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Equilibrium in Macroeconomics April 22, 2011

Posted by tomflesher in Macro, Teaching.
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One of the things macroeconomists focus on quite a bit is calculating equilibrium conditions, or equilibria. Sometimes these account for random shocks or long-term growth – these have names like Dynamic stochastic general equilibrium and they’re outside the scope of this blog, which has so far focused on introductory-level material. We’re going to develop an idea of what an equilibrium is supposed to be and show how to figure out an equilibrium in a simple, open macroeconomy.

Equilibrium has a connotation of balance. The idea is that two (or more) things need to be balanced for some definition of balance that makes sense in the discussion. In economics, we generally think of equilibrium as representing a point where everything that’s produced is consumed. In a market for an individual good, that means we need to find a point where enough of those goods are produced so that everyone who wants to buy a good can do so.

That’s not very exact, though – it’s very rare that we see a goods market where everyone who wants the good can get it. There has to be some sort of incentive for the item to be produced, and generally that isn’t the satisfaction of seeing people using your trinket. (Sometimes it is – for example, the satisfaction of producing this blog and the fact that it forces me to think clearly are incentives for me to produce.) In general, that incentive is a price for the good – by producing, you get the opportunity to sell the good and get some money in exchange. That also provides a mechanism by which people self-select whether or not they participate in the market – at a certain price, people are willing to buy if they value the product at least that much. If the price is too high, they might still want the item, but they aren’t willing to pay for it so they’re no worse off.

How does that generalize to a macroeconomy, where we’re concerned about lots of goods and lots of prices? Well, it can be difficult to do so. That’s part of what makes grad macro so difficult. We, however, are going to make a couple of simplifying assumptions.

First of all, think back to the idea of the GDP Factory, where everyone works. Instead of producing individual goods, imagine that everyone just produces Stuff. The Stuff goes out on the market and is sold for money, the money is used to pay workers, and the workers go back to work and produce more Stuff. So, we can think of all goods as being part of the larger concept of production. So, everything we produce is supplied to the market. Remember that the supply equation is

Y^S = A \times f(K,H,N,L)

where Y^S is Stuff supplied, A is technological knowledge, K is capital, H is human capital, N is natural resources, and L is labor.

Then, remember that all the Stuff we produce has to be bought, stored in inventory, or exported, so our demand equation is

Y^D = C + I + G + NX

where Y^D is Stuff demanded, C is consumption, I is investment, G is government spending, and NX is Stuff exported less Stuff imported.

In order to find an equilibrium, we need to make another pair of assumptions:

  • The more you can sell for, the more you want to produce.
  • The more goods cost, the less you’ll want to buy.1

Since we’re simplifying away from individual goods, instead of a price, think about the price level of the economy as a whole (which we’ll abbreviate as PL). Also since we’re not thinking too much about individual goods, we don’t have to worry too much about changes in relative prices. (We can talk about those a little bit later.) So, basically, we’re looking at things statically – we don’t need to figure out what happens if coffee’s price goes up more than tea, for example.

The price level determines, on average, how much Stuff sells for. As the price level increases, we’ll produce more. As the price level decreases, we’ll buy less. There’s just one more condition we need to allow an equilibrium:

  • At 0 production, we need an incentive to produce more. So, at 0 production, demand is greater than 0 and supply is 0 by definition. At infinite production, demand is less than infinite.

So, these conditions say 2 things: At a low level of production, demand outstrips supply. As the price level increases, we produce more and demand less. These conditions guarantee that there’s a price level at which we’ll want to supply exactly as much as we want to demand – a little bit lower in price and more will be demanded than produced, and a little bit higher and more will be produced than demanded. So, at that price level,

Y^D = Y^S

Supply equals demand.

Equilibrium.

1Mathematically,

\frac{\partial Y^D}{\partial PL} > 0
\frac{\partial Y^S}{\partial PL} < 0

What’s so Gross about the Domestic Product? March 17, 2011

Posted by tomflesher in Macro, Teaching.
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The Gross Domestic Product (GDP) is one of the fundamental ideas of introductory macroeconomics. That’s because GDP is the core of one of the best ways to measure citizens’ well-being. We’ll get to that in a future post, though. For now, let’s talk about what GDP measures, and pretend that we’re not going to allow international trade. That makes this a closed economy model.

Let’s start with a simple premise: Everything that’s produced is purchased by someone. That makes sense in a couple of ways. A household can buy something, another business can buy something, the government can buy something, or… businesses can produce goods and store them for future use. For now, let’s treat this as the business buying its own goods to resell later.

GDP is defined as the market value of all final goods and services produced within a country in a given period of time. If we’re talking about the United States’ GDP for 2010, then it amounts to the prices of everything that was made in the US in 2010. The word ‘final’ means that if one company produces something that’s used as an input for another product, then only the last product counts. That means that some goods, like flour, might be final goods sometimes and intermediate goods other times. If I own a bakery, then I’ll buy a five-pound sack of flour to use in making bread, and so the flour is intermediate (since it’s used to produce another, final good). If I buy flour to make the same loaf of bread at home, then the flour might be used in home production, but since home-produced goods aren’t sold, then the flour is last sold to a consumer, and so it’s a final good. Since a consumer makes the purchase, it’s called Consumption.

Imagine that a box factory produces 600 boxes on December 31, 2010 and then sells them on January 1, 2011. Then, we have a sale of final goods, but the final goods weren’t produced in 2011, so they can’t count toward 2011 GDP. This requires the idea of inventory, which can be defined as goods that are produced but not sold. Inventory sales need to be subtracted from spending when calculating GDP.

Spending by businesses is on two things: intermediate goods (to produce final goods) and capital production (that is, stuff that allows them to be more efficient). All together, we call this spending by businesses Investment, which has a special definition in macroeconomics. Make sure not to confuse ‘investment’ in macro with the idea of putting money in stocks and bonds and hoping it grows. When taking a macro class, ‘investment’ pretty much means ‘spending by businesses.’ Inventory gets subtracted from investment, because it represents using past-produced goods. Those goods would have been counted as GDP in a previous year, so they need to be subtracted now even though a consumer purchased them.

Consumption and business spending aren’t the only things that need to be counted, though. Sometimes a business will produce a good that isn’t bought by a consumer. (I, for example, have never purchased a space shuttle, even though clearly someone’s producing them.) This is why we need to count Government spending.

Everything that’s produced is purchased, as long as we define ‘purchased’ to include ‘stored in inventory,’ and then we can subtract inventory sales from future GDP. Even though someone consumes a good that might have been produced in the previous year, subtracting it as inventory spending allows us to maintain the definition of GDP as ‘everything produced in the US in 2010’ while at the same time having an easy way to calculate it: just add up everything we buy!

This leads directly to the expenditure method for calculating GDP: just add up all the spending by consumers, by businesses, and by the government. In math, the letter Y is often used to represent output, and GDP represents the production (i.e. output) in an economy. So, we can use the formula

Y = C + I + G

where C is consumption spending, I is business spending (including subtracting inventory) and G is government spending. (In an open economy we’d need to account for imports and exports. That will come later.)

These two definitions (“the final market value of all goods and services produced in an economy in a given period of time” and “C + I + G”) are equivalent. In a future post, we’ll talk about how to put that to use.