Economics and Statistics

Let's have an exercise on deriving a long run average cost curve in order to fully understand how this process works: Assume that you have the following production function, wage (w) , and rent (r): Then, solve for L: Create a short run total cost function where the whole function is expressed in terms of Q and K: Find the level of capital (K)  that minimizes the total cost function. Simply take the derivative of the short run total cost function with respect to K and set it equal to zero. Solve for K: We have enough information to derive the long run cost function. Simply replace L and K by equivalent functions that are expressed in terms of Q only: The last step needed to obtain the average long run cost function is to divide the long term cost function by Q: We can see that this production function is experiencing economies of scale, as the quantity produced increases, the long term average cost diminishes. Let's graph this: Minimize short run average cost: Remember th...

We have so far introduced the concept of demand, supply, and consumer choice theory. It is time to pay attention to the agents that compose the supply curve. Firm: a firm is composed of one or more individual that work in order to produce goods or services. A firm's revenue is the total amount of money collected from selling its products. Profit is equal to the revenue minus the cost associated to produce the goods or services. Firms decide the quantity of goods they will produce based on their available factors of production: land, labor, R&D, and capital. These factors of production form a firm's production function, which is used to determine the quantity to produce. The production function is the amount of output (total product) a firm can produce given its inputs. It is often assumed that the level of capital (machines) and technology is fixed in the short run. Therefore, in this period the only variable amount of input is labor. As a general rule, by i...