Introduction
The long-run cost curve is also referred to as the marginal cost of the plant. It compares the total cost of a plant with its output size. It is the slope of the long-run cost curve. If the long-run cost curve is plotted on the x-axis and the size of the plant on the y-axis, the slope will show the long-run cost of the plant. In the long-run cost curve, we see that for every increase in the output size, the long-run cost of the plant increases. It follows that the long-run cost curve for a plant is in fact the average cost of the plant and the rate of return.
Cobb-Douglas Production Function
The Cobb-Douglas Production Function is a production function that can be used to explain the production, consumption and income of an economy. The Cobb-Douglas production function is described below:
Where: Cobb-Douglas Production Function is given by
Y = A * Lᵝ * Kᵅ
where K is a constant, L is the level of output (the amount of goods that the economy produces per hour of labour) and P is the output price (the rate of output that the economy receives per hour of labour). K is the constant of the production function and L and P are the variables to the production function. P is the variable in the production function. It is a price that is paid for output.
The long-run cost curve can also be considered as the average cost curve. This is since the long-run cost is the price of output. This is the average price that the firms will pay to the firm and the rate of return. It is the long-run cost curve that is also referred to as the average cost curve.
Marginal Cost Curves
Marginal cost curves are part of the microeconomics sub-discipline and deal with costs related to production. This cost curve measures the price the firm will charge for a certain product or service. The following image shows an example of a marginal cost curve.
The following graph shows an example of a marginal cost curve for a firm in manufacturing. This graph shows the cost of producing each unit of output. This graph is also called the cost-volume or production-volume curve. The horizontal axis shows the volume of output produced, and the vertical axis shows the unit cost of producing this quantity. The solid line indicates the marginal cost of producing an additional quantity of output. The marginal cost curve is useful for determining how much profit the firm will earn at each point along the production curve.
Price-Volume Relationship
Price-volume graphs are important for understanding how the firm's profit is related to how much they make. A firm’s production and price are related by the following equation,
In the equation above, the price is given by the vertical axis and the volume is given by the horizontal axis. In this equation, P is the price per unit and K is the quantity produced. This equation can be restated as
P = K/V
Where,
P = the price per unit
K = the quantity produced per unit
V = the volume produced per unit
Marginal Cost Curve
The marginal cost curve can be thought of as a cost-volume graph. It is possible to plot all of the different costs associated with a product and add them together. To do this, we can rewrite our above equation as
A producer’s marginal cost is determined by the intersection of its cost curve with its supply curve. The intersection between a supply and a demand curve is called a Nash equilibrium.
Marginal Cost and Price Margin
A producer’s cost curve shifts from left to right as the quantity produced increases. We can illustrate this on the cost-volume curve. If the quantity produced doubles and the price doubles, the producer’s cost will double. Therefore, the change in price per unit is equal to the change in quantity produced. This is the definition of the price margin. The price margin is calculated by dividing the change in price by the change in quantity produced.
Therefore, the price margin is defined as follows:
Price Margin = (P2 – P1) / (K2 – K1)
Example
The marginal cost and price margin curves are illustrated in the following graphs.
A firm can produce three different quantities of steel. The graphs on the left demonstrate what happens when quantity is increased. As the quantity increases, the cost increases but the price decreases. In the graph on the right, the opposite is true. As price decreases, the cost is decreased but quantity is increased. The curves cross at the equilibrium price-quantity point.
When a firm starts to produce at some price and volume, it experiences a shock in production quantity and price. The firm must wait until its equilibrium price-quantity point is reached. For the graph to the left, at first, only a small amount of steel is produced. As volume increases, the price decreases and the amount of steel produced increases. The price-quantity point is reached and further changes in production will not change the equilibrium price-quantity point. The graph to the right shows what happens when volume and price are both increased. At first, only a small amount of steel was produced. As volume increases, the price decreases. Then the price-quantity point is reached and quantity is increased.
The first step in calculating price margin is to find the point at which the marginal cost and marginal revenue curves cross. To find that point, we take the derivative of each curve and find where they are equal to one another. The points are as follows:
We can substitute for P1 and P2 to get the following results:
Price Margin = (5.0 – 3.2) / (2.8 – 1.5)
Price Margin = 4.5 / 3.0
The price margin of 3 is the same as the profit margin. Because the price-quantity point is at 4.5, quantity is 4.5 units per year.
In order to find the point where the price margin and marginal cost curves cross, you must find the point at which MC = MR.
The long-run cost curve is a part of macroeconomics which deals with the production and size of a plant in an organisation. This section speaks of the variables and factors which affect the curve of the production and cost in the long run. It is important to note that there is no difference between the Long-run total costs, and the long-run cost is variable. It depends on the ability of a firm and its changing inputs at a lower price.
Apart from understanding the terms, a student needs to gain knowledge about short-run and long-run costs. A long-run is different from a short-run in various factors and inputs. Ideally, a long-run cost curve and short-run curve are distinguished with Long-run Marginal, Total and Average costs.
The Factors Needed to Determine Short Run and Long-Run Cost Curves
To determine the long-run total cost curve, an individual must know factors that affect changes in production.
Mentioned below are some factors of the long-run cost curve for drawing its graph.
1. Long-run Total Cost
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The Long-run Total Cost (LTC) is the minimum cost by which a given level of output can be determined. This long-run total cost, according to Leibhafasky, is the least cost possible in producing various output with variable inputs. It represents the smallest amount of multiple measures of production. It is seen that LTC is either less or similar to short-run total cost but can never be more than it.
2. Long-run Average Cost
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Long-run Average Cost (LAC) is the total cost divided by any level of output. It is ideally derived by long-run average price from short-run average cost curve. In the short-run turn, a firm or plant remains fixed, and the curve corresponds to a respective plant. Here the long average cost curve is termed as planning or envelope curve due to its function in preparing plans for enlarging production at a minimum cost.
A good example will be taking three sizes of plants where nothing else can be built. In the short-run curve, this plant size remains fixed, which can increase or decrease the variables. However, in the long term, a firm has the flexibility to choose the options of plants which can aid in the highest output at minimum cost.
3. Long-run Marginal Cost Curve
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In Long run Marginal Cost (LMC), the added cost of production and the unit of a product becomes a variable. This cost can be derived from short-run marginal cost.
The long-run cost curve is a vast chapter with diagrams and explanations on determining variables. These graphs and curves make a significant part of a firm's production and sale.
A student needs to understand these theories and concepts better to secure a good ranking in exams. Vedantu is one such educational site that offers an in-depth explanation of the short-run cost and long-run cost and its function.
They also offer pocket-friendly study material and solutions on a long-run cost function with exercises. To enjoy these features, download the app or log in to the website now.
FAQs on Long-Run Cost Curves: Analysis and Trends
1. What is the fundamental difference between short-run and long-run cost analysis in economics?
The key difference lies in the flexibility of production inputs. In the short run, a firm operates with at least one fixed input (like factory size or machinery) and other variable inputs (like labour). In the long run, all production inputs are considered variable. This means a firm can change its plant size, adopt new technology, or alter any factor to find the most efficient production method for a desired output level.
2. What does the Long-Run Average Cost (LAC) curve represent?
The Long-Run Average Cost (LAC) curve illustrates the minimum possible average cost for producing any given level of output when a firm has the flexibility to adjust all of its inputs. Each point on the LAC curve corresponds to a different scale of operation or plant size, representing the lowest per-unit cost achievable for that output in the long term.
3. Why is the LAC curve often called the 'planning curve' or 'envelope curve'?
The LAC curve is known as a 'planning curve' because it helps a firm plan its future expansion and decide on the optimal plant size to build to achieve a target output at the lowest possible cost. It is called an 'envelope curve' because it tangentially envelops or encloses a series of Short-Run Average Cost (SAC) curves, with each SAC curve representing a specific plant size. The LAC curve is the locus of these tangent points.
4. What causes the typical U-shape of the Long-Run Average Cost (LAC) curve?
The U-shape of the LAC curve is determined by the laws of returns to scale. Initially, as a firm increases its scale of production, it experiences economies of scale, causing the average cost to fall. After reaching an optimal point, further expansion leads to diseconomies of scale, causing the average cost to rise. This transition from falling to rising average costs gives the LAC curve its characteristic U-shape.
5. What are examples of economies and diseconomies of scale?
These concepts explain why long-run average costs change with the scale of production.
- Economies of Scale (Falling Costs): These are advantages of large-scale production, such as technical economies from using specialized machinery, managerial economies from division of labour, and financial economies from getting better loan terms.
- Diseconomies of Scale (Rising Costs): These occur when a firm becomes too large, leading to challenges like poor communication between departments, coordination difficulties, and decreased employee morale, all of which increase the per-unit cost.
6. How is the Long-Run Marginal Cost (LMC) curve related to the LAC curve?
The relationship between LMC and LAC is similar to any marginal-average relationship.
- When LMC is below LAC, it pulls the average cost down, so the LAC curve is falling.
- When LMC is above LAC, it pulls the average cost up, so the LAC curve is rising.
- The LMC curve intersects the LAC curve at its lowest point. This point represents the most efficient scale of production for the firm in the long run.
7. What does the Long-Run Total Cost (LTC) curve show?
The Long-Run Total Cost (LTC) curve shows the minimum total cost of producing various levels of output when all inputs are variable. Unlike the short-run total cost curve, the LTC curve always starts from the origin (0,0), because in the long run, a firm incurs zero cost if it produces zero output, as there are no fixed costs.
