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
1. Why is the long-run cost curve in u shape?
The long-run curve is usually U in shape due to various reasons. The economies and diseconomies of a scale cause the angle to change. If a company has high fixed costs, then the increasing output leads to a lower average price. They can also experience diseconomies in a specific production if variable changes. The variable like increased output which leads to a higher average cost in an economy.
A good example will be a big firm where communication and coordination between co-workers are difficult. It is essential to know that not all firms will experience this diseconomy of scale. There are chances that LARC could be sloping downwards.
2. What is LRAC in production and cost run?
The long-run average cost (LRAC) curve shows all possible output levels against an average cost In a U-shaped curve. It is made of ATC curve tangency points that are short-run curves in nature. Here the point of the efficient scale is the LRAC curve with a minimum average cost for a firm.
Moreover, each output point on the LARC curve shows a particular combination of labour and capital. It is essential to know that a firm can change both capital and labour that is possible in the long run. In the short run, money can get frozen.
3. What is a LAC curve?
LAC or the long-run cost curve shows the relation between average total cost and output at a fixed price to minimise average total cost. There are ideally no fixed inputs in the long run as all the inputs are variable. In the long term, a firm can easily change all its inputs. There are Scale returns to a decreasing point when a long-run average total cost increases with an increase in output.
In the short run, the size of a scale or plant remains fixed whereas in the long-run changes can be made accordingly. Moreover, in the long run, a firm can give rise to various cost relationships as it can move from one plant to another. It can also build a large plant or smaller one depending on the need.
