![]() The fixed-proportions production function comes in the form f ( x 1, x 2, …, x n ) = M i n. Isoquants provide a natural way of looking at production functions and are a bit more useful to examine than three-dimensional plots like the one provided in Figure 9.2 "The production function". It is illustrated, for a 0 = 1, a = 1/3, and b = 2/3, in Figure 9.1 "Cobb-Douglas isoquants". For example, with two goods, capital K and labor L, the Cobb-Douglas function becomes a 0 K aL b. The constants a 1 through an are typically positive numbers less than one. It takes the formį ( x 1, x 2, …, x n ) = a 0 x 1 a 1 x 2 a 2 … x n a n. is the product of each input, x, raised to a given power. is the mapping from inputs to an output or outputs.įor the most part we will focus on two inputs in this section, although the analyses with more than inputs is “straightforward.”Įxample: The Cobb-Douglas production function A production function that is the product of each input, x, raised to a given power. The production function The mapping from inputs to an output or outputs. The production function that describes this process is given by y = f( x 1, x 2, …, xn). We can describe this firm as buying an amount x 1 of the first input, x 2 of the second input, and so on (we’ll use xn to denote the last input), and producing a quantity of the output. Hence, it is useful to begin by considering a firm that produces only one output. However, we can view a firm that is producing multiple outputs as employing distinct production processes. Starbucks takes coffee beans, water, some capital equipment, and labor to brew coffee. A computer manufacturer buys parts “off-the-shelf” like disk drives and memory, with cases and keyboards, and combines them with labor to produce computers. An earth moving company combines capital equipment, ranging from shovels to bulldozers with labor in order to digs holes. For example, a bakery takes inputs like flour, water, yeast, labor, and heat and makes loaves of bread. ![]() Are there any convenient functional forms?.How is the output of companies modeled?.
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