Economics doesn't require advanced thinking

[WinePusher]

In another thread, Danmark stated that economics doesn't require advanced thinking. In order to disparage a subject one must first study the subject, otherwise what they say about the subject doesn't mean anything. I challenge Danmark to solve the following problems and show, first hand, that economics doesn't require advanced thinking and that the problems in economics are easily solved with only simple thinking:

1) Given the following model where

Y (National Income)=C+Io+Go
C (Consumption)=a+b(Y-T)
T (Taxes)=d+tY

List the number of endogenous variables and find the equilibrium level for national income (Y) consumption (C) and taxes (T).

This is a very simple question for someone who is capable of advanced thinking should be able to solve. The next problem is a bit more complicated and requires usage of lagrange multipliers, and multivariable calculus as a result. However, an advanced thinker should already have knowledge of multivariable calculus and should know how to solve optimization problems subject to constraints.

2) The production function for a manufacturer is given in Cobb-Douglass form by f(x,y)=100x^3/4*y^1/4 where x represents labor units ($150 per unit), and y represents capital units ($250 per unit). The total cost of labor and capital is constrained by $50,000. Given the following information, maximize the production level for the manufacturer.

[JoeyKnothead]

From the OP:

Economics doesn't require advanced thinking

"Advanced", being a subjective term, is a consideration bound only to the individual.

Now, how to keep the deer off the apples, that takes some doin'.

[bluethread]

From the OP:

Economics doesn't require advanced thinking

"Advanced", being a subjective term, is a consideration bound only to the individual.

Now, how to keep the deer off the apples, that takes some doin'.

The question is calcilatin' how many of them apples need to be eaten by the deer before it is worth me gettin' up off the porch and chasen them away. Personally, I have no problem with WinePusher doin' all of his calcilatin', but I just figure puttin' them deer in the freezer can offset any discomfort that might result from me gettin' off the porch. But, then there is the problem of the flat caps thinkin' I shouldn't be a shootin' them deer. Them politician are always messin' up my well thought out economic plans.

[WinePusher]

Personally, I have no problem with WinePusher doin' all of his calcilatin',

I believe we've already spoken through pm about the use of mathematics and statistics in economics, and if I remember correctly you expressed your disapproval about it. You're certainly not alone, many heterodox schools of thought like the Austrians and the Institutionalists to a certain extent hate how widespread math and stats are used in econ.

To put it shortly, they are wrong. Math and statistics are merely 1) tools used in economics research and 2) a formal, precise language that economics can be expressed it. For any theory to hold true it must be quantifiable, and this is exactly how the history of economics proceeds. An ancient economic theorist comes up with a theory, and a future economist comes up with the mathematical formalization that solidifies the theory. I'll give you three examples:

1) The invisible hand. Adam Smith posited that selfish people acting in their own self interest will ultimately produce outcomes that are favorable and desirable to the entire society at large. This would be brought about by what Smith called the invisible hand. We may all think that this is a profound piece of insight, but looking back retrospectively this was just Adam Smith's opinion, nothing more and nothing less. However, as economics progressed and new economists came forward and proved Smith's conjecture. The first being Leon Walras, with his mathematical model of general equilibrium, followed by Kenneth Arrow (Arrow-Debreu Model) and the fundamental theorems of welfare, highly mathematical theorems that formalize Adam Smith's notion of the invisible hand.

2) Utility. Utility (a concept at the core of utilitarianism) is simply the amount of satisfaction derived from the consumption of goods and services. When you buy something you receive some level of happiness from what you bought, and this is referred to as utility. The concept seems obvious at first, but it wasn't really thought about until Jeremy Bentham, who asserted that human behavior can be understood simply as an exercise in utility. That is, humans choose to do those things and purchase those goods that provide them with high levels of utility and avoid those things that don't give them much utility (formally known as Felicific calculus). Again, this seems obvious so why exactly must there be some type of mathematical proof and formalism for it. Well, for the same reason why something as obvious as gravity required rigorous mathematical formalization, and later economists offered mathematical formalizations of utility showing the concept of the valid and true, the most notable being John von Neumann and Paul Samuelson.

3) Free trade. Again, since the founding of economics free trade has always been viewed favorably. Both Adam Smith and David Ricardo offered arguments for free trade (absolute and comparative advantage) and these two concepts can actually be expressed mathematically yet no one objects to this. So perhaps they only object to advanced mathematics that they don't understand being implemented in economics, but I digress. Smith justified free trade using absolute advantage, however Smith's justification rested upon the assumption that all nations had an absolute advantage in at least one commodity and this may not always be the case. So Ricardo dropped the assumption, allowed for a world where some nations did not have an absolute advantage, and still managed to justify free trade based on comparative advantage. Then, the Hecksher-Ohlin model dropped the assumption of comparative advantage and justified free trade based upon factor intensity. And then, Paul Krugman of all people dropped all of these assumptions and still managed to justify free trade based on scale economics and imperfect/monopolistic competition.

So to the contrary, mathematics is very useful in economics. It also serves as a restriction on entry into the field and a signal of capability.

Everybody out there seems to have opinions on economic issues, whether it be income inequality or the TPP trade deal, and just because they have these opinions they think they're somehow qualified to expound on economics and deride it as 'simple.' Luckily, just having opinions and reading popular articles isn't sufficient to enter the economics field and start producing research, a rigorous understanding of math required. Knowledge of things like multivariable calculus, linear algebra, ordinary differential equations (partial differential equations and stochastic calculus for top finance guys), proof based probability theory, mathematical statistics and real analysis.

And as I said, math also serves as a signal of capability. Math is an extremely difficult and advanced field and anyone who is able to understand it is intellectually capable. Btw, the economics profession has a high average IQ, ranking in fifth place behind engineering and science: http://www.statisticbrain.com/iq-estima ... ege-major/

[bluethread]

Personally, I have no problem with WinePusher doin' all of his calcilatin',

I believe we've already spoken through pm about the use of mathematics and statistics in economics, and if I remember correctly you expressed your disapproval about it. You're certainly not alone, many heterodox schools of thought like the Austrians and the Institutionalists to a certain extent hate how widespread math and stats are used in econ.

I wouldn't say I disapprove of it et al. I just have my reservations regarding the use of it as a true determinant of human behavior. When dealing with large numbers, as with the house side at a casino, it has some value. When dealing with individual cases or small numbers, as with an individual or table in a card room, not so much.

To put it shortly, they are wrong. Math and statistics are merely 1) tools used in economics research and 2) a formal, precise language that economics can be expressed it. For any theory to hold true it must be quantifiable, and this is exactly how the history of economics proceeds. An ancient economic theorist comes up with a theory, and a future economist comes up with the mathematical formalization that solidifies the theory.

Yes, I understand it's value in academics and politics.

I'll give you three examples:

1) The invisible hand. Adam Smith posited that selfish people acting in their own self interest will ultimately produce outcomes that are favorable and desirable to the entire society at large. This would be brought about by what Smith called the invisible hand. We may all think that this is a profound piece of insight, but looking back retrospectively this was just Adam Smith's opinion, nothing more and nothing less. However, as economics progressed and new economists came forward and proved Smith's conjecture. The first being Leon Walras, with his mathematical model of general equilibrium, followed by Kenneth Arrow (Arrow-Debreu Model) and the fundamental theorems of welfare, highly mathematical theorems that formalize Adam Smith's notion of the invisible hand.

Yes, I agree with the invisible hand, but the academic models only serve to add certain level of credibility, that is useful in an academic debate. However, they do not make the invisible hand visible. People still go about their lives oblivious to their contribution to a free market and market manipulators have little patience in a market downturn. In my experience, it is consistent observation over a long period of time that shows how market manipulation is ineffective at best.

2) Utility. Utility (a concept at the core of utilitarianism) is simply the amount of satisfaction derived from the consumption of goods and services. When you buy something you receive some level of happiness from what you bought, and this is referred to as utility. The concept seems obvious at first, but it wasn't really thought about until Jeremy Bentham, who asserted that human behavior can be understood simply as an exercise in utility. That is, humans choose to do those things and purchase those goods that provide them with high levels of utility and avoid those things that don't give them much utility (formally known as Felicific calculus). Again, this seems obvious so why exactly must there be some type of mathematical proof and formalism for it. Well, for the same reason why something as obvious as gravity required rigorous mathematical formalization, and later economists offered mathematical formalizations of utility showing the concept of the valid and true, the most notable being John von Neumann and Paul Samuelson.

To this point, the economist in our shul told me of a discussion he had with one of his professors in his undergraduate years. The professor illustrated the point by saying that one can apply this principle to a basket of shrimp. The first shrimp has a large util designation, because, it is the most satisfying. The second has a little less. By applying statistical analysis one can find the point at which there is negative satisfaction and thus stop. The problem, my friend posited, is that if one throws up before reaching equilibrium, was the calculation of the utils assigned to the last shrimp consumed correct?

3) Free trade. Again, since the founding of economics free trade has always been viewed favorably. Both Adam Smith and David Ricardo offered arguments for free trade (absolute and comparative advantage) and these two concepts can actually be expressed mathematically yet no one objects to this. So perhaps they only object to advanced mathematics that they don't understand being implemented in economics, but I digress. Smith justified free trade using absolute advantage, however Smith's justification rested upon the assumption that all nations had an absolute advantage in at least one commodity and this may not always be the case. So Ricardo dropped the assumption, allowed for a world where some nations did not have an absolute advantage, and still managed to justify free trade based on comparative advantage. Then, the Hecksher-Ohlin model dropped the assumption of comparative advantage and justified free trade based upon factor intensity. And then, Paul Krugman of all people dropped all of these assumptions and still managed to justify free trade based on scale economics and imperfect/monopolistic competition.

Again, I do not disagree with the philosophy. However, statistics do not take into account factors like the overwhelming use of force, as Rush Limbaugh calls it. Free trade models presume a world where maximum productivity is the goal. In much of the world trade is as much a weapon as an economic tool. As an economic tool market manipulation is counterproductive. However, as a weapon or political tool it is very useful. That is why I oppose the use of it in these United States. It is being sold as an economic tool, when it is really being used as a political tool.

So to the contrary, mathematics is very useful in economics. It also serves as a restriction on entry into the field and a signal of capability.

Ah, here you have the point I will whole heartedly agree with. It is a rite of passage for those who wish to be part of the academic aristocracy.

Everybody out there seems to have opinions on economic issues, whether it be income inequality or the TPP trade deal, and just because they have these opinions they think they're somehow qualified to expound on economics and deride it as 'simple.' Luckily, just having opinions and reading popular articles isn't sufficient to enter the economics field and start producing research, a rigorous understanding of math required. Knowledge of things like multivariable calculus, linear algebra, ordinary differential equations (partial differential equations and stochastic calculus for top finance guys), proof based probability theory, mathematical statistics and real analysis.

Yes, if one wishes to discuss the latest theories one must be up on the tools of the trade. That said, I do not think economics is easy. In fact, I think statistical analysis oversimplifies it. It is a dynamic organism and, as with all organisms, one can analyze the various parts and systems, but there is always the X factor that throws a wrench into the works. Even if one were able to accurately predict how an economy works, that knowledge is also a commodity, that would be traded in the market place of ideas resulting in some applying it at the "right" time and others applying it at the "wrong" time. In my opinion, a national economy is way too big to predict or control, let alone a global economy.

And as I said, math also serves as a signal of capability. Math is an extremely difficult and advanced field and anyone who is able to understand it is intellectually capable. Btw, the economics profession has a high average IQ, ranking in fifth place behind engineering and science: http://www.statisticbrain.com/iq-estima ... ege-major/

Yes, I understand that the scholatariat must be assured that it is populated by only those who possess the right statistical resume'. No offense intended. I am just hoping to show that theology and science are not the only religious institutions. Every discipline has it's rituals and a long list of well reasoned justifications for them. Also, as with all religious institutions, it is important to not become so enamored with the rituals that one looses one's awe of the vastness of the universe.

[WinePusher]

Thanks for the post bluethread, it's very interesting and thought provoking. I appreciate your comments and respect your perspective.

I believe we've already spoken through pm about the use of mathematics and statistics in economics, and if I remember correctly you expressed your disapproval about it. You're certainly not alone, many heterodox schools of thought like the Austrians and the Institutionalists to a certain extent hate how widespread math and stats are used in econ.

I wouldn't say I disapprove of it et al. I just have my reservations regarding the use of it as a true determinant of human behavior. When dealing with large numbers, as with the house side at a casino, it has some value. When dealing with individual cases or small numbers, as with an individual or table in a card room, not so much.

Interesting you'd say that. Before we discuss this let's get our definitions in order. When we talk about individual cases in the economy, we're dealing with microeconomics. When we talk about 'large numbers, such as the house side at a casino' we're talking about macroeconomics. As a body of knowledge, microeconomics is far more coherent, precise, mathematical and scientific than macroeconomics is. Microeconomics is one of the most math intensive fields out there other than physics and maybe chemistry and computer science. So the point is, when dealing with individual economic cases like an individual consumer or an individual firm, mathematics has been extremely crucial. When dealing with the economy overall, mathematical models have largely failed which is why a large majority of economists consider macro to be no good.

And btw, mathematics is used to model and describe economic behavior, it isn't used to determine it.

I'll give you three examples:

1) The invisible hand. Adam Smith posited that selfish people acting in their own self interest will ultimately produce outcomes that are favorable and desirable to the entire society at large. This would be brought about by what Smith called the invisible hand. We may all think that this is a profound piece of insight, but looking back retrospectively this was just Adam Smith's opinion, nothing more and nothing less. However, as economics progressed and new economists came forward and proved Smith's conjecture. The first being Leon Walras, with his mathematical model of general equilibrium, followed by Kenneth Arrow (Arrow-Debreu Model) and the fundamental theorems of welfare, highly mathematical theorems that formalize Adam Smith's notion of the invisible hand.

Yes, I agree with the invisible hand, but the academic models only serve to add certain level of credibility, that is useful in an academic debate.

Correct.

However, they do not make the invisible hand visible.

In a sense it absolutely does. These mathematical models and theorems give us far more insight into how the invisible hand operates in a free market and how it produces good economic outcomes.

People still go about their lives oblivious to their contribution to a free market and market manipulators have little patience in a market downturn. In my experience, it is consistent observation over a long period of time that shows how market manipulation is ineffective at best.

The same can be said about gravity bluethread. People go through most of their lives oblivious to the effects of gravity and it's role in maintaining the orbit of the earth. The force of gravity is obvious, yet physicists delve deeper into the subject, formulating highly mathematical models and theorems in order to understand it better. The same process applies to economics. The beneficial effects of the free market are obvious (to most people) as is the presence of the invisible hand. And the task of economists is to delve deeper into the concept in order to understand it better, and sadly this requires math. If you want to understand something about the world, you need to quantify it, and this requires math.

2) Utility. Utility (a concept at the core of utilitarianism) is simply the amount of satisfaction derived from the consumption of goods and services. When you buy something you receive some level of happiness from what you bought, and this is referred to as utility. The concept seems obvious at first, but it wasn't really thought about until Jeremy Bentham, who asserted that human behavior can be understood simply as an exercise in utility. That is, humans choose to do those things and purchase those goods that provide them with high levels of utility and avoid those things that don't give them much utility (formally known as Felicific calculus). Again, this seems obvious so why exactly must there be some type of mathematical proof and formalism for it. Well, for the same reason why something as obvious as gravity required rigorous mathematical formalization, and later economists offered mathematical formalizations of utility showing the concept of the valid and true, the most notable being John von Neumann and Paul Samuelson.

To this point, the economist in our shul told me of a discussion he had with one of his professors in his undergraduate years. The professor illustrated the point by saying that one can apply this principle to a basket of shrimp. The first shrimp has a large util designation, because, it is the most satisfying. The second has a little less. By applying statistical analysis one can find the point at which there is negative satisfaction and thus stop. The problem, my friend posited, is that if one throws up before reaching equilibrium, was the calculation of the utils assigned to the last shrimp consumed correct?

Yes, his description of utility is absolutely correct. Utility is said to be diminishing, meaning that if you're thirsty and you go to drink a cup of water, the first gulp will supply you with many utils, but the second gulp will supply you with less, and the third gulp will even less, and eventually you will stop consuming the water when you have reached maximum satisfaction.

Now, this is actually a topic of controversy among economists because the notion of utils is seemingly unquantifiable. If we take your shrimp example, you may receive a lot of utility from eating shrimp however I may not necessarily like shrimp, so eating it will actually supply me with dis-utility/unsatisfaction. Also, there is no way to numerically measure how much happiness you're getting from eating the shrimp. All we know for certain is that there will be a point where you stop consuming shrimp because you've already reached your maximum level of satisfaction.

And we do not necessarily apply statistical analysis to this. We use mathematical optimization to find the level of shrimp consumption that would maximize your utility, just as how the 2nd problem in my OP used the optimization technique to maximize the production level of a business.

3) Free trade. Again, since the founding of economics free trade has always been viewed favorably. Both Adam Smith and David Ricardo offered arguments for free trade (absolute and comparative advantage) and these two concepts can actually be expressed mathematically yet no one objects to this. So perhaps they only object to advanced mathematics that they don't understand being implemented in economics, but I digress. Smith justified free trade using absolute advantage, however Smith's justification rested upon the assumption that all nations had an absolute advantage in at least one commodity and this may not always be the case. So Ricardo dropped the assumption, allowed for a world where some nations did not have an absolute advantage, and still managed to justify free trade based on comparative advantage. Then, the Hecksher-Ohlin model dropped the assumption of comparative advantage and justified free trade based upon factor intensity. And then, Paul Krugman of all people dropped all of these assumptions and still managed to justify free trade based on scale economics and imperfect/monopolistic competition.

Again, I do not disagree with the philosophy. However, statistics do not take into account factors like the overwhelming use of force, as Rush Limbaugh calls it. Free trade models presume a world where maximum productivity is the goal. In much of the world trade is as much a weapon as an economic tool. As an economic tool market manipulation is counterproductive. However, as a weapon or political tool it is very useful. That is why I oppose the use of it in these United States. It is being sold as an economic tool, when it is really being used as a political tool.

So I'm not sure what you're saying. Are you against free trade because some countries use it as a weapon?

So to the contrary, mathematics is very useful in economics. It also serves as a restriction on entry into the field and a signal of capability.

Ah, here you have the point I will whole heartedly agree with. It is a rite of passage for those who wish to be part of the academic aristocracy.

Yes, and this is bad how? Like I said, only smart people understand math. By requiring a lot of math training to become an economist, the field benefits. I'd actually like to see more mathematical training required in order to prevent economics from degenerating into a soft field like the humanities.

Everybody out there seems to have opinions on economic issues, whether it be income inequality or the TPP trade deal, and just because they have these opinions they think they're somehow qualified to expound on economics and deride it as 'simple.' Luckily, just having opinions and reading popular articles isn't sufficient to enter the economics field and start producing research, a rigorous understanding of math required. Knowledge of things like multivariable calculus, linear algebra, ordinary differential equations (partial differential equations and stochastic calculus for top finance guys), proof based probability theory, mathematical statistics and real analysis.

Yes, if one wishes to discuss the latest theories one must be up on the tools of the trade. That said, I do not think economics is easy. In fact, I think statistical analysis oversimplifies it. It is a dynamic organism and, as with all organisms, one can analyze the various parts and systems, but there is always the X factor that throws a wrench into the works. Even if one were able to accurately predict how an economy works, that knowledge is also a commodity, that would be traded in the market place of ideas resulting in some applying it at the "right" time and others applying it at the "wrong" time. In my opinion, a national economy is way too big to predict or control, let alone a global economy.

Yes, but you would like to know how the national economy works, right? And you'd like to know how the global economy works too. This requires research in order to produce knowledge about how these economic systems operate and function. And the question is, how is one to produce any meaningful research on this subject without the use of math and statistics? Statistical inference is used in biology, and is very prominently used in physics. And these are subjects where direct experimentation subject to controls is possible. In economics there's no way to perform controlled experimentation so all we're left with is statistical inference and regression analysis.

And as I said, math also serves as a signal of capability. Math is an extremely difficult and advanced field and anyone who is able to understand it is intellectually capable. Btw, the economics profession has a high average IQ, ranking in fifth place behind engineering and science: http://www.statisticbrain.com/iq-estima ... ege-major/

Yes, I understand that the scholatariat must be assured that it is populated by only those who possess the right statistical resume'. No offense intended. I am just hoping to show that theology and science are not the only religious institutions. Every discipline has it's rituals and a long list of well reasoned justifications for them. Also, as with all religious institutions, it is important to not become so enamored with the rituals that one looses one's awe of the vastness of the universe.

No offense taken. I'm sympathetic to what you're saying here and I get your point of view. But just remember, we're just talking about math. Economic academics require proficiency in mathematics, nothing more nothing less. In otherwords, in order to become an economist you must go through the ritual of becoming a logical thinker, a person who is good with numbers, and a person who is a good problem solver. So I'm ok with this ritual.

[WinePusher]

2) The production function for a manufacturer is given in Cobb-Douglass form by f(x,y)=100x^3/4*y^1/4 where x represents labor units ($150 per unit), and y represents capital units ($250 per unit). The total cost of labor and capital is constrained by $50,000. Given the following information, maximize the production level for the manufacturer.

One of the most common applications of calculus to economics is the method of lagrange multipliers. Lagrange multipliers are used to solve for the optimal levels in an optimization problem subject to a particular constraint. Thus, our goal will be to maximize or minimize the objective function (f) subject to a constraint equation (g), so if f and g must have continuous first order partial derivatives the lagrangian will given by:

∇f(x,y)=λ∇g(x,y)

This equation states that the gradient of the objective function is equal to lambda times the gradient of the constraint equation, and remember that the gradient is just the partial derivatives in vector form. Thus, our first step will be to take partial derivatives of the objective function and the constraint equation.

∇f(x,y)=<75x^(-1/4)*y^(1/4), 25x^(3/4)*y^(-3/4)>

Now, the constraint equation is given by 150x+250y=50,000. Thus,

∇g(x,y)=150λ+250λ

The next step will be to equate each component of the ∇f(x,y) and ∇g(x,y) which will give us a system of equations that we will need to solve (we will also throw in the constraint equation at the end):

75x^(-1/4)*y^(1/4)=150λ
25x^(3/4)*y^(-3/4)=250λ
150x+250y=50,000

We must now simultaneously solve this system for lambda, and doing so will give us the maximum level of production for this firm. We will solve for lambda in the first equation:

λ=[75x^(1/4)*y^(1/4)]/150
λ=[x^(1/4)*y^(1/4)]/2

We will now substitute this value for lambda into the second equation, which will give us:

25x^(3/4)*y^(-3/4)=250 * [x^(-1/4)*y^(1/4)]/2
25x=125y
x=5y

We will now substitute this x value into the constraint equation to find the optimal units of capital and labor that maximize production:

150(5y)+250y=50,000
1000y=50,000
y=50
x=250

Now, finally, we will plug these values into the objective function to find the maximum level of production:

f(250,50)=100(250)^3/4*(50)^1/4

Putting this in a calculator will give the approximate solution 16,719.