Cost analysis in the long run is quite different from short run cost analysis. Period analysis tells us that in the long run all factors are variable; this flexibility of factors will consequently be reflected in the long-run cost curves. This long-run curve will be formed by different period short-run curves and will serve as an envelope for all of them. Isoquants are used to compare the short-run periods with the long-run one. At each period we have a combination of labour and capital such that the firm will choose to minimise costs at each output level. The curve that joins the points of tangency between different isocost lines and isoquants is known as the expansion path.

One of the key features of the long-run is the possibility of firms entering and/or exiting the market. Economic profits will attract new entries to the market while economic losses will throw firms out of it. This process will occur whenever profits are different to 0. The equilibrium price will be influenced by the number of firms in the market, decreasing as the number of firms increases. Let’s say we start at E₁, where the firm we consider has profits equal to area A. It is able to supply products from point X onwards, due to its minimum efficiency requirements. Since there are profits, other firms will be attracted and will enter the market. Due to a new firm entering the market, market supply will shift to the right, since there are now more firms supplying the same goods. This increase in supply will force prices down to p₂. The firm we’re analysing still has profits at this point, but these profits decreased because of the new firm entering the market. Let’s say another firm enters the market, pushing again market supply to the right. This has the same effects, but this third firm has pushed marginal costs to its minimum, as well as average costs. Now, the three firms (including the one we’re analysing) supply such a quantity at such a price that there are no profits, nor losses, which will mean this market has reached its equilibrium, with no firms entering or exiting it. 

Once this market equilibrium is reached, one might ask: what happens if there is an increase in demand? First, this will shift market demand to D’, increasing prices because supply (for the moment) is given. This increase in prices allows for profits to be made, at point 1. However, as seen before, these profits will attract new firms, which will force supply to the right (S’), going to an equilibrium such as E₂, where our firm will produce the exact same initial quantity (point 2).

The long-run market equilibrium is conformed of successive short-run equilibrium points. The supply curve in the long run will be totally elastic as a result of the flexibility derived from the factors of production and the free entry and exit of firms (imagine the firm-entry process portrayed before a few more times). In the long run, market demand will only affect the number of firms but not to the quantity produced by each of these firms. Therefore we can assume that the equilibrium in the long run is the point where profits are maximised (although each firm achieves zero economic profit), there are no firms entries nor exits and there is market clearance.

Short run cost analysis would not be properly taught without the inclusion of demand and supply curves and their correct understanding, specially how its shifts may affect firms’ cost functions. The total supply of the industry is the aggregate of the supply of all the individual firms.

The amount that is produced by each individual firm is subject to its optimal level of production. We must consider that the optimum production level of a firm is that in which marginal revenue (price) equals marginal cost, as long as it also covers its average variable costs. If this is not the case the firm will not achieve its highest level of profit and could even be incurring in losses.

It is common that input prices vary over time, causing firms to have to make adjustments. In order to optimise, firms will have to constantly adapt their production to the changes in their marginal costs. If a firm fails to adequate its production to the new marginal costs, there will be a loss in profits.

The equilibrium point between the aggregate demand of a product and its aggregate supply will be subject to variations if one of them suffers a change, and thus producing a new equilibrium price and quantity. These shifts may come from either the demand or the supply side. Let’s analyse thoroughly what happens to quantity sold by a given firm when there is a shift in either the demand or the supply curve.

Examples of shifts in demand include changes in income or changes in the price of the substitute goods. It must be noted that the aggregate supply curve starts at X, and not before, because a lower quantity would get producers to incur in losses. Also, notice that we assume firms are getting at least some profits (area A) because in the short term only labour is variable, which means that there are no firms entering this market, even though profits exist. Let’s say there is an increase of consumers’ income, which would increase the aggregate quantity demanded at a given price, thus shifting the demand curve to the right (D’ would be our new demand curve). Because there are no changes affecting the supply curve, the new equilibrium would be E₁, which means more quantity sold by each firm, as well as an increase in total quantity sold (Q₁). Since the cost functions of each firm are the same, each firm would be selling more quantity at a higher price (p₁), which would increase their profits (from area A to area B). To sum up, in the short term, an increase in demand would increase each firm’s profits by the area B-A, which would depend on both the marginal and average total cost, as well as the increase on quantity. 

Shifts in the supply curve are caused by changes in outputs’ prices, technological innovations and changes in the number of firms in the industry. The last two cases, however, are not associated to the short-run. So let’s say there is a drop in the price of an input, used by all firms during their production process. This would decrease marginal costs and therefore average variable and total costs, which shifts each curve downwards (left, in red). Since the supply curve we consider is the aggregate of all firms’ supply, the aggregated supply curve also shifts downwards. Note that, since there are now lower marginal and average costs, the lowest point of the supply curve drops to X’. The new equilibrium would be E₂, with a decreased price of p₂. The new profits of each firm, C, is determined by both the new quantity produced and the drop in marginal and average costs. Even though in this case profits increase, profits can either increase or decrease. To sum up, in the short term, a reduction of inputs’ prices shifts the supply curve to the right and decreases market prices, but has undetermined effects on each firm’s profits.

Demand and supply are possibly the two most fundamental concepts used in economics. The concept of market is usually defined as a number of buyers and sellers of a given good or service that are willing to negotiate in order to exchange those goods. We will first explain them separately and then jointly to show their interaction.

Demand:

Demand is the global market value that expresses the purchasing intentions of consumers. The demand curve shows the quantity of a specific product that individuals or society are willing to buy according to its price and their income. This curve shows an inverse relationship between price and quantity demanded giving it a downward slope. The reason why this happens is known as the law of demand: ceteris paribus, and considering ordinary goods, the higher the price the lower the quantity demanded, and vice versa.

We can start by analysing demand from a purely microeconomic point of view: a single individual, let’s say her name is Joan. Joan’s demand for, let’s say, books, is such as shown in the adjacent graph. If the price of a book is $35 or more, Joan won’t demand any (point a), given her preferences (basically, she would rather spend her money on something else). However, if the price of books goes down to $30, she will want to buy one (point b). If it decreases to $20, Joan will buy two books (point c), and so on. By joining all the points (a-h), we’ll get Joan’s demand curve. It’s worth mentioning that, for simplicity’s sake (though violating monotonicity), we consider that the demand curve ends at the axes.

From a macroeconomic point of view, the demand curve is just the aggregation of all demand curves from all buyers in a particular market. Let’s say the market for books has only two buyers: Joan and her classmate Edward. The horizontal sum of Joan and Edward’s demand curves will give us the market demand: 

Supply:

On the other side, supply is the set of offers made in the market for the sale of goods and services. The supply curve records the location of the points corresponding to the amount offered for a particular good or service at the different prices. This curve shows a direct relationship between price and quantity supplied, giving it an upward slope. The reason why this happens is known as the law of supply: ceteris paribus, and considering ordinary goods, the higher the price the higher the quantity supplied, and vice versa.

Let’s see how the supply curve can be built, starting with an individual’s offer, let’s say his name is Robert. Robert is willing to supply books for $10 or more, this is, Robert won’t supply any books for $5 (point a). However, if the price of books goes up to $10, he will be willing to sell one book (point b). If it increases to $15, Robert will sell two books (point c), and so on. By joining all the points (a-g), we’ll get Robert’s supply curve. Notice that the supply curve goes up and seems not to have limits, an assumption made for simplicity’s sake. Of course Robert will have troubles to supply more than a certain amount of books, but let’s keep it simple and not think about the upper end of the supply curve.

Again, the market’s supply curve is just the aggregation of all supply curves from all sellers in a particular market. Let’s say the market for books has only two sellers: Robert and the librarian next door, Gregory. The horizontal sum of Robert and Gregory’s supply curves will give us the market supply:

Equilibrium and market clearing:

The demand and supply curves define the market clearing, that is, where the demand of the products meets its supply. At this point we have what is known as, an equilibrium point, with its corresponding price and quantity of equilibrium.

It is possible for disequilibrium to occur when the amount demanded does not equal the amount supplied. There are a series of scenarios in which this can happen. In situations in which the quantity demanded is higher than the quantity supplied, the market is suffering from an excess demand. When the opposite occurs we will be talking about an excess supply. Prices will have to gradually adjust through different market mechanisms until the equilibrium price is met.

Movements vs. shifts:

When analysing demand and supply and their respective curves, it is important to distinguish between two aspects: movements along curves and shifts in curves.

A movement refers to a change in either the demand or supply curve, which occurs when a change in the quantity is caused by a change in price and vice versa. An increase in the price of a good or service would cause a movement along its demand curve, decreasing the amount demanded. In the case of supply curves, as we previously saw, an increase in price would also increase quantity. It’s important to understand that movement along the curves does never actually change the equilibrium point, as movements along the curves do not affect it. In the adjacent figure we can see a price increase (let’s say, because an increase of VAT), which causes a movement along the demand curve.

Sometimes the market suffers from changes due to a displacement (shift) of the demand and/or the supply curve. This shift in curves will always result in a new market equilibrium. When a shift occurs, the curve moves, meaning that for each price there will be a new different quantity being demanded or offered. This curve shifts can occur in two directions, upwards and downwards, or if preferred, rightwards and leftwards. Depending in what curve we are considering one is equal to another one.

Demand curves may shift for multiple reasons, for example, an increase in the consumers’ level of income would increase the aggregate demand of a normal good for each price, and hence shift the demand curve to the right (left figure). Other examples would include changes in the price of competitors (substitute goods), changes in complementary goods, tastes, expectations, number of buyers, seasonality, etc.  Supply curve shifts may be also motivated by a variety of different reasons, such as input prices: an increase on the price of paper would shift the supply curve to the left, since the same quantity would be sold at a higher price (right figure). Other variables that can shift the supply curve include technological progress, expectations, number of sellers, etc.

In the long run, no cost is fixed. We can determine our production level and adjust plant sizes, investment in capital and labour accordingly. As we can see in the diagrams below, this gives us unlimited options. Depending on the scale we choose to implement, each level of production will be associated to new, short run cost curves. When we exhaust the infrastructure these provide us, we can upgrade to a new production level and so forth. The actual long run cost curve is made up of all of these individual scenarios, built up year after year.

If we look at average costs, the curve these draw is also the build up of the individual short run curves. These form a U shape, as we can see in the diagram. When average cost is decreasing with each additional investment, we are enjoying economies of scale, but not yet working at maximum efficiency. We reach this maximum efficiency at the minimum point, before the average cost per unit begins growing again.

Marginal costs only really make sense in the long run for each individual level of production. At optimal levels of production for each level, they intersect the long run average cost curve where this meets the short run average cost curve. This is what determines our optimal level of production. In summary, at our optimal level of production:

AC_SR = AC_LR = MC_SR = MC_LR

which is known as Le Châtelier’s principle.

The other important lesson to take away from this is the fact that, when we reach the optimal point where efficiency is at its best, average and marginal costs are the same, as happened in the short run (see detailed graph below these lines). At this point, the slope of the tangent line, that is, the derivative, of the short run total cost (TC_SR) is equal to zero, which is consequent with the fact that we are operating at maximum efficiency. What we can also glean from the graph is the fact that TC_SR and TC_LR are tangent where short run average cost (AC_SR) and AC_LR also meet, which is not necessarily an optimum. In fact, the only time where these junctions do suppose an optimum is in case 2.

In the short run, fixed costs include capital, K, whereas labour, L, is considered variable. Fixed costs are represented as a horizontal line and do not vary whatever level of production we achieve.

The two graphs show how the two phases pan out. In the first phase (I), variable costs (and therefore total costs, seeing as fixed costs are a constant) grow slower than growth at first, before reaching a point of inflection (II) and beginning to grow much faster than the output they are capable of generating.

This is related with returns to scale. In phase I, where the elasticity of scale is greater than 1, there are increasing returns to scale, while phase III corresponds to decreasing returns to scale. In point II, the elasticity of scale equals 1, which represents constant returns to scale.

If we translate this into average and marginal costs, an optimal level is reached along the stretch between which marginal costs are equal to average variable and fixed costs respectively. This coincides with the stretch just before costs begin to grow exponentially.

Period analysis show the inter-temporal dimension of production theory. It was developed by Alfred Marshall in his “Principles of Economics”, 1890, and has remained practically unaltered since. It tries to explain how equilibrium is achieved and explains the adjustment processes to reach it, going from the short-run equilibrium to the long-run equilibrium. His method is able to classify forces with references to the length of time needed for the production process; and then confine in ceteris paribus those forces that are of less importance with regards to the specific time we are considering. Four periods can be distinguished: very short-run, short-run, long-run and very long-run.

The very short-run period is normally not studied as it is considered irrelevant. It is a period characterized by having all its production factors or inputs, fixed; thus implying there can be no change in their quantities. Costs are therefore considered to be fixed and logically there is inexistence of technological progress in this period.

The short-run period is a period in which some factors remain fixed while others may vary in their quantity. Capital elements, such as equipment, are considered fixed factors while labour is considered to be a variable factor.  During this period, cost analysis has a large dependence on marginal cost and average total costs. But, since not all factors can be increased, this will result in diminishing returns, which will imply that marginal costs will increase.  A firm should stop production until marginal costs reach average total costs in order to maximize profits. In this period technological progress is still non-existing.

The long-run period is formed by the succession of several short-run periods and it is considered to be like an envelope of many of these. As inputs can be increased, economies of scale can be achieved, so the cost of producing an extra unit of output will decrease, and thus reduce the average costs. Inputs and outputs should be increased until the point where the optimum size of the firm is achieved and from whereon an increase in size will only mean diseconomies of scale. All inputs may be varied but the basic technology of production still cannot be changed.

Finally, it is in the very long-run period when new production processes and new products come as a result of the existence of technological changes within this period, which allow for new ways of producing and different input requirements.

Perfect competition or competitive markets -also referred to as pure, or free competition-, expresses the idea of the combination of a wide range of firms, which freely enter or leave the market and which considers prices as information, since each bidder only provides a relative small share of the good to the market and thus do not exert a noticeable influence on it. Therefore, perfect competitors cannot influence the levels of market clearing prices. Also, buyers are numerous and disperse, which also means that they cannot influence prices.

This market model is based on a set of assumptions, each of them representing a necessary but insufficient condition to ensure perfect competition. These assumptions are:

-Homogeneous product: all firms offer the same goods, with the same characteristics and quality as the others, without any variations.

-Large number of agents: there should be a sufficient quantity of buyers and sellers, so that no action from a single agent will affect the market structure or its prices.

-No entry or exit barriers: there has to be free entry and exit of agents in the market. This assumption is of special interest for firms, which must be able to enter or leave the market freely.

-Price flexibility: price adjustments to changes happen as fast as possible. Usually, price changes are assumed instantaneous.

-Free and perfect information: all agents have perfect knowledge of products and their prices, and everything else related to them, as well as free access to this information.

-Perfect factor mobility: all factors should be able to change so adjustments processes can be carried out with the greatest efficiency.

-No government intervention: markets should be left alone as government intervention would only lead to imbalances in perfectly competitive markets. 

Perfect competition markets are almost impossible to find in the real word as all markets have some type of imperfection. This is the reason they are mostly considered only theoretically. However, its study helps understand real world markets and their phenomena.

It must be noted that the theory of contestable markets, developed by William J. Baumol in his “Contestable Markets: An Uprising in the Theory of Industry Structure”, 1982, that perfect competition prices and output can be reached with just a few of these assumptions. Furthermore, Bertrand’s duopoly model determines that oligopolistic markets can reach the same prices as in perfect competition as long as oligopolists compete by changing their prices, instead of the quantity offered.