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пятница, 14 июля 2023 г.

Production I. Production duality

 



Production maximisation


Production maximisation must be seen as an optimisation problem regarding the production function, represented by isoquants, and a constraint regarding production costs, represented by an isocost line.

Producers are therefore faced with the following problem: faced with a set of possible production levels and a fixed budget, how to choose the level which maximises their production?

If we know the production function of a certain producer, and we know their budget, we have the two restrictions necessary to maximise their production. This can be done graphically, with the point where isocost and isoquant meet defining an optimum, as shown in the adjacent figure.

It can be also done mathematically, through a Lagrangian, where the first derivatives determine a system of equations that can be resolved by submitting our production function to the restriction presented by the budget:


Video – Production maximisation:




Cost minimisation


Cost minimisation tries to answer the fundamental question of how to select inputs in order to produce a given output at a minimum cost.

A firm’s isocost line shows the cost of hiring factor inputs. This line gives us all possible combinations of inputs (here labour and capital) that can be purchased at a given cost.


Assuming that a certain amount of output wants to be achieved, we have several possible combinations to achieve it, but only one that minimises costs. The isocost line tangent to the isoquant, which represents the amount of output targeted, will reveal the input combination that results in the lowest cost, for that given output.

We can also use the method of Lagrangian systems to analytically solve a constrained minimisation problem. The first derivatives determine a system of equations that can be resolved by submitting our sought output to the restriction presented by the minimisation of costs:


Video – Cost minimisation:


Production duality


As in consumer’s theory (where consumption duality is analysed), the firm´s input decision has a dual nature. Finding the optimum levels of inputs, can not only be seen as a question of choosing the lowest isocost line tangent to the production isoquant (as seen when minimising cost), but also as a question of choosing the highest production isoquant tangent to a given isocost line (maximising production). In other words, having a cost function that sets a budget constraint, solving for the inputs allocation that gives the highest output.

The way to solve either problem is very similar: we look for the Lagrangian function and obtain first order conditions, then solve the system.



Video – Production duality:



https://policonomics.com/lp-production1-production-duality/

четверг, 8 июня 2023 г.

Types of Costs

 A list and definition of different types of economic costs.

Fixed Costs (FC) The costs which don’t vary with changing output. Fixed costs might include the cost of building a factory, insurance and legal bills. Even if your output changes or you don’t produce anything, your fixed costs stay the same. In the above example, fixed costs are always £1,000.

Variable Costs (VC) Costs which depend on the output produced. For example, if you produce more cars, you have to use more raw materials such as metal. This is a variable cost.

Semi-Variable Cost. Labour might be a semi-variable cost. If you produce more cars, you need to employ more workers; this is a variable cost. However, even if you didn’t produce any cars, you may still need some workers to look after an empty factory.

Total Costs (TC)  = Fixed + Variable Costs

Marginal Costs – Marginal cost is the cost of producing an extra unit. If the total cost of 3 units is 1550, and the total cost of 4 units is 1900. The marginal cost of the 4th unit is 350.

Definition of Marginal Cost

Marginal Cost is the cost of producing an extra unit.

It is the addition to Total Cost from selling one extra unit.

QTotal Cost (TC)Marginal Cost (MC)Average Cost (AC)
1101010
21668
32377.6
43298
545139
6662111
  • For example, the marginal cost of producing the fifth unit of output is 13.
  • The total cost of producing five units is 45.
  • But, for the marginal cost, we find, the change in total cost of producing the fifth unit.
    • Total cost of 4 units 32
    • Total cost of 5 units 45
    • Marginal cost of 5th unit = 13

Diagram Showing Marginal Cost


Note:  Marginal cost is often shaped like this in the short term because of the law of diminishing marginal returns.

Opportunity Cost – Opportunity cost is the next best alternative foregone. If you invest £1million in developing a cure for pancreatic cancer, the opportunity cost is that you can’t use that money to invest in developing a cure for skin cancer.

Economic Cost. Economic cost includes both the actual direct costs (accounting costs) plus the opportunity cost. For example, if you take time off work to a training scheme. You may lose a weeks pay of £350, plus also have to pay the direct cost of £200. Thus the total economic cost = £550.

Accounting Costs – this is the monetary outlay for producing a certain good. Accounting costs will include your variable and fixed costs you have to pay.

Sunk Costs. These are costs that have been incurred and cannot be recouped. If you left the industry, you could not reclaim sunk costs. For example, if you spend money on advertising to enter an industry, you can never claim these costs back. If you buy a machine, you might be able to sell if you leave the industry. See: Sunk cost fallacy

Avoidable Costs. Costs that can be avoided. If you stop producing cars, you don’t have to pay for extra raw materials and electricity. Sometimes known as an escapable cost.

Explicit costs – these are costs that a firm directly pays for and can be seen on the accounting sheet. Explicit costs can be variable or fixed, just a clear amount.

Implicit costs – these are opportunity costs, which do not necessarily appear on its balance sheet but affect the firm. For example, if a firm used its assets, like a printing press to print leaflets for a charity, it means that it loses out on revenue from producing commercial leaflets.

Absorbed costs

Absorbed costs involve including all the variable and fixed costs in producing a unit of output.

For example, in producing a motor car, the absorbed costs include the variable raw material costs and the associated fixed manufacturing costs, such as the factory, safety inspections and maintenance of machines.

Absorbed costs would not include general administration of a firm or expenditure on advertising.

Absorbed vs variable costs

Absorbed costs can be contrasted with the variable costs or the direct costs of producing a good. The direct costs are those specific to the good – labour, raw materials. However, this excludes those fixed costs which are part of the overall cost.


Which is better to use absorbed costs or variable costs?

For certain decisions, firms may prefer to use variable costs. Variable costs give a guide to operating profit – given that fixed costs have already been spent. For short-term decision making, a firm will look at marginal cost (which will be the extra variable costs associated with increasing output) and marginal revenue.

For external accounting and evaluation in the long-term, absorption costs are needed. They give a fuller picture of the long-term profitability of the firm and real costs associated with producing a good.

Evaluation of absorbed costs

  • One issue with absorbed costs is deciding what will count as a fixed manufacturing overhead cost.
  • The cost per unit will typically fall with increased output. Economies of scale will reduce the manufacturing average fixed costs.

Isoquant and isocosts

  • An isoquant shows all combination of factors that produce a certain output
  • An isocost show all combinations of factors that cost the same amount.
  • Isocosts and isoquants can show the optimal combination of factors of production to produce the maximum output at minimum cost.

Definition isoquant

An isoquant shows all the combination of two factors that produce a given output

In this diagram, the isoquant shows all the combinations of labour and capital that can produce a total output (Total Physical Product TPP) of 4,000. In the above isoquant, this could be

  • 20 capital and 18 labour or (more capital intensive)
  • 9 capital and 35 labour. (more labour intensive

An isoquant is usually shaped convex to the origin because of the law of Marginal Rate of Technical Substitution (MRTS) which means there are diminishing returns from using more of one factor of production.

Marginal rate of factor substitution



The marginal rate of substitution is the amount of one factor (e.g. K) that can be replaced by one factor (e.g. L). If 2 units of capital could be replaced with one-factor labour, the MRS would be 2


Diminishing marginal rate of substitution

If the firm employs 2 L and 40 K. Then employing one extra worker can enable it to save 10K. This is quite an efficient saving. The firm only has to pay one extra worker but can save the cost of 40.

However, at a combination of 9 Labour, employing an extra worker enables a saving of only 2 capital. Therefore, the more that workers are employed, there is diminishing rate at which you can substitute the other factor. There comes a point, where employing more workers barely saves any capital at all. This is when diminishing returns of labour is very high – workers effectively get in each other’s way.

As one moves down the isoquant, output remains the same. Therefore the output gained from employing more labour must equal the output lost from employing more capital.

MPP (L) x ΔL = MPP (K) x ΔK

This equation gives us


Isoquant map

An isoquant map shows different levels of output. For example

  • I1 may show the combinations of capital and labour that can produce 4,000 TPP.
  • I2 may show the combinations of capital and labour that can produce 5,000 TPP.
  • I5 is a higher output than I4

In the short-term, a firm faces a trade-off along one particular isoquant. But, in the long-term, a firm can invest in increasing capital stock and produce at a higher output for the same quantity of labour.

Isocost

An isocost shows all the combinations of factors that cost the same to employ.

In this example, a unit of labour and capital cost £6,666 each.

  • If we employ 30K and 30L, the total cost will be £200,000 + £200,000
  • If we employ 10 K and 50L, the total cost will be £66,666 +£333,333 = £400,000

Change in labour costs


  • In this example, initially, the cost of labour and capital is both £5,000. (e.g. 60L = 60 x £5,000 = £300,000)
  • However, if Labour cost rises to £10,000, then the isocost shifts to the left. Now, to keep cost at £300,000, a firm could only employ 30 workers (30 x £10,000)
  • The slope of an isocost is, therefore, Pι / Pκ

Profit maximisation

To maximise profits, a firm will wish to produce at the point of the highest possible isoquant and minimum possible isocost

In this example, we have one isocost and three isoquants. With the isocost of £400,000 the maximum output a firm can manage would be a TPP of 4,000. If it produced at say 13 K and 48 Labour, it would only be able to produce a TPP of 3,500.

A total TPP of 4,500 is currently not possible without increasing costs beyond £400,000

Profit maximisation – the least cost method of production


Another way of seeking to maximise profits is to target an output of say 4,00 and then find the isocost with the lowest possible cost. In this case, the isocost which touches the tangential point of the TPP is a TC of £400,000.

Market Failure

  • Social Costs. This is the total cost to society. It will include the private costs plus also the external cost (cost incurred by a third party). May also be referred to as ‘True costs’

Social Cost

Definition of social cost – Social cost is the total cost to society. It includes private costs plus any external costs.

Example of driving to work


  • Costs of paying for petrol (personal cost)
  • Costs of increased congestion (external cost)
  • Pollution and worse air quality (external cost)
  • The social cost includes all the above. (Petrol + congestion + pollution)

Example of social cost – smoking

If you smoke, the private cost is £6 for a packet of 20 cigarettes. But, there are also external costs to society

  • Air pollution and risks of passive smoking
  • Litter from discarded cigarette butts
  • Health costs to society

The social costs of smoking include the total of all private and external costs.

Example of social cost of building airport

Private costs of airport

  • Cost of constructing an airport.
  • Cost of paying workers to run airport

External costs of airport

  • Noise and air pollution to those living nearby.
  • Risk of an accident to those living nearby.
  • Loss of landscape.

Importance of social cost

Rational choice theory suggests individuals will only consider their private costs. For example, if deciding how to travel, we will consider the cost of petrol and time taken to drive. However, we won’t take into consideration the impact on the environment or congestion levels for other members in society.

Therefore, if social costs significantly vary from private costs then we may get a socially inefficient outcome in a free market.

Marginal social cost (MSC)

The marginal social cost is the cost to society of producing/consuming one extra unit of output.

Example of Marginal social cost


  • PMC = Private marginal cost
  • XMC = External marginal cost
  • SMC = Social marginal cost

Diagram showing marginal social costs


For goods with negative externalities the social cost is greater than the private cost.

In a free market, if people ignore the external costs, the equilibrium will be at output 20. But, social efficiency (where social marginal cost = social marginal benefit) would be at output 16.

  • External Costs. This is the cost imposed on a third party. For example, if you smoke, some people may suffer from passive smoking. That is the external cost.
  • Private Costs. The costs you pay. e.g. the private cost of a packet of cigarettes is £6.10
  • Social Marginal Cost. The total cost to society of producing one extra unit. Social Marginal Cost (SMC) = Private marginal cost (PMC) + External marginal Cost (XMC)

Diagram of Costs Curves

  • Total Fixed Cost (TFC) – costs independent of output, e.g. paying for factory
  • Marginal cost (MC) – the cost of producing an extra unit of output.
  • Total variable cost (TVC) = cost involved in producing more units, which in this case is the cost of employing workers.
  • Average Variable Cost AVC = Total variable cost / quantity produced
  • Total cost TC = Total variable cost (VC) + total fixed cost (FC)
  • Average Total Cost ATC = Total cost / quantity

Costs in the short run

Short run cost curves tend to be U shaped because of diminishing returns.

In the short run, capital is fixed. After a certain point, increasing extra workers leads to declining productivity. Therefore, as you employ more workers the marginal cost increases.

Diagram of Marginal Cost 


Because the short run marginal cost curve is sloped like this, mathematically the average cost curve will be U shaped. Initially, average costs fall. But, when marginal cost is above the average cost, then average cost starts to rise.

Marginal cost always passes through the lowest point of the average cost curve.

Average Cost Curves


  • ATC (Average Total Cost) = Total Cost / quantity
  • AVC (Average Variable Cost) = Variable cost / Quantity
  • AFC (Average Fixed Cost) = Fixed cost / Quantity

Costs


  • Fixed costs (FC)  remain constant. Therefore the more you produce, the lower the average fixed costs will be.
  • To work out the marginal cost, you just see how much TC has increased by.
  • For example, the third unit sees TC increase from 450 to 500, therefore, the increase in MC is 50.
  • The 12th unit sees total cost rise from 1,700 to 2,400, so the marginal cost is 700

Average fixed costs


Fixed, variable and total cost curves


Total cost (TC) = Variable cost (VC) + fixed costs (FC)

Long Run Cost Curves

The long-run cost curves are u shaped for different reasons. It is due to economies of scale and diseconomies of scale. If a firm has high fixed costs, increasing output will lead to lower average costs.


However, after a certain output, a firm may experience diseconomies of scale. This occurs where increased output leads to higher average costs. For example, in a big firm, it is more difficult to communicate and coordinate workers.

Diagram for Economies and Diseconomies of Scale 


Note, however, not all firms will experience diseconomies of scale. It is possible the LRAC could just be downward sloping.




https://www.economicshelp.org/

Module 13: Perfect Competition

 

“Sandakan Sabah Shell-Station” photo by CEphoto, Uwe Aranas, available on commons.wikipedia.organd is licensed under CC BY-SA

THE POLICY QUESTION
SHOULD THE GOVERNMENT ALLOW OIL COMPANIES TO MERGE RETAIL GAS STATIONS?

In the late 1990s and early 2000s, there were a number of mergers of big oil companies in the United States: Exxon acquired Mobil, BP Amoco acquired ARCO, Chevron acquired Texaco, and Phillips merged with Conoco. This led to massive consolidation in the oil business. In response, US government regulators required the sell-off of some refineries to maintain competitiveness in regional refined gas markets. For the most part, however, the same regulators were unconcerned about the reduction in competition in the retail gas market. In this chapter, we will explore perfectly competitive markets and, in so doing, will be able to better understand why regulators were relatively unconcerned about concentration in the retail gas industry.

EXPLORING THE POLICY QUESTION

  1. Why were retail gas stations not considered a main concern of regulators?
  2. Does the merger of major oil companies necessarily lead to higher gas prices? Why or why not?

13.1 CONDITIONS FOR PERFECT COMPETITION

Learning Objective 13.1: Describe the characteristics of a perfectly competitive market.

In perfectly competitive markets, firms and consumers are all price takers: their supply and purchasing decisions have no impact on the market price. This means that the market is so big and any one individual seller or buyer is such a small part of the overall market, their individual decisions are inconsequential to the market as a whole. It is worth mentioning here at the start that this is a very strong assumption, and thus this is considered an almost purely theoretical extreme, along with monopolies at the other extreme. We can and will describe markets that come pretty close to the assumptions underlying perfect completion, but most markets will lie somewhere in between purely competitive and monopolistic. It is important to study these extremes to better understand the full range of markets and their outcomes.

Before we describe in detail perfectly competitive markets, let’s consider how we categorize market structure, the competitive environments in which firms and consumers interact. There are three main metrics by which we measure a market’s structure:

  1. The number of firms.
  2. More firms mean more competition and more places to which consumers can turn to purchase a good.
  3. The similarity of goods.
  4. The more similar the goods sold in the market are, the more easily consumers can switch firms, and the more competitive the market is.
  5. The barriers to entry.
  6. The more difficult it is to enter a market for a new firm, the less competitive it is.

The first is relatively straightforward; more firms mean more competition in the sense that it is hard to charge more for a product that consumers can find easily from other sellers. The second is a little subtler because products can be differentiated by something as simple as a brand or more tangible aspects like colors, features, and other characteristics. Finally, the third can be barriers of law like patents or technology, even if not covered by legal patent protection, or more natural barriers like a very high cost of starting up a firm that is not justified by the expected revenue.

We will study four market types in more detail where these metrics will be discussed further, but for now, they are described along the three metrics in table 13.1.

Table 13.1 The four basic market structures described
The Four Basic Market Structures Described
NamePerfect competitionMonopolistic competitionOligopolyMonopoly
Number of firmsManyManyFewOne
Similarity of goodsIdenticalDifferentiatedIdentical or differentiatedUnique
Barriers to entryNoneNoneSomeMany
Chapter13201915

With this categorization in place, we can turn to the definition of perfect competition. Perfect competition is a market with many firms, an identical product, and no barriers to entry. Let’s take these three metrics one by one.

Many Firms

Having many firms means that from the perspective of one individual firm, there is no way to raise or lower the market price for a good. This is because the individual firm’s output is such a small part of the overall market that it does not make a difference in terms of price. Firms are, therefore, price takers, meaning that their decision is simply how much to sell at the market price. If they try to sell for a higher price, no one will buy from them, and they could sell for a lower price, but if they did so, they would only be hurting themselves because it would not affect their quantity sold. Thus from an individual firm’s perspective, they face a horizontal demand curve. We assume they can sell as much as they want but only at the market price. This is an extreme assumption, as mentioned before, but there are some markets that resemble this description. Take the market for corn in the United States. The annual US corn crop is roughly twelve billion bushels, and there are roughly 315,000 corn farms in the country. Thus average output per farm is about thirty-eight thousand bushels annually, or about 0.000003 percent of the total supply of corn in the United States. If one farmer of average corn acreage decided to withhold output, there would not likely be any effect on the market price. It is also true that consumers are price takers as well, meaning no one consumer has a large enough impact to affect prices.

Identical Goods

The existence of identical goods means there is nothing to distinguish one firm’s goods from another. To use the corn example, once all the corn is dumped into the grain elevator, there is absolutely no way to tell from which farm a particular kernel of corn came. This means there is no way for one seller to differentiate their output to try to sell it at a different price on the premise that it is different. Contrast this to the automotive market, where the products are heterogeneous. Cars manufactured by Audi are very different than cars manufactured by Kia. An Audi A6 is very different than a Kia Optima in many substantive ways. Even when there is very little substance that is different, branding can be used to differentiate. Take, for example, polo shirts from Lacoste and Ralph Lauren. The shirt might be almost identical in terms of style, fabric, color, and so on, but by branding them with a logo—a crocodile or polo player—the manufacturers are able to differentiate them in the minds of consumers.

Barriers to Entry

It is very easy for firms to start and stop selling in this market. For example, if a farmer decides to plant corn instead of soybeans, there is nothing preventing them from doing so. Likewise, a farmer who wishes to plant soybeans instead of corn faces no barriers. In general, free entry and exit mean that there are no legal barriers to entry, like needing a special permit only given to a limited number of firms, and no major cost obstacles, like needing to invest millions of dollars in a manufacturing plant, as a new car manufacturer would. This ensures that firms remain price takers even when demand increases. If there is suddenly more demand for corn, perhaps from ethanol producers, farmers can quickly adjust their crops so existing growers do not have an opportunity to raise prices. Free exit is important as well because if firms know they cannot exit easily, they might be reluctant to enter in the first place.

There are two other implicit assumptions worth mentioning here. The first is that we assume that buyers and sellers have full information, meaning that they know the prices charged by every firm. This is important because without it, a firm could possibly charge an uninformed consumer more, and this violates the price-taker condition. The second is that there are negligible transaction costs, meaning it is easy for customers to switch sellers and vice versa. This is also important to ensure price taking, for if transactions costs were high, customers might accept higher prices from existing suppliers to avoid the cost of initiating a new transaction with another supplier at a lower price.

Take a moment and think about the policy example, retail gas, and how well it matches our definition of a perfectly competitive market.

  • Are there many sellers?
  • Is the product identical?
  • Are there barriers to entry?

Your answers to these questions will be the basis of our evaluation of the policy stance the federal government took in assessing the oil company mergers.

In chapter 9, we studied profit maximization for a price-taking firm. We now know in what type of market we find price-taking firms: perfectly competitive markets. In the three other market types we will consider, firms will all have some control over the price of the goods they sell. It is worth taking a moment to review the principles of profit maximization for price-taking firms.

We now know clearly what leads a firm’s demand curve to be horizontal and thus the same as the marginal revenue curve: the fact that the firm is in a perfectly competitive market and has no influence on prices.

13.2 PERFECT COMPETITION AND EFFICIENCY

Learning Objective 13.2: Explain how perfectly competitive markets lead to Pareto-efficient outcomes.

In chapter 10.4, we studied the concepts of consumer and producer surplus and defined Pareto efficiency. We saw how prices adjust to conditions of excess supply and excess demand until a price that equates to supply and demand is reached. What this means is that the market ensures that everyone who values the good more than or equal to the marginal cost of producing it will find a seller willing to sell the good and that all opportunities for consumer and producer surplus will be exploited. This is how we know that total surplus is maximized.

In a perfectly competitive market, neither consumers nor producers have any influence over prices in the market, leaving them free to adjust to supply and demand excesses. Because of this, there is no deadweight loss, total surplus is maximized, and the outcome of the market is Pareto efficient. Prices in competitive markets act as demand and supply signals that are independent of institutional control and ensure that in the end, there are no mutually beneficial trades that do not happen. By mutually beneficial, we mean that buyers and sellers wish to engage in them because they will both be made better off.

It is in this sense that “free” markets are considered efficient. By “free,” we mean that prices freely adjust—there are no institutional or competitive controls that prevent prices from adjusting to equilibrate the market until the efficient outcome is achieved. By efficient, we mean Pareto efficient—there is no deadweight loss. With this chapter, we understand the conditions that must hold for a market to achieve the efficient outcome. There must be many buyers and sellers, the good must be homogenous, there must be free entry and exit, and there must be complete information about the good and prices on the part of buyers and no transactions costs. If this sounds like a lot, it is. In later chapters, we will examine the effects of other market structures and when assumptions like complete information fail to hold.

13.3 POLICY EXAMPLE
SHOULD THE GOVERNMENT ALLOW OIL COMPANIES TO MERGE RETAIL GAS STATIONS?

Learning Objective 13.3: Use the perfectly competitive market model to evaluate the decision to allow the consolidation of retail gas stations under fewer brands.

We are now well equipped to address our policy example. What we need to do is evaluate the retail gas market using the description of a perfectly competitive market to try to decide how closely it resembles a perfectly competitive market. We then need to determine if the market looks like a competitive one pre-merger and if that would change significantly after the merger.

Number of Firms

Overall, there are many retail gas stations in the United States—more than 150,000 in 2012. But the United States is too big a geographical area to use for our purposes. For most consumers of retail gas, a reasonable example of a market is the metropolitan area in which they live if they live in urban areas or perhaps a ten-mile radius for rural residents. The number of major branded gas stations was reduced from ten to five with the mergers, but there are also a number of independent or non-name brand gas stations in most retail markets. Post-merger, most communities affected by the merger, those that had stations that represented each of the company brands that merged, still had more than one competing station. But how many competing stations is enough? We will study this question in more detail in chapter 19.

Identical Goods

Retail gas is essentially identical, but major brands do a lot of advertising to try to convince customers that their brand is better. How successful they are at this strategy is beyond our analysis here, but one clue to this is how much more the major branded stations charge over independent stations. However, in this case, the question is how much major brands are able to charge. Casual observation suggests that the answer is not very much. Major branded stations located close to each other almost always charge prices very close to each other, suggesting that though consumers consider their gas higher quality than that of the independent brands, they consider all major branded gas essentially identical.

Free Entry and Exit of Firms

The market for retail gas is fairly open but with some particular aspects. The first is that retail gas requires buried tanks, which often require special permitting. There may also be more zoning restrictions than for other businesses in some areas. But in general, there are few restrictions that prevent new stations to open and existing stations to close.

Retail gas is also one of the most transparent markets in terms of pricing. Most stations prominently display their prices on signs seen easily from the roadway, so the assumption about full information is more apt here than for most retail markets. There are also few transactions costs. There is virtually no cost to purchasing from one station or switching to another. The major gas brands try to create some frictions by establishing loyalty programs or credit card tie-ins that qualify customers for lower prices, but the extent of these programs is clearly limited based on the price matching that most stations do that are located close together.

It appears, then, that the retail gas market is fairly close to a competitive market, if not quite perfect, and that it remains fairly competitive even after the string of mergers. To fully answer the question of whether total surplus is reduced by the merger, we would need to look more closely at real-world price data, but on the face of it, the mergers of retail gas station brands appear relatively benign.

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