3.7. Costs

In order to produce output, the firm needs to employ inputs. But a given level of output, typically, can be produced in many ways. There can be more than one input combinations with which a firm can produce a desired level of output. In Table 3.1, we can see that 50 units of output can be produced by three different input combinations (L = 6, K = 3), (L = 4, K = 4) and (L = 3, K = 6). The question is which input combination will the firm choose? With the input prices given, it will choose that combination of inputs which is least expensive. So, for every level of output, the firm chooses the least cost input combination. Thus the cost function describes the least cost of producing each level of output given prices of factors of production and technology.

This chunk discusses how firms choose the combination of inputs to produce outputs efficiently. Firms can produce the same output using different combinations of inputs, but they will always opt for the least expensive combination. Thus, the cost function helps determine the minimum cost required to reach a desired output level based on input prices and the firm's technology.

Imagine you're baking cookies. You could use either chocolate chips or nuts as an ingredient alongside flour and sugar. If chocolate chips are on sale, you might choose them over nuts to keep your costs down. Just like in baking, firms look to minimize their costs while still achieving the desired quantity of cookies—or in their case, products.

In the short run, some of the factors of production cannot be varied, and therefore remain fixed. The cost that a firm incurs to employ these fixed inputs is called the total fixed cost (TFC). Whatever amount of output the firm produces, this cost remains fixed for the firm. To produce any required level of output, the firm can adjust only variable inputs. Accordingly, the cost that a firm incurs to employ these variable inputs is called the total variable cost (TVC). Adding the fixed and the variable costs, we get the total cost (TC) of a firm: TC = TVC + TFC.

This chunk explains the differentiation between fixed and variable costs in the short run. Total fixed cost (TFC) remains constant regardless of output levels, while total variable cost (TVC) increases as production levels increase. The total cost (TC) incurred by the firm is the sum of TFC and TVC. Understanding these cost types is crucial for firms to manage their expenses effectively.

Think of a gym membership as your fixed cost; whether you go often or not, you pay the same fee. In contrast, your variable costs could be your expenses for drinks, snacks, or gear, which change based on how often you visit or how much you engage in different activities. Your total gym expenses reflect both fixed fees and your variable spending.

The short run average cost (SAC) incurred by the firm is defined as the total cost per unit of output. We calculate it as SAC = TC/q. Similarly, average variable cost (AVC) is defined as the total variable cost per unit of output, calculated as AVC = TVC/q. Average fixed cost (AFC) isTFC/q. Clearly, SAC = AVC + AFC.

This chunk introduces average costs, which are calculated by dividing total costs by the quantity of output produced. The average costs provide insight into how efficiently a firm is utilizing its resources. As output increases, these average costs can change, impacting the firm's profitability.

Consider you're running a lemonade stand. If you sell 10 cups for a total cost of $20, your average cost per cup is$2. If you then improve your stand and can sell 20 cups for the same total $20 cost, your average cost per cup drops to$1. It illustrates how scaling up production can reduce overall costs per item.

Now let us see what these short run cost curves look like. You could plot the data from in Table 3.3 by placing output on the x-axis and costs on the y-axis. Total cost is the vertical sum of total fixed cost and total variable cost.

This chunk explains how cost curves are represented graphically, illustrating the relationship between output levels and costs. By plotting fixed and variable costs together, one can visualize how total costs change with varying levels of production. Typically, the representation includes the shapes of various cost curves, showing increases in costs as production expands.

Picture a mountain rising in the distance. As you hike upwards (increasing output), you begin to feel the effort of climbing (increased costs). The further you go, the more effort it takes, much like how a business's costs can increase as it scales its production. Eventually, you may find an easier path that requires less energy even as you push on (showing economies of scale).

In the long run, all inputs are variable. There are no fixed costs. The total cost and the total variable cost therefore, coincide in the long run. Long run average cost (LRAC) is defined as cost per unit of output, i.e. LRAC = TC/q. Long run marginal cost (LRMC) is the change in total cost per unit of change in output.

In the long run, firms can adjust all inputs according to their needs, eliminating fixed costs and allowing for total cost to equal total variable cost. This flexibility enables firms to better respond to changes in demand and production while efficiently managing costs. Understanding long run costs is essential for planning future growth.

Imagine a restaurant expanding from just take-out to offering dine-in service. Initially, your investment in kitchen equipment (fixed costs) doesn't change. But as you decide to add seating, hire more staff, and adjust your menu (all variable inputs), your operational expenses adapt to this growth. The cost structures shift to accommodate new business models in a competitive landscape.

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