Solow Model Graphing: A Visual Guide

Welcome to the Solow Growth Model! Today we'll explore how economies grow and develop over time.Let's start by setting up our coordinate system. The horizontal axis represents capital per worker, while the vertical axis shows output per worker.First, we'll draw the production function, f of k. This curve shows how output increases as we add more capital per worker.Notice how the curve becomes flatter as capital increases. This represents diminishing returns to capital - each additional unit of capital produces less additional output.Next, we'll add the depreciation line. This straight line starting from the origin shows how capital wears out over time and must be replaced.The slope of this line represents the combined effect of population growth rate n and depreciation rate delta.Let's review the key components of our model. These variables will be crucial for understanding economic growth.Let's note some important technical details about these curves that will be crucial for understanding the model's dynamics.Now that we have our basic framework set up, we're ready to explore how investment affects this model.Now that we have our production function and depreciation line, we can identify the steady state.To find the steady state, we first multiply the production function by the savings rate s, which in this case is 0.6. This gives us the investment curve.The steady state occurs where the investment curve intersects the depreciation line. At this point, k-star, investment exactly equals depreciation.At the steady state, the amount of new investment precisely equals the amount of capital that needs to be replaced due to depreciation and population growth.When the economy reaches this point, it will remain there unless external factors change the savings rate, depreciation rate, or production technology.At this steady state, the capital per worker is 4 units, resulting in an output per worker of 4 units.Now that we have our steady state identified, let's analyze how the economy moves toward this equilibrium point.The steady state occurs at k-star, where investment equals depreciation.When capital per worker is below k-star, investment exceeds depreciation. This gap represents additional capital accumulation.Conversely, when capital per worker is above k-star, depreciation exceeds investment, causing capital to decrease.Let's watch how an economy with low capital converges to the steady state.Similarly, an economy with excess capital will naturally converge back to k-star.Let's summarize what we've learned about economic dynamics in the Solow model.This concludes our exploration of the Solow Growth Model.