Principles of Economics - Perfect Competition

Perfect Competition is a market structure that follows these assumptions:

• Firms are price takers - each firm has no impact on the price in the market, they take the price the market forces set.
• Freedom of entry into the market - there are low barriers to entry so anyone could potentially set up in this market.
• Firms produce identical products - the taxi market for example, each taxi firm offers an identical product.
• Producers and consumers have perfect knowledge - both producers and consumers know everything there is to be known about the market.

However, few, if any, industries are actually perfectly competitive.

In the short run, the number of firms is fixed. In the long run, if supernormal profits are being made then new firms will enter the industry. If losses are being made, firms will leave the industry. 

Short run equilibrium of the firm:

This is what the market looks like in the short run in perfect competition. The price is Pe, and is set by the demand and supply forces. It is horizontal because firms are price takers. Due to price being constant, the red dotted line is also the average revenue, the marginal revenue and the demand for the firm as they're all the same. Qe is the amount produced by the firm because this is the amount at which profits are maximised (MC = MR). There is slight profit being made because the average revenue is higher than the average cost at the production point.

This is where the long run can be introduced. In the long run, firms see these profits being made and enter the industry. These means the industry supply increases, shifting the supply curve to the right on the left hand diagram above. Price falls, which means each firms demand falls until the point it is equal to the average cost. At this point, firms break even and make no profit. Firms will stop entering the industry now.

As far as the public interest goes with perfect competition, it has its benefits and drawbacks. The benefits are as follows:

• Firms produce at the least cost output.
• Firms that are inefficient will be forced out.
• Prices are minimised.
• Consumers determine what and how much is produced.

The drawbacks are:

• There us very little incentive to invest in new technology.
• Goods are all the same, lack of variety for consumers.

That ties up this post about perfect competition. Thank you for reading, keep checking back and sharing. Have a good day!

Sam.

Common Agricultural Policy Part 3 - Buffer Stocks

A tool at the EU's disposal within the CAP is buffer stocks. They can use these to either stabilise the prices of farm produce or to stabilise farmers income.

First case we'll analyse is the case of buffer stocks being used to stabilise prices of farm produce.

We have a market for a crop here, Q1 and P1 being the equilibrium quantity and price respectively. Lets assume one year there is a good harvest, supply increases to S1. We notice that this would create a fall in price, however as the policy is aiming to stabilise prices this isn't what we want. So, in order for this supply increase to come with stable prices, the governments need to buy up the difference between Q1 and Q2 and put them into buffer stocks. This means, the quantity available to the public is the original level of Q1, and therefore price won't change. 

Alternatively, if there is a bad harvest and supply falls to S2, a price rise would occur. The governments would have to intervene here and sell the difference between Q1 and Q3 to the market, releasing them from buffer stocks so the quantity available is the same and therefore the price remains stable. 

The areas on the diagram represent a few different things. Area a is an income that the farmers are guaranteed, even in the worst times. Area a + b is the normal income for a farmer, assuming that the harvest is a normal one. Area c is extra income the farmer would earn given a good harvest. Notice this policy of stabilising the farming prices has created more fluctuation in the farmers incomes, something the CAP aims to eradicate. Controversial.

Now, onto how buffer stocks can be used to stabilise a farms income. This involves using the elasticity formula. If elasticity of the good equals to 1, then the percentage increase in quantity is the same as the percentage fall in price. Therefore, if these are the same then the income of the farmer will remain constant. 

This diagram shows the principle of stabilising a farmers income using buffer stocks. We have an initial equilibrium of P1 and Q1, and supply increases because of a good harvest. This essentially means that a new equilibrium will be formed at P2 and Q2. However, at this point the farmers income has changed because demand doesn't have unitary elasticity. Therefore, the government needs to intervene. Using the curve above, we can see where the price and quantity should be for farmers income to remain stable: P2' and Q2'. So, what the government needs to do is buy up the difference between Q2 and Q2' and put them into buffer stocks. This means that the quantity now available will mean that price is at P2' and therefore farmers income will be stable. We can see this visually, the farmer has lost area c in terms of income due to the price fall,but gained area a + b due to the increase in quantity. These areas should be identical and therefore the farmers income has remained constant. 

This concept also works the other way if supply were to fall. Just in this case the governments would be releasing from the buffer stocks in order to regulate the price and quantity so that the farmers income remains stable. 

Buffer stocks is one method the government has to try and stop price fluctuations or income fluctuations, however it cannot be used to control both at the same time. Next up will be the use of subsidies for the same reasons. 

Sam.

Statistics - Sampling Methods and Estimation

In statistics we have to use samples because it's normally near on impossible to get data for the entire population. As long as the sampling is done well, the results will usually be good enough. Logic would tell you that the larger the sample, the better.. and this is true. There are two concepts we need to understand here, those are random sampling and sampling distribution.

• Random sampling - The goal of this is representativeness, we aim to get an equal probability of selection to every member of the population. There are a few methods:
• Simple random sampling - A sample so that every item or person in a population has the same chance of being included.
• Systematic random sampling - Items or individuals are arranged in some sort of order. A random starting point is selected and then every nth member is selected. Alphabetic order for example. 
• Stratified random sampling - A population is divided into sub groups (strata) and a sample is selected from each strata.
• Cluster sampling - A population is divided up into primary units and then samples are selected from the primary units.
• Non-probability sampling - Inclusion in the sample is based on the judgement of the person selecting the sample. (Eeek!)

• Sampling Distribution - This is the theoretical distribution of a statistic for all possible samples of a certain sample size, N. It's a device to link the samples characteristics to the population.
• If repeated sample sizes of size N are drawn from a normal population with a mean of mew and a standard deviation, σ, then the sampling distribution of sample means will be normal with a mean of mew and a standard deviation of σ / SqrRoot(N).
• The 'Central Limit Theorem' states that if repeated samples of size N are drawn from a population, as N becomes large the sampling distribution or sample means will approach normality.
• Or, in easier terms: Large samples are more reliable!

The more basic method of estimation is confidence intervals. From a sample we don't know the population mean, but we would like to estimate this with maximum efficiency. To do this we use a range, and say how certain we are that this range includes the population mean. We give a confidence interval in the form of a percentage, for example we could say that at a 99% confidence interval, between 33% and 39% of adults will vote for Labour in the next election (Made up!). A bigger confidence interval is more likely to contain the true population mean.

The next post will go further into the concept of confidence intervals and we will introduce such things as error margins. Stay tuned, thanks guys!

Sam. 

Common Agricultural Policy Part 2 - Declining Farm Incomes

The next thing the CAP aims to eradicate is declining farm incomes. These are mainly caused by two things: low income elasticity of demand and/or increases in supply. As usual, we'll display this diagrammatically. Lets suppose we have a fairly inelastic demand curve and at the same time farm efficiency has improved, we can expect the market to now look as follows:

We can see that prices have fallen from P1 to P2 and quantity has risen from Q1 to Q2. However, we can also see that this has caused a fall in income of area a and an additional income of area b for the farmers. Area a is clearly larger than area b, meaning the farmers income as a whole has fallen. The way for farmers to gain is for demand to shift out by a larger amount, as even a small shift in demand would leave farm incomes still falling. 

What the farmers need is a more elastic demand curve for any increases in supply efficiency to actually increase farmers income. However, demand for grown crops is generally more inelastic because it's a necessity and therefore a change in price really doesn't affect demand all that much. This is why the government needs to intervene with the CAP because else there would be no incentive for farmers to make their production mechanisms more efficient as they'd effectively be losing money due to it.

Now we have covered both reasons as to why the CAP is necessary; fluctuating crop prices and declining farm incomes. We will next cover how the EU uses it's policies to correct these issues. Stay tuned!

Sam.

Statistics - The Normal Probability Distribution

This post will bring in an application of standard deviation. It can help give us units to measure distances between points in a data set as well as to measure the distance from the mean.

Chebyshev had a theorem. He said that for any set of observations, the minimum proportion of values that lie withing k standard deviations of the mean is 1- (1/k^2), as long as k is greater than 1. If k is 3, 89% of the observations lie withing the region and if k is 4, 94% of observations lie within the region.

For a normal probability distribution we need to use a normal curve, or a bell curve. It has a single peak in the centre of the distribution. This centre point is where the mean equals the median equals the mode. We can now introduce a new concept of z-values. A z-value is the distance between a selected value (Xi) and the population mean, divided by the population standard deviation. Another note on the normal curve is that is has a Kurtosis of 0. A higher Kurtosis means it's peak is higher and more pointy, a lower Kurtosis means it's a flatter shape.

Back to the z scores. They link together the theoretical normal distribution to the observed observations. It tells us how many standard deviations away from the mean an observation lies. So, we need to calculate the z-score. When calculating the z score it is essentially converting your data into a distribution with a mean of 0 and a normal curve shape. The formula is as follows:

Once the score has been calculated, you refer to a z score table. On this table, the first decimal goes down the side and the second decimal goes along the top. So, if using the formula above you were given a z score of 1.24, then you'd look for 1.2 down the side and 0.04 along the top. The score at which these match is your z score. That score is 0.3925. What to do with that score becomes more understandable with an example and some context. 

At a party, lemonade is distributed among the party-goers with a mean of 20cl and a standard deviation of 5cl. What is the likelihood that a person selected at random will get between 17cl and 23cl of lemonade? Right, so we plug in the values to start. z will equal (17 - 20) / 5 = -0.6. It will also equal (23-20) / 5 = 0.6. Now, from here we look for 0.6 down the side of the z score table and 0.00 along the top. We will be given a value of 0.2257. This score caters for one of the results, but as they are both the same size we can double it and get 0.4514. And that's the answer. 45.14% of people get between 17 and 23cl of lemonade, so the likelihood of any given person getting between that amount is 45.14%.

Another use for z scores isn't just finding the amount included, it can be used to find excluded regions too. That may sound quite complex, but I'll show you a picture to visualise it.

We need some context once again to work this out. Let's say that a teacher has said to achieve an A* on a test, students must get in the top 10% of the scores. The mean score for the test was 75 and there was a standard deviation of 5. We can now work out what score is needed to get a A*. The whole region to the right of the mean makes up 50%, we know we want to exclude 10%, so we need to find a z-score that marks 40% - 0.4. On the z-score table 0.4 doesn't appear (remember this time we know the size of the region, so we are looking at the values in the table and looking for a corresponding z score), 0.3997 is the closest so we'll go with that. That gives a z-score if 1.28. Now we need to refer back to the z score formula. We know z, we know s and we know the mean... we are trying to work out Xi. So, we plug in the numbers we have an rearrange to find Xi. 1.28 = (Xi - 75) / 5. Xi - 75 = 6.4. Xi = 81.4. There we have it, the answer. To make it more realistic this score could be rounded to 81 or 82, but one of these scores is needed to achieve the top 10% of the class and therefore get an A*. Simples!

That's it from me, z-scores are a fairly complex topic so feel free to ask any questions if i haven't been entirely clear in the explanation. Good luck!

Sam.

Common Agricultural Policy Part 1 - Price Fluctuations

The Common Agricultural Policy is a massive deal in Europe and the European Union. It's a very expensive policy that started out back in 1962 as a simple price support policy. It has two key objectives: to stabilise prices and to provide income support for social reasons. If you look at the distribution of farms across Europe, it is clear to see why this is needed. The biggest 7% of farmers own roughly half the land, whilst the smallest 50% of farmers own only 7% of land. This is a massive inequality and could lead to monopoly powers, outlandish prices and other such problems if it went unregulated.

We'll first look at a few of the characteristics of the agricultural industry. There are many producers, all are price takes. There are also many consumers, all of which are also price takers. There is generally freedom of entry and exit into the industry. It's about as close to perfect competition as you could get in a realistic scenario. Governments need to intervene for many reasons:

• To reduce price fluctuations.
• Raise farm incomes.
• Protect rural communities.
• To encourage greater self-sufficiency.

Firstly, I'm going to focus on the price fluctuations. In the short term they are caused by instability and the fluctuations in the harvest (good or bad!). Let's assume that the demand for a crop were to rise one year, which would cause a shift to the right of the demand curve. Supply in the short term obviously cannot react to this because supply is fixed each year depending on what is planted. This demand rise will cause a rise from price P1 to P2. This is all shown on the diagram below.

The farmers observe this rise in price and then next year they increase their supply to the market. At P2 the farmers decide that Q2 is the correct quantity to supply to the market. However, at this amount supplied, demand is outstripped and therefore price must fall to P3. The year after, at price P3 a different amount is supplied by the farmers, but at this supply more is demanded and therefore price rises again. This will continue, as shown on the diagram below we can see that the market is slowly spiralling towards a point of equilibrium at which both consumers and producers would be happy. 

We call this concept a stable cobweb. This price fluctuations and changes are supply are making the market more and more stable as over time the fluctuations get smaller until equilibrium is finally met. In this case, the government wouldn't need to intervene in the agricultural industry. However, there is the opposite case. An unstable cobweb could appear. The case of this occurs when the supply of the crop is very elastic. Diagramatically, the supply curve will be much flatter. The same instance as above will occur, demand increases causing a price rise as supply is fixed. In the second term supply is increased due to this new price, but there is oversupply and price has to fall... and so on and so forth. Except, when the supply curve is elastic this doesn't spiral towards equilibrium, it spirals away from it as can be seen in the diagram below.

This shows one of the cases in which the government would need to intervene in the agricultural industry, hence the Common Agricultural Policy. The price fluctuations in this unstable cobweb would keep getting worse and worse if left to market forces. 

Next we'll move on too supply side shocks. This is when supply is affected, either for good or for bad, and therefore the supply of the crop isn't as expected. Once again, diagrams are an easier way of showing this. The first case will be a bad harvest, where supply of the crop is less than what was expected. The diagram below shows this. Supply of the crop has fallen from the expected level of Qe to the actual level of Qa. The area labelled 'b' is income that the farmer has lost, the area labelled 'c' is income gained from this supply side shock. The expected income for the farmer was area 'ab', but the actual income of the farmer is now area 'ac'. If area c is greater than area b then the farmer has gained, otherwise the farmer has lost out due to the bad harvest. Generally, the more inelastic demand is, the greater are 'c' is and therefore the more likely the farmer will benefit. 

I'll quickly go through the other supply side shock as well. As you can guess, this is when there is a better harvest than expected. This causes a shift to the right of actual supply from Qe to Qa. A fall in price is seen from Pe to Pa and once again the farmers income may be affected. Area 'c' is the income gain, area 'b' is the income loss and area 'a' is the income that has stayed constant. If area 'b' is bigger than area 'c' then the farmer has lost out. 

What we have achieved in this blog post is the causes of the fluctuations in prices of harvested goods. This is one of the things the Common Agricultural Policy aims to stop, as stable prices is an aim. In the next post we'll look at what is causing the decline of farmers income and then we'll move on to look at how the government intervenes in this policy to correct these issues.

Stay tuned guys, enjoy!

Sam.

Statistics - Measures of Dispersion

The first measure of dispersion of data we'll mention is the range. The range is the difference between the highest value and the lowest value in a set of data. Only these two values are used in the calculation and it is very easy to compute. It has a slight issue, however, that extreme values do influence the result. 

A step on from this range is the interquartile range. This is the difference between the first quartile and the third quartile - giving us the middle 50% of observations. To work out the first quartile, we take N (number of observations) and divide it by 4. This will give us the number of the observation at which the first quartile point is. To work out the third quartile we take N and divide it by 4 and then multiply the result by 3. This gives us the number of the observation at which the third quartlile mark is. From there, we just subtract the value of the first quartile figure away from the third quartile figure. 

The quartiles are then displayed on a box plot diagram. A box plot will look generally as follows:

Mean deviation is another measure of dispersion. This measures the mean of the absolute values of the deviations from the mean. Similar to standard deviation, but not quite. The formula is as follows:

• Mean Deviation = (Σ|Xi - x̄|) / n
• Xi = each observation
• x̄ = the sample mean.
• n = number of observations.

We take the absolute values here for a very specific reason. It stops the negative and positive values from cancelling each other out, which would give us a mean deviation of close to 0 - very unhelpful! Dispersion is very important, key statistical methods such as regression rely heavily on measures of dispersion. 

The population variance and sample variance are two more concepts I'm going to introduce now. The population variance measures the arithmetic mean of the squared deviations from the population mean. The sample variance essentially does the same, but for a sample. The formula for both are as follows:

• Population variance = (Σ|X - μ|)^2 / N
• Sample variance = (Σ|Xi - x̄|)^2 / (n - 1)

These variances can be easily turned into the standard deviations, a very important concept for statisticians. To do this, we just square root the result. We denote the standard deviation of a population and a sample differently. A population is given with this symbol: σ and a sample is given with the letter s. The standard deviation principle will come in key in the next few posts when we begin to introduce confidence intervals, so learn it!

Thanks for reading, have a good day.

Sam.