To do this, we must remember two rules: i) the power rule and ii) the product rule. By using the properties of natural logarithmic functions (ln) to linearize the Cobb-Douglas function, we will use a regression model to provide estimations for Beta 1, Beta 2, and thus find out A.ġ) Transform the Cobb-Douglas function into a ln function. In order to find out A, we would need to estimate the elasticities for both labour and capital with respect to output (the Beta 1 and Beta 2 values). Using the labels from your example, Y represents GDP, K represents capital formation, and L represents total employment. ![]() (Note: Beta 1 can also be known as alpha and Beta 2 referred to as beta nevertheless, we use Beta 1 and Beta for simplicity)Įssentially, this equation above highlights that Y is impacted by total factor productivity, labour (dependent on its elasticity Beta 1 with respect to Y), and capital (dependent on its elasticity Beta 2 with respect to Y). The typical Cobb-Douglas production model looks like this: In addition, this model takes into account total factor productivity, represented as A below. I used a Cobb-Douglas production function for the productivity calculation because this model demonstrates a relationship between output and two key inputs-capital (K) and labour (L)- which are featured in your example. ![]() Calculating Total Factor Productivity (A) in a Cobb-Douglas Production Function (Output Generated by Capital and Labour Inputs)
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |