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 explored the concept of the costs in the short run, it is now time to determine the costs in the long run. But first, let's define the term long run. In economics, the long run occurs when all variables are not fixed. In other words, the long run for a firm is when a firm can change all of its inputs. Then, all costs are variable in the long run. In this time frame a firm is not only able to change the number of workers but also the size of its factories and the number of machines (also known as capital). In the graph below, you can see a number of different short run average total cost (SRATC) curves that depend on the different levels of fixed inputs. At first, the SRATC curves get lower as the firm increases its size, then it flattens out. Finally,  the SRATC curves get higher. These three effects are caused by different economies of scale. The leftward region on the graph represents the economy of scale, where by increasing each input by a constant increas...

We have so far talked about the short run cost for firms. It is now time to do some problems to make sure that the reader gets conformable with these types of problems. Exercise 1 requires the use of a cost data table, and exercise 2 requires knowledge in Calculus. 1). A firm has the following cost data: Ouput (Q)  Total Cost (TC)   Variable Cost (VC)  523 $6500 $2500  524 $6725 $2725  525 $7025 $3025 Find the ATC, AFC, AVC, and MC at these output levels. Remember the total cost formula: Then, in order to find FC just do the following: Finally all you need to do is to divide each of these terms by  each output level to find the ATC, AFC, and AVC.  Regarding the MC, remember the formula: Then, Solution to problem 1: ATC  AFC  AVC  MC $(6500/523) $(4000/523) $(2500/523) n.a $(6725/524) $(4000/524) $(2725/52...

In Economics, the term short run refers to a time period where at least one variable of interest does not change . In our case, the short run for a firm is when at least one input  (labor, land, capital) stays fixed. Usually land and capital are considered fixed in the short run.  If an input is fixed during a period time, no matter how much the total product a firm produces, its cost stays the same. This cost is commonly known as fixed cost (FC). Examples of fixed costs: rent, property taxes, loan payments. Labor is often considered to be a part of the  variable cost (VC) . Variable cost can be defined as the cost a firm has control over during the short run. Unlike fixed cost, variable cost increases (decreases) as a firm's total product increases (decreases). Examples of variable costs include: utility bills, wages, raw materials A firm's total cost (TC) is the sum of its variable and fixed costs. As you can see, the fixed cost...

You are given the following table of production, fill in the blank. Then graph the total product, average product and marginal product curves with respect to labor. Labor (L)  Capital (k)  Output (Q)  Average Product (Q/L)   Marginal Product 4 3 51 ... n.a 5 3 ... 12.4 ... 6 3 ... ... 7 7 3 ... ... 2 8 3 ... 8.75 ... The solution is: Labor (L)  Capital (k)  Output (Q)  Average Product (Q/L)   Marginal Product 4 3 51 (51/4) n.a 5 3 62 (62/5) 11 6 3 69 (69/6) 7 7 3 71 (71/7) 2 8 3 70 (70/8) -1 If you know the average output and the number of workers (labor) then you know the output at each level (recall the formula for AP). If you know the marginal pro...

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...

You are given a table containing the quantities, price, and marginal utilities of two goods, fudge and coffee, which consumer A purchases. Table:  Fudge  Coffee Quantity of purchase 11 pounds 6 pounds Price per pound $3 $3 Marginal utility of last pound 13 24 If consumer A spends all of their income on these two goods, what should consumer A do in order to maximize their utility? (hint: remember the utility maximizing rule) since we know that the utility is maximized when: Let's use the information from the table above,  we can clearly see that the marginal utility for coffee is greater than that of fudge. Utility is subjected to the law of diminishing marginal utility ; marginal utility (MU) diminishes as consumers buy more. Thus, in order to maximize their utility, consumer A needs to buy more coffee and less fudge up until the ratio of the MU of coffee over its price is equal to the ratio ...