Economics and Statistics

Perfect competition happens when both buyers and producers are price takers, meaning they have no (individual) influence over the price of a product. Conditions for perfect competition: Large number of producers such that no individual producer's production represents a significant part of the total output in the market. Producers must sell their products (no matter the quantity) at a market price that is outside of their control (price-taker). This means that for firm that is a price-taker, its demand is perfectly elastic (horizontal). Producers sell homogeneous goods, meaning that consumers do not care from which sellers they buy the goods from. Producers do not face barriers to entry or exit. Producers are able to enter or exit the market freely. Understanding economic graphs under perfect competition: The price (Pm) is determined in the market becomes the demand curve for an individual firm (remember the firm is price-taker). Then, if the demand is horizontal, it follows by the...

Assume that you are the owner of a small business that produces T-shirts. Your the total revenue for your business can be modeled by the following equation: and your total cost corresponds to this function: Find the point at which your firm maximizes its profit. Then, find how much profit the firm if able to earn at that point. Using the total cost and total revenue functions we can set up the profit function: Then, realize that if you want to find the maximum profit, take the derivative of the function and set it up equal to zero, and solve for Q. This is equivalent of taking the derivative of the total cost and total revenue functions and setting them equal to each other. In this problem, I chose the latter option as it was explained in the previous lessons. Notice that profit is often denoted by a capital pi.  We are assuming that the TR>TC for some positive value, you can check for yourself. However, if we did not know that, we would first take the first ...