe the technology of a firm is the production function,
- Measurement of inputs and outputs: A firm produces outputs from various combinations of inputs. In order to study firm choices we need a convenient way to summarize the production possibilities of the firm, i.e., which combinations of inputs and outputs are technologically feasible.
- Specification of technology:
the firm has n possible goods to serve as inputs and/or outputs.
- Cobb-Douglas technology: Let a be a parameter such that 0 < a < 1. Then the Cobb-Douglas technology is defined in the following manner.
- Leontief technology: Let a > 0 and b > 0 be parameters. Then the Leontief technology is defined in the following manner.
- Profit maximization:
The profit-maximizing amount of input occurs where the slope of is profit line equals the slope of the production function.Let us consider the problem of a firm that takes prices as given in both its output and its factor markets. Let p be a vector of prices for inputs and outputs of the firm. The profit maximization problem of the firm can be stated as
π (p) = max py such that y is in Y.
Since outputs are measured as positive numbers and inputs are measured as negative numbers, the objective function for this problem is profits: revenues minus costs. The function π(p), which gives us the maximum profits as a function of the prices, is called the profit function of the firm.
- Difficulties:
- It may happen that the technology cannot be described by a differentiable production function, so that the derivatives described above are inappropriate.
- The calculus conditions derived above make sense only when the choice variables can be varied in an open neighborhood of the optimal choice.
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