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In microeconomics, the elasticity of substitution is the rate at which you can substitute one type of input with another, such as substituting labor with capital. Analyzing the elasticity of substitution is especially relevant when dealing with production that can involve varying levels of input. The elasticity of substitution will depend entirely on the nature of the firm's production function.
The Production Function
The production function shows the relationships of a firm's inputs with its outputs, and expresses such a relationship by a mathematical formula. The two inputs are classified as either labor or capital. The equation is: Y = aK + bL; where "Y" is output, "K" is capital and "L" is labor. Additionally, both capital and labor are multiplied by a constant, called alpha, or "a," for capital and beta, or "b," for labor. This is known as the linear production function. Another type of production function, known as the Cobb-Douglas production function, has both capital and labor multiplied together instead of added up. Additionally, both capital and labor are raised to alpha and beta, not multiplied by it.
Behavior of the Production Function
When a firm increases its inputs, output will increase to an extent. The extent to which output increases depends on the two constants alpha and beta. So, if labor increases by one, and if beta equals 0.5, output would then increase by 0.5 units. Also note that if alpha and beta are added together, the sum would be equal to one. Therefore, both alpha and beta are always less than one but greater than zero. When graphed with labor on the y-axis and capital on the x-axis, the production function takes a form of a series of straight and parallel lines connecting both axes. With the Cobb-Douglas function, the graph takes a convex shape that is bent towards the graph's origin.
The Elasticity of Subsititution Between Production Factors
The elasticity of substitution is applicable in many areas in economics. In terms of a production function, it measures the degree to which one factor of production can substitute for another factor to produce the same level of output. For example, if you have to figure out how many units of labor have to substitute for one unit of capital to obtain the same level of production, you will need to utilize the production function employed by a firm.
Types of Substitution
In the case of the linear production function, perfect substitution takes place. In other words, one unit of labor may be exchanged for one unit of capital. In terms of a Cobb-Douglas production function, however, a unit elasticity of substitution occurs. The rate of substitution depends on both alpha and beta in such a case. Put more simply, the more convex or "bent" a Cobb-Douglas production function is, the lower the elasticity of substitution.
The Production FunctionThe production function shows the relationships of a firm's inputs with its outputs, and expresses such a relationship by a mathematical formula. The two inputs are classified as either labor or capital. The equation is: Y = aK + bL; where "Y" is output, "K" is capital and "L" is labor. Additionally, both capital and labor are multiplied by a constant, called alpha, or "a," for capital and beta, or "b," for labor. This is known as the linear production function. Another type of production function, known as the Cobb-Douglas production function, has both capital and labor multiplied together instead of added up. Additionally, both capital and labor are raised to alpha and beta, not multiplied by it.
Behavior of the Production Function
When a firm increases its inputs, output will increase to an extent. The extent to which output increases depends on the two constants alpha and beta. So, if labor increases by one, and if beta equals 0.5, output would then increase by 0.5 units. Also note that if alpha and beta are added together, the sum would be equal to one. Therefore, both alpha and beta are always less than one but greater than zero. When graphed with labor on the y-axis and capital on the x-axis, the production function takes a form of a series of straight and parallel lines connecting both axes. With the Cobb-Douglas function, the graph takes a convex shape that is bent towards the graph's origin.
The Elasticity of Subsititution Between Production Factors
The elasticity of substitution is applicable in many areas in economics. In terms of a production function, it measures the degree to which one factor of production can substitute for another factor to produce the same level of output. For example, if you have to figure out how many units of labor have to substitute for one unit of capital to obtain the same level of production, you will need to utilize the production function employed by a firm.
Types of Substitution
In the case of the linear production function, perfect substitution takes place. In other words, one unit of labor may be exchanged for one unit of capital. In terms of a Cobb-Douglas production function, however, a unit elasticity of substitution occurs. The rate of substitution depends on both alpha and beta in such a case. Put more simply, the more convex or "bent" a Cobb-Douglas production function is, the lower the elasticity of substitution.
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