Log-linearisation in Short

Log-linearisation in Short with an example

There exist many different types of models of equations for which there exists no closed form solution. In these cases, we use a method known as log-linearisation. One example of these kinds of models are non-linear models like Dynamic Stochastic General Equilibrium (DSGE) models. DSGE models are non-linear in both parameter and in variables. Because of this, solving and estimating these models is challenging.

Hence, we have to use approximations to the non-linear models. We have to make concessions in this, as some features of the models are lost, but the models become more manageable.

In the simplest terms, we first take the natural logs of the non-linear equations and then we linearise the logged difference equations about the steady state. Finally, we simplify the equations until we have linear equations where the variables are percentage deviations from the steady state. We use the steady state as that is the point where the economy ends up in the absence of future shocks.

Usually in the literature, the main part of estimation consisted of linearised models, but after the global financial crisis, more and more non-linear models are being used. Many discrete time dynamic economic problems require the use of log-linearisation.

There are several ways to do log-linearisation. Some examples of which, have been provided in the bibliography below.

One of the main methods is the application of Taylor Series expansion. Taylor’s theorem tells us that the first-order approximation of any arbitrary function is as below.

We can use this to log-linearise equations around the steady state. Since we would be log-linearising around the steady state, x* would be the steady state.

For example, let us consider a Cobb-Douglas production function and then take a log of the function.

The next step would be to apply Taylor Series Expansion and take the first order approximation.

Since we know that

Those parts of the function will cancel out. We are left with –

For notational ease, we define these terms as percentage deviation of x about x* where x* signifies the steady state.
Thus, we get

At last, we have log-linearised the Cobb-Douglas production function around the steady state.

Bibliography:
Sims, Eric (2011). Graduate Macro Theory II: Notes on Log-Linearization – 2011. Retrieved from https://www3.nd.edu/~esims1/log_linearization_sp12.pdf


Zietz, Joachim (2006). Log-Linearizing Around the Steady State: A Guide with Examples. SSRN Electronic Journal. 10.2139/ssrn.951753.


McCandless, George (2008). The ABCs of RBCs: An Introduction to Dynamic Macroeconomic Models, Harvard University Press


Uhlig, Harald (1999). A Toolkit for Analyzing Nonlinear Dynamic Stochastic Models Easily, Computational Methods for the Study of Dynamic
Economies, Oxford University Press

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Learning Central Limit Theorem with Microsoft Excel

Many statistical and econometric procedures depend on the assumption of normality. The importance of the normal distribution lies in the fact that sums/averages of random variables tend to be approximately normally distributed regardless of the distribution of draws. The central limit theorem explains this fact. Central Limit Theorem is very important since it provides justification for most of statistical inference. The goal of this paper is to provide a pedagogical introduction to present the CLT, in form of self study computer exercise. This paper presents a student friendly illustration of functionality of central limit theorem. The mathematics of theorem is introduced in the last section of the paper. 

CENTRAL LIMIT THEOREM

We start by an example where we observe a phenomenon and than we will discuss the theoretical background of the phenomenon.

Consider 10 players playing with identical dice simultaneously. Each player rolls the dice large number of times. The six numbers on the dice have equal probability of occurrence on any roll and before any player. Let us ask computer to generate data that resembles with the outcomes of these rolls.

We need to have Microsoft Excel ( above 2007 preferable) for this exercise. Point to ‘Data’ tab in the menu bar, it should show ‘Data Analysis’ in the tools bar. If Data Analysis is not there, than you need to install the data analysis tool pack, for this  you have to click on the office button, which is the yellow color button at top left corner of Microsoft Excel Window.  Choose ‘Add Ins’ from the left pan that appears, than check the box against ‘Analysis Tool Pack’ and click OK.

Select Office Button Excel OptionsSelect Add Ins Þ  Analysis ToolPack ÞGo from the screen that appears

Computer will take few moments to install the analysis toolpack. After installation is done, you will see ‘Data Analysis’ on pointing again to Data Tab in the menu bar. The analysis tool pack provides a variety of tool for statistical procedures.

We will generate data that matches with the situation described above using this tool pack.

Open an Excel spread sheet, write 1, 2, 3,…6 in cells A1:A6,

Write ‘=1/6’ in cell B1 and copy it down

This shows you possible outcomes of roll of dice and their probabilities.

 This will show you following table:

10.167
20.167
30.167
40.167
50.167
60.167

Here first column contain outcomes of roll of dice and second column contain probability of outcomes. Now we want the computer to have some draws from this distribution. That is, we want computer to roll dice and record outcomes.

For this go to Data Þ Data AnalysisÞ Random Number Generation and select discrete distribution. Write number of variables =10 and number of random number =1000, enter value input and probability range A1:B6, put output range D1 and click OK.

This will generate a 1000×10 matrix of outcomes of roll of dice in cells A8:J1007. Each column represent outcome for a certain player in 1000 draws whereas rows represent outcomes for 10 players in some particular draw. In the next column ‘K’ we want to have sum of each row. Write ‘=SUM(A8:J8) and copy it down. This will generate column of sum for each draw.

Now, we are interested in knowing that what distribution of outcome for each player is:  

Let us ask Excel to count the frequency of each outcome for player 1. Choose Tools/Data Analysis/Histogram and fill the dialogue box as follows:

The screenshot shows the dialogue box filled to count the frequency of outcomes listed observed by player A. The input range is the column for which we want to count frequency of outcomes and bin range is the range of possible outcomes.  This process will generate frequency of six possible outcomes for the single player. When we did this, we got following output:

BinFrequency
1155
2154
3160
4169
5179
6183
More0

The table above gives the frequency of the outcomes whereas same frequencies are plotted in the bar chart. You observe that frequency of occurrence is not approximately equal. The height of vertical bars is approximately same. This implies that the distribution of draws is almost uniform. And we know this should happen because we made draws from uniform distribution. If we calculate percentage of each outcome it will become 15.5%, 15.4%, 16%, 16.9%, 17.9% and 18.3% respectively. These percentages are close to the probability of these outcomes i.e. 16.67%.

Now we want to check the distribution of column which contain sum of draws for 10 players, i.e. the column K. Now the range of possible values of column of sum varies from 10 to 60 (if all column have 1, the sum would be 10 and if all columns have 6 than sum would be 60, in all other cases it would be between these two numbers). It would be in-appropriate to count frequencies of all numbers in this range. Let us make few bins and count the frequencies of these bins. We choose following bins; (10,20), (20, 30),…(50, 60). Again we would ask Excel to count frequencies of these bins. To do this, write 10, 20,…60 in column M of Excel spread sheet (these numbers are the boundaries of bins we made). Now select Tools/Data Analysis/Histogram and fill the dialogue box that appears.

 The input range would be the range that contains sum of draws i.e. K8 to K1007 and bin range would be the address of cells where we have written the boundary points of our desired bins. Completing this procedure would produce the frequencies of each bin. Here is the output that we got from this exercise.

BinFrequency
100
205
30211
40638
50144
602
More0

First row of this output tells that there was no number smaller than starting point of first bin i.e. smaller than 10, and 2nd, 3rd …rows tell frequencies of bins (10-20), (20,30),…respectively. Last row informs about frequency of numbers larger than end point of last bin i.e. 60.

Below is the plot of this frequency table.

 Obviously this plot has no resemblance with uniform distribution. Rather if you remember famous bell shape of the normal distribution, this plot is closer to that shape.

Let us summarize our observation out of this experiment. We have several columns of random numbers that resemble roll of dice i.e. possible outcomes are 1…6 each with probability 1/6 (uniform distribution). If we count frequency of these outcomes in any column, the outcomes reveal the distributional shape and the histogram is almost uniform. Last column was containing sum of 10 draws from uniform distribution and we saw that distribution of this column is no longer uniform, rather it has closer match with shape of normal distribution.

Explanation of the observation:

The phenomenon that we observed may be explained by central limit theorem. According to central limit, let  be independent draws from any distribution (not necessarily uniform) with finite variance, than distribution of sum of draws  and average of draws would be approximately normal if sample size ‘n’ is large.

Mean and SE for sum of draws:

From our primary knowledge about random variables we know that:

And

Suppose

Let , than and

These two statements tell the parameters of normal distribution that emerges from sum of random numbers and we have observed this phenomenon described above.

Verification

Consider the exercise discussed above; column A:J are draws from dice roll with expectation 3.5 and variance 2.91667. Column K is sum of 10 previous columns. Thus expected value of K is thus 10*3.5=35 and variance 2.91667*10. This also implies that SE of column K is 5.400 (square root of variance.

The SD and variance in the above exercise can be calculated as follows:

Write ‘AVERAGE(K8:K1007)’ in any blank cell in spreadsheet. This will calculate sample mean of numbers in column K. The answer will be close to 35. When I did this, I found 34.95.

Write ‘VAR(K8:K1007)’ in any blank cell in spreadsheet. This will calculate sample variance of numbers in column K. The answer will be close to 29.16, when I did this, I found 30.02

Summary:

In this exercise, we observed that if we take draws from some certain distribution, the frequency of draws will reflect the probability structure of parent distribution. But when we take sum of draws, the distribution of sum reveals the shape of normal distribution. This phenomenon has its root in central limit theorem which is stated in Section …..

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A brief mathematical revision of the Ramsey Model

We mentioned in the last post the Solow-Swan model in order to explain the importance of the specification related to theories and the regression analysis. In this post, I’m going to explain a little bit more the neoclassical optimization related to consumption, in this case, it’s going to be fundamental to the theory of Ramsey (1928) related to the behavior of savings & consumption.

We declare first some usual assumptions, like closed economy XN=0, net investment equals I=K-δK where δ is a common depreciation rate of the economy for all kinds of capital. There’s no government spending in the model so G=0. And finally, we’re setting a function which is going to capture the individual utility u(c) given by:

This one is referred to as the constant intertemporal elasticity function of the consumption c over time t. The behavior of this function can be established as:

This is a utility function with a concave behavior, basically, as consumption in per capita terms is increasing, the utility also is increasing, however, the variation relative to the utility and the consumption is decreasing until it gets to a semi-constant state, where the slope of the points c1 and c2 is going to be decreasing.

We can establish some results of the function here, like

And that

That implies that the utility at a higher consumption point is bigger than on a low consumption point, but the variation of the points is decreasing every time.

The overall utility function for the whole economy evaluated at a certain time can be written as:

Where U is the aggregated utility of the economy at a certain time (t=0), e is the exponential function, ρ is the intergenerational discount rate of the consumption (this one refers to how much the individuals discount their present consumption related to the next generations) n is the growth rate of the population, t is the time, and u(c) is our individual utility function, dt is just the differential which indicates what are we integrating.

Think of this integral as a sum. You can aggregate the proportion of individual utilities at a respective time considering the population size, but also you need to bring back to the present the utility of other generations which are far away from our time period, this is where ρ enters and its very familiar to the role of the interest rate in the present value in countability.

This function is basically considering all time periods for the sum of individuals’ utility functions, in order to aggregate the utility of the economy U (generally evaluated at t=0).

This is our target function because we’re maximizing the utility, but we need to restrict the utility to the income of the families. So, in order to do this, the Ramsey model considers the property of the financial assets of the Ricardian families. This means that neoclassical families can have a role in the financial market, having assets, obtaining returns or debts.

The aggregated equation to the evolution of financial assets and bonuses B is giving by:

Where the left-side term is the evolution of all of the financial assets of the economy over time, w refers to the real rate of the wages, L is the aggregate amount of labor, r is the interest rate of return of the whole assets in the economy B, and finally, C is the aggregated consumption.

The equation is telling us that the overall evolution of the total financial assets of the economy is giving by the total income (related to the amount of wages multiplied the hours worked, and the revenues of the total stock of financial assets) minus the total consumption of the economy.

We need to find this in per capita terms, so we divide everything by L

And get to this result.

Where b=B/L and c is the consumption in per capita terms.  Now we need to find the term with a dot on B/L, and to do this, we use the definition of financial assets in per capita terms given by:

And now we difference respect to time. So, we got.

We solve the derivate in general terms as:

And changing the notation with dots (which indicate the variation over time):

We have

We separate fractions and we got:

Finally, we have:

Where we going to clear the term to complete our equation derived from the restriction of the families.

And we replace equation (2) into equation (1). And we have

To obtain.

This is the equation to find the evolution of financial assets in per capita terms, where we can see it depends positively on the rate of wages of the economy and the interest rate of returns of the financial assets, meanwhile it depends negatively on the consumption per capita and the growth rate of the population.

The maximization problem of the families is giving then as

Where we assume that b(0)>0 which indicates that at the beginning of the time, there was at least one existing financial asset.

We need to impose that utility function is limited, so we state:

Where in the long run, the limit of utility is going to equal 0.

Now here’s the tricky thing, the use of dynamical techniques of optimization. Without going into the theory behind optimal control. We can use the Hamiltonian approach to find a solution to this maximization problem, the basic structure of the Hamiltonian is the following:

H(.) = Target Function + v (Restriction)

We first need to identify two types of variables before implementing it in our exercise, the control variable, and the state variable. The control variable is the one that focuses on the agent which is a decision-maker, (in this case, the consumption is decided by the individual, and the state variable is the one relegated in the restriction). The state variable is the financial assets or bonus b. Now the term v is the dynamic multiplier of Lagrange, consider it, as the shadow price of the financial assets in per capita terms, and it represents an optimal change in the individual utility given by one extra unit of the assets.

We’re setting what is inside of our integral as our objective, and our restriction remains the same and the Hamiltonian is finally written as:

The first-order conditions are giving by:

One could ask why we’re setting the partial derivates as this? Well, it’s part of the optimum control theory, but in sum, the control variable is set to be maximized (that’s why it’s equally to 0) but our financial bonus (the state variable) needs to be set negatively to the shadow prices of the evolution of the bonus because we need to find a relationship where for any extra financial asset in time we’ll decrease our utility.

The solution of the first-order condition dH/dc is giving by:

To make easier the derivate we can re-express:

To have now:

Solving the first part we got:

To finally get:

 

Now solving the term of the first-order condition we obtain:

thus the first-order condition is:

Now let’s handle the second equation of first-order condition in dH/db.

Which is a little bit easier since:

So, it remains:

Thus we got.

And that’s it folks, the result of the optimization problem related to the first-order conditions are giving by

Let’s examine these conditions: the first one is telling us that the shadow price of the financial assets in per capita terms it’s equal to the consumption and the discount factor of the generations within the population grate, some better interpretation can be done by using logarithms. Lets applied them.

let’s differentiate respect to time and we get:

Remember that the difference of logarithms it’s equivalent approximately to a growth rate, so we can write this another notation.

Where

In equation (4) we can identify that the growth rate of the shadow prices of the financial assets is negatively related to the discount rate ρ, and the growth rate of consumption. (in the same way, if you clear the consumption from this equation you can find out that is negatively associated with the growth rate of the shadow prices of the financial assets). Something interesting is that the growth rate of the population is associated positively with the growth in the shadow prices, meaning that if the population is increasing, some kind of pull inflation is going to rise up the shadow prices for the economy.

If we multiply (4) by -1, like this

and replace it in the second equation of the first order which is

Multiplied by both sides by v, we get

Replacing above equations drive into:

Getting n out of the equation would result in:

Which is the Euler equation of consumption!

References

Mankiw, N. G., Romer, D., & Weil, N. D. (1992). A CONTRIBUTION TO THE EMPIRICS OF ECONOMIC GROWTH. Quarterly Journal of Economics, 407- 440.

Ramsey, F. P. (1928). A mathematical theory of saving. Economic Journal, vol. 38, no. 152,, 543–559.

Solow, R. (1956). A Contribution to the Theory of Economic Growth. The Quarterly Journal of Economics, Vol. 70, No. 1 (Feb., 1956),, 65-94.

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The evil in the heart of the good: Unfolding the role of remittances in the escalating trade deficit figures of the MENA region.

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

The MENA region is ranked first in terms of remittance receipts (3.83% of GDP) worldwide, it has also the highest non-oil trade deficit among other developing regions (World Bank, 2018). This study uses panel data from 11 Labor-abundant MENA countries (main destination of remittance receipts) to examine the trade balance effect of remittances. We postulate that the main driver of the trade deficit in the MENA region is the weak industrial sector, which fails to provide domestic substitutes for imports of manufactured products (El Wassal 2012). Based on our hypothesis, we imply that in countries with weaker domestic absorptive capacity, the excessive demand of remittance-recipient families will not be compensated by domestic production, but rather imports of the consumption good, thus worsening the trade balance deficit.

The empirical work from the MENA region on the trade balance effects of remittances is limited. Bouhga-Hagbe (2004) supported the evidence of this effect in Morocco, wherein remittances covered the trade deficit and contributed to the observed surpluses of the external current account. Kandil and Mirzaie (2009) showed that remittances promote both exports and imports in Jordan while nourishing only exports in Tunisia. In the case of Egypt, El Sakka, and McNabb (1999) reported that imports financed through remittances have a high-income elasticity, thereby implying
that they are either consumer durables or purchased by high-income groups. In a study, involving interviews of 304 remittance-receiving families across 16 Egyptian governorates during 2015–2016, Farzanegan et al. (2017) examined further the causes and effects of
remittances. Using a panel of 17 remittances receiving countries in the MENA and Central Asia regions over a period of 1990–2009, Abdih et al. (2012) concluded that a significant portion of remittances is
used to purchase foreign goods.

Our empirical results confirm the import triggering effects of remittances, however these effects are mitigated as the investment capacity of a country gets stronger and become able to neutralize foreign purchases with domestic products. Many policymakers are pushing to increase remittances as a reliable source of income by reducing transfer costs. The real challenge is promoting the productive use of these remittances in financing domestic production capabilities and non-oil exports. The channel of promoting domestic capital formation through encouraging private savings and productive use of remittances could improve the balance of trade. This can be realized by promoting financial services, which targets repatriates and their families, like saving incentives, interest rate premium on migrant’s deposits, and the issuance of remittances back bonds. Although
remittances may carry some development-related outcomes, such as income smoothing, reducing poverty, and promoting education, the applied literature is still equivocal about the magnitude of these effects and the governing conditions to realising these effects. Our paper is an
example of a study that has highlighted a rather countercyclical effect of the
inflow of remittances on the recipient countries’ trade balance. This piece of
evidence among others suggests that promoting remittances does not always come in favour for the recipient economies and is conditioned to the prevailing economic and institutional environments.

Reference:

Mohammad Reza Farzanegan & Sherif Maher Hassan (2019) How does the flow of remittances affect the trade balance of the Middle East and North Africa?, Journal of Economic Policy Reform, DOI: 10.1080/17487870.2019.1609357

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Oil war: GCC stability Vs. EU stability

https://www.desitrending.com/wp-content/uploads/2018/08/1533689404_

After the dramatic turmoils that took place in France and then have spread across other European countries. These turmoils were mainly triggered by the hikes in Oil prices in the last few months, These surges have caused rigorous supply shock to prices, causing thousands maybe million of Mid-class people in EU to struggle. Lives casts from Paris and Belgium brought back memories from the Arab spring in early 2011, the similar domino effect of the tragedic sequences where people get into the streets to demand something, then other people who suffer from a different thing – etc. labor reforms- use the chance and start raising their voices, a different group, farmers start asking for higher prices for their products, an escalations of social frustration that build on as days pass by.

However these problems start to loosen up as oil prices start to sharply decline again, and as this was the main trigger for these social escalations, it was the main lessor for these as well. besides other measures that were adopted by these countries’ governments, but none of these could have worked without first the stabilization and reduction of oil prices. OPEC countries that are dominated by GCC oil hubs such as Saudi Arabia, UAE, and Kuwait have been pushed to increase oil production and this will automatically bring down oil prices. A strategy that indeed comes in favor of these conflicted first class developed countries, yet it does not necessarily come in the favor of the people living in oil exporting countries, especially in such times where domestic inflation rates in Saudi Arabia and UAE are escalating, budget deficits in the new Saudi Budget reaches historical records, however, the political pressure simply cannot be overseen. GCC countries have to react in favor for the big ones instead of their people, as oil is their major budget components, few dollars reduction in its prices will cause millions of budget revenue to be lost.

One lesson here is that the economy is no longer free, the political influence of the big ones govern economic laws of supply and demand as well as the strategic products prices. However, for developing countries, governments need to fight back against this political dominance and strongly hold to the power of rejection to decide what’s good for their own people.

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Why minimum wages and why not?

https://upload.wikimedia.org/wikipedia/commons/thumb/5/5e/Assorted_United_States_coins.jpg/280px-Assorted_United_States_coins.jpg

Understanding the economic intuition behind minimum wages
law is of great importance, given the economic fluxes spreading all over the
world, from the Arab spring in Middle East, to budget deficits in USA and the debt crises in euro zone. Regarding the debatable and controversial outcomes of minimum wages, I will try to explain why governments tend to be quite hesitant when it comes to agree on such law settlement.

A typical labor market with an upward supply of labor that shows the number of employees willing to work at different wages levels, it
might be viewed as the marginal cost (MC) of each additional unit of
labor. The demand curve for labor by employers at given fixed level of Marginal productivity and price level is downward slopping; any changes in those exogenous variables would lead to inward/outward shifts in this curve. The equilibrium wage and No. of workers are determined at the intersection of the two curves at W*, L*.

The government may at any point of time intervene and set a price floor for wages (wages cannot decrease below this level) in form of a minimum wage that is higher than the equilibrium wage. Why any government think
to apply such law, simply because the government considers the equilibrium wage insufficient for sustaining poor people, so the government uses its legislative authority and force employers to offer workers higher wages than competitive wage level.

Notably to mention that low skilled job seekers are the target group by this law, because low skilled or teenagers who lack the sufficient educational and job experiences have no chance to compete in such market, in
other words, they are more eligible for internships with no payment, or on job training with wages lower than equilibrium wages.

With wages at the minimum floor, we might observe the following:

1- The No. of people who actively seek jobs would rise, this increase in supply of labor might come from existing labor force who were employed as interns or on job trainees, and people who are counted as voluntary unemployed, such wage rate now meet their expectations and force them to get back to the play yard.

2- The cost of hiring workers now is higher, employers are obliged to pay higher wages, which would force them to reduce the demand for employees, except for really skilled, highly efficient ones.

3- The outcome would be a surplus in the labor market, where the supply of labor by employees exceeds the demand for labor by employers.

4- Only highly skilled labor (LD) are being employed and receive the benefits of higher wages “ Not the target group “

5- Teenage unemployment tends to increase, No. of students who drop out of schools might increase (as now it is more tempting to seek jobs than before) , the rate of job creating in the shadow “underground” economy might hike, because of the legal market surplus (No minimum wage laws in shadow economies)

This is not the end of the story, otherwise things would be quite easy and simple, and we can conclude that minimum wages are bad, and
governments should seek better –less costly-ways to do its job for supporting low-income people (i.e. Earned income tax credit).

More than 200 academic researchers have been studying the
effects of minimum wages on labor markets over the last century, and have been trying to observe the patterns of teenage unemployment after setting this wage floor. Opponents argue that it causes unemployment, lead to discrimination for the favor of highly skilled workers (or black people as observed in the minimum wage law settlement in USA during the 1930s), schools drop out increase, illegal and criminal activities increase, inflation rises.

Proponents -on the contrary- argue that minimum wages are
not bad, however, when, how and where they are applied is the crucial issue.
They advocate that minimum wages would hike productivity of workers and
increase the opportunity cost of leisure, moreover the hike in prices would
increase the demand for labor because the accession in employer’s profits, and thus the observed unemployment rise is transitory. In addition, the marginal propensity to consume (MPC) of low income people is much higher than high income people, consequently the whole aggregate demand might rise and instigate the rate of job creation in the economy, not mentioning, moral, ethical norms of providing better life for low income people and the reduction of criminal/illegal acts in the economy.

However, empirical evidence stands for the side of proponents; a typical econometric analysis of this phenomenon has shown that, an increase of 10% in minimum wage would reduce employment by only 1-3%,
depending upon the elasticity of the demand for labor in this market, and the degree of wage raise.

To fully understand the whole picture we should also incorporate our analysis with the case of removal of fringe benefits. Observing
employer’s reaction to the imposed minimum wages, possibly by removing fringe benefits from their employees “transportation, health insurance, memberships, relaxed work conditions, free coupons, etc…” , we might conclude a different outcome, as both employees and employers tend to be worse off in terms of gained utility in favor of lower reduction in employment levels in the labor market.

To recap, each market should be considered separately; there is no general catalog for the spillovers of minimum wages. Governments should
treat such decision very carefully, also to consider the amount of wage raise, the elasticity of the demand in each market, and others law or legalization that might hinder/strut the negative spillovers of minimum wages. Favorably a government could seek better – in sense of controversy- , stable -in sake of predicted outcomes-, and less costly -in terms welfare losses- than this dangerous remedy for poverty.

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The interaction between monetary and macroprudential policies

There is an increasing concern among policy makers and economists about macro prudential policies that aim to stabilize the economy and alleviate financial distortions through affecting output and inflation levels . This paper by Claessens, and Valencia, (2013) at VOX tries to study the possible interactions between monetary and macro prudential policies. In addition, it highlights the stylized fact that neither monetary nor fiscal policies are sufficient to stabilize the economy, additional tool is needed to continue this job.

“The newly emerging paradigm is one in which both monetary policy and macro prudential policies are used for counter cyclical management: monetary policy primarily aimed at price stability; and macro prudential policies primarily aimed at financial stability. But these policies interact with each other and thus each may enhance or diminish the effectiveness of the other”

When prices rigidities are the only distortion, then momentary policy goal of stabilizing prices will also stabilize output and maximize welfare, but in the presence of financial market imperfections, which affect people expectations and predicted risks, this will hinder the influence of monetary policy on output stabilization. If this is the case, then monetary policy is not enough, because financial distortions might not directly/indirectly be related to liquidity levels. A combination of both monetary and macroprudential policies -with one focusing on liquidity and other focusing on altering aggregate demand of this liquidity- to reduce financial risks and stabilize the economy is required.

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What looks like a discount is not actually a discount

What is the goal of any firm,  store, mall, service provider or even a rocket factory? The answer is, either earning enough money(Accounting profit) to run the business, and cover operational costs (variable costs), or filling the stakeholder pocket’s with more profits (Economic profits), which include the accounting profit in its calculation and the opportunity cost forgone from running a different business.

Let us keep it simple, firms aim to make economic profits, but it would not
mind so much if it is stuck with accounting profits.What can firms do? Well
this requires good managers, financial analysts, smart accountants, production factors, and some microeconomics

Assume that we have a firm that is doing a good job, or it has some power over its prices, hence, this market is an imperfect competitive market. The Demand curve of this firm’s product/service is downward, which means higher prices would distort sales. Nevertheless, remember that higher prices mean more bucks in the pockets. Therefore, firms always have an incentive to charge higher prices, along with selling more products to accesses their economic profits, while equating the firm’s marginal revenue with marginal cost (Profit maximizing condition)

Firms can use magicians to flip aside the demand curve and make it upward slopping. Unfortunately, I cannot recommend the former trick, because I suspect its applicability. However, Microeconomics proposes a different trick.

Firms can achieve this by more costly and sophisticated ways, either establishing good connections with Government officials to restrict entering this market along with producing a product that is needed and has no close substitutes (AKA. monopolist), or to dowhat is known as imperfect price discrimination (Market segmentation).

The idea here is to sell the same product at different prices for different consumers, depending upon their price sensitivities. Conclusively, people who tend to be more sensitive (segment 2) should be assigned lower prices; others should have high prices (Segment 1). As elasticity rises, people will be willing to pay lower prices for this product or service, because of their preferences, accessibility of closer substitutes, income, age, etc…. For example, when you regularly do your weekly shopping from the grocery store nearby, and a big, shiny advertisement blocks your way, which
announces that you can buy more of your favorite jam with lower price, buy one with 40 cents, 2 with 75 cents and three with 1.05 cent. Your mind
automatically deduce the total price of buying 3 single jars with 40 cents each (price of a single jar in this offer) and the total price of 3 jars in this
offer(1.05 cents), so the difference will save you 15 cents.

This is what I was talking about, this offer is not for the sake of consumers, otherwise the grocery manager is trying to price discriminate you ( or run you along your demand curve) and guess what he always wins. Because the profit from selling only one jam jar with say 30 cents (lowest price possible to instigate sales) is lower than his profit from the discrimination strategy (both cases, he assign a price higher than his marginal cost). Therefore, what looks like a discount for you, is simply a technique of profits accession for the owner.

Successful Price discrimination based upon the uniqueness of sold product and the inability to resell this product (Taking benefit from price differentials between consumers). We can find price discrimination strategies in airline industries at which the price of last minute traveler ticket is higher than regular ticket prices (regular in sense of their rush and the opportunity cost of their times which determines their willingness to pay).

At cinemas, children are usually offered lower ticket prices, because they tend to buy pop corn, cola and stuff, which would cover up the discounted value of their tickets. Juniors tend to have discounts at their outlets, because they are price sensitive, and tend to have more time to search for cheaper alternatives than older people do.

Tip for sellers:

– Your challenge is to find ways to know people willingness to pay while segmenting your markets (as people do not walk with their elasticity coefficients on their shirts), make unique products, and make it harder to resell your sold units. The more accurate you deduce the degree of sensitivity of your costumers, the more successfully you will be able to price discriminate and earn more profits.

Tip for buyers

– Do not be so inelastic; do not give any signals implicitly or explicitly to sellers that you are eager to buy this product now, and spend some time searching for better and cheaper alternatives.

Sure thing, this simple analysis misses a lot of salient information about firm’s pricing and producing behaviors.

 

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