The IS-LM (Investment Savings-Liquidity preference Money supply) model focuses on the equilibrium of the market for goods and services, and the money market. It basically shows the relationship between real output and interest rates.

It was developed by John R. Hicks, based on J. M. Keynes’ “General Theory”, in which he analysed four markets: goods, labour, credit and money. This model, firstly named IS-LL, appeared in his article “Mr. Keynes and the Classics: a Suggested Interpretation”, published in 1937 in the journal Econometrica.

In order to understand how this model works, we’ll first see how the IS curve, which represents the equilibrium in the goods market, is defined. Then, the LM curve, which represents the equilibrium in the money market. Finally, we’ll analyse how the equilibrium is reached.

IS curve: the market for goods and services

In a closed economy, the equilibrium condition in the market for goods is that production (Y), is equal to the demand for goods, which is the sum of consumption, investment and public spending. This relationship is called IS. If we define consumption (C) as C = C(Y-T) where T corresponds to taxes, the equilibrium would be given by:

Y = C (Y- T) + I + G

We consider that investment is not constant, and we see that it depends mainly on two factors: the level of sales and interest rates. If the sales of a firm increase, it will need to invest in new production plants to raise production; it is a positive relation. With regard to interest rates, the higher they are, the more expensive investments are, so that the relationship between interest rates and investment is negative. The new relationship is expressed as follows (where i is the interest rate):

Y = C (Y- T) + I (Y, i) + G

If we keep in mind the equivalence between production and demand, which determines the equilibrium in the market for goods, and observe the effect of interest rates, we obtain the IS curve. This curve represents the value of equilibrium for any interest rate.

An increasing interest rate will cause a reduction in production through its effect on investment. Therefore, the curve has a negative slope. The adjacent graph shows this relationship. 

LM curve: the market for money

The LM curve represents the relationship between liquidity and money. In a closed economy, the interest rate is determined by the equilibrium of supply and demand for money: M/P=L(i,Y) considering M the amount of money offered, Y real income and i real interest rate, being L the demand for money, which is function of i and Y.

The equilibrium of the money market implies that, given the amount of money, the interest rate is an increasing function of the output level. When output increases, the demand for money raises, but, as we have said, the money supply is given. Therefore, the interest rate should rise until the opposite effects acting on the demand for money are cancelled, people will demand more money because of higher income and less due to rising interest rates.

The slope of the curve is positive, contrary to what happened in the IS curve. This is because the slope reflects the positive relationship between output and interest rates.

IS-LM model

At any point of these curves the equilibrium condition in the corresponding market is true, but only at the point where the two curves intersect, both equilibrium conditions are satisfied. We can see this intersection in the following graph:

The IS and LM curves undertake changes due to many factors, such as different kinds of economic policies. These variations will explain the changes in the values of production and of interest rates taking place in the economies.
For instance, if there is an increase in government spending, which is considered a fiscal policy, the IS curve will shift to the right, as seen in the graph in the left. This happens because more government spending means more production for any interest rate. This shift, as seen in the adjacent graph, will consequently change the equilibrium from point E₁ to point E₂, with a greater level of output, but also at greater interest rates.

On the other hand, if we consider a monetary policy, such as an increase in the money supply, the curve that shifts will be the LM curve, as seen in the graph in the right. An increase in the money supply will decrease the interest rate, shifting the LM curve to the right, thus increasing output.

Monetarists’ views on the IS-LM model:

Monetarists greatly criticized the IS-LM model, highlighting some different views regarding the elasticity (and therefore the slope) of both curves. In their opinion, the LM curve is very inelastic, while the IS curve is very elastic. The most important thing we derive from these different views is the different consequences and effectiveness of expansionary fiscal and monetary policies.

Monetarists argue that monetary policies are more effective. Take the same example as before, an increase in the money supply. This will shift the LM curve to the right, displacing the equilibrium from E₁ to E₂ in the figure below. However, monetarists consider also two other effects: direct and indirect wealth effect. The first one, also known as Pigouvian effect, considers that, because of the increase in money supply, people will consume more, shifting the IS curve and changing the equilibrium to point E₃. The second one considers that, because of the initial drop in the equilibrium interest rates, people will invest more, thus shifting even more the IS curve and changing the equilibrium to point E₄.

Now, monetarists are more sceptic than Keynesians about fiscal policy. This is because, as seen in the figure below, the initial shift of the IS curve (from point E₁ to point E₂) will be partly offset by a second shift of the same curve. This, known as crowding-out, happens because the increase in government spending increases interest rates, which decreases the attractiveness of investment. Therefore, the more the government spends, the less private capital will be invested, which moves the equilibrium from point E₂ to E₃. Also, because of higher output, money demand increases, which shifts the LM curve to the left, to point E₄.

Both views have a great army of researchers and professors defending them, as part of the modern division on such matters into two main doctrines: New Keynesian Economics and New Classical Macroeconomics. All the effects presented here must be taken into consideration when analysing the IS-LM model. However, it must be noted that some of these conclusions change when considering an open economy, which is analysed by the IS-LM-BoP or Mundell-Fleming model.

John R. Hicks, in his article “Mr. Keynes and the Classical; a Suggested Interpretation”, published in 1937 in the journal Econometrica, developed a model known as IS-LL, which will later become IS-LM. The purpose of the article was to compare classical economists’ view on the goods and money market, with Keynes’ views.
In a few words, Hicks would assume Keynes’ innovations (possibility of frictional unemployment, the impact of animal spirits on investment, as well as money illusion effects) to take place in the short run, while classical views (such as full employment, perfect competition and the ability of the economy to re-equilibrate itself without government intervention) to be valid on the long run.
Hicks starts with the following assumptions, which we will maintain:

-he considers the short period;

-the quantity of physical equipment is fixed;

-homogeneous labor;

-depreciation can be neglected;

-rate of money wages (w) can be taken as given;

-quantity of money (M) is given;

-price level of goods equals their marginal cost.

(For the sake of simplicity, we will not consider differences between investment and consumption goods, nor the differences on the distribution of income.)

He also defines the following variables, which we will reformulate according to the level of simplicity we are aiming at:

-Y: total income;

-M: money quantity (which is given);

-I: investment;

-S: savings;

-i: rate of interest.

By uniting both classical and Keynesian views, Hicks writes the following three equations:

-M(Y,i) : we see that money quantity depends on both total income and the rate of interest;

-I(i) : investment depends on the rate of interest;

-I=S(Y) : investment must equal savings, which depend on total income.

From these three equations, we can see the relation between total income and the rate of interest in both markets:

-money market: since the money quantity is given, the LL curve (blue) will slope upwards, because an increase in income usually raise the demand for money (people need cash to consume goods) and an increasing rate of interest tend to lower money demand (the explanation of this can be made from two different angles: people will rather save more money since the interest rate is higher, therefore will spend less and demand less cash; or people are less willing to borrow money from banks, to spend it or invest it, because of the higher rate of interest);

-goods market: the IS curve (green) shows the relation between income and interest needed to make savings equal to investment. It slopes downwards because the lower the interest, the more people will invest, and therefore the higher will the total income be.

Income and the rate of interest are therefore determined where the IS and LL curves intersect (point P).

This model (more precisely, the IS-LM) is used nowadays to show the effect of diverse economic policies on a closed economy, and served as a starting point for the later Mundell-Fleming model, which helps understand their effects on an open economy.

John R. Hicks was a British economist (1904-1989), professor at the London School of Economics, Cambridge University and University of Oxford. He took special interest on issues concerning microeconomics, growth, economic fluctuations and monetary theory. In his most famous work “Value and Capital”, 1939, Hicks referred to aggregation problems, interest rate, etc. It was also in this book where he developed further the comparative statics, the analysis in economics when describing two possible outcomes. His book “The Social Framework: an Introduction to Economics”, 1942, is a veritable treatise on structural analysis by means of social accounting.

However, Hicks is mainly known for the development of a general equilibrium model, based on J. M. Keynes’ “General Theory”, in which he analyzed four markets: goods, labor, credit and money, called the IS-LM model. This model, firstly named IS-LL, appeared in his article “Mr. Keynes and the Classics: a Suggested Interpretation”, published in 1937 in the journal Econometrica.

He was awarded the Nobel Prize in Economics in 1972, along with Kenneth Joseph Arrow, for his contributions to general equilibrium theory and welfare economics.

Keynes was a British economist (1883-1946), son of the economist and methodologist John Neville Keynes. J. M. Keynes first gained notoriety with his work during the Versailles Peace Conference, when he cleverly proposed in his book “The Economic Consequences of the Peace”, 1919, not to punish Germany to avoid future retaliation. Later, during the Great Depression, he fought the conservative views advocating for a restoration of the gold standard in the famous pamphlet “The Economic Consequences of Mr. Churchill”. After a series of papers on monetary issues, he published in 1936 the most important of his works, the “General Theory of Employment, Interest and Money”, which was the foundation of the then called New Economic Science, or Keynesianism. Keynes’ main thesis was that unemployment during the Great Depression was the result of the decrease in effective demand. Therefore, to achieve full employment, it was necessary to revive the economic system through public investment. In the last years of his life, J. M. Keynes participated in the negotiations of Bretton Woods, in 1944, leading to the creation of the International Monetary Fund.

At the Bretton Woods conference, where he was part of the British delegation, he raised the idea that the IMF should be constituted as a true worldwide central bank, capable of issuing paper currency for international payments, for which he proposed the name “bancor”. Most of the ideas mentioned in the “Keynes Plan” were not followed through, since they competed with the U.S. proposals specified in the “White Plan”.

Great disciples of Keynes, part of the Cambridge School, were Joan Robinson, Nicholas Kaldor and John R. Hicks, to name a few.

Cobweb models explain irregular fluctuations in prices and quantities that may appear in some markets. The key issue in these models is time, since the way in which expectations of prices adapt determines the fluctuations in prices and quantities. Cobweb models have been analysed by economists such as Ronald H. Coase, Wassily Leontief or Nicholas Kaldor. It was in Kaldor’s paper on the subject, “A Classificatory Note on the Determinateness of Equilibrium”, 1934, where the analysis of these models became of great interest, and where the phenomenon took the name of Cobweb theorem. Four years later, in 1938, economist Mordecai Ezekiel wrote the paper “The Cobweb Theorem”, which gave the phenomenon and its particular diagrams popularity.

Cobweb models are easily explained using the example used by Kaldor in 1934: agricultural markets. Let’s say weather conditions aren’t optimal during a year, which causes the quantity supplied of a certain crop to be quite small (Q_t, see figure below, first diagram). This excessive demand, or shortage, causes prices to be unusually high (P_t). When farmers realise how high prices are, they’ll plant more in order to supply more the following year. However, supply is so high the following year (Q_t+1) that prices decrease to meet consumers’ demand (P_t+1). Since prices are low, farmers decide to lower their supply the following year (Q_t+2), resulting in high prices again (P_t+2). This process will go on until an equilibrium is reached after a few fluctuations. This unique equilibrium is reached because in this first scenario, the elasticity of the demand curve, in absolute terms, is higher than the elasticity of the supply curve, which implies a convergent fluctuation.

The second diagram shows that a continuous fluctuation between two equilibriums will take place when both elasticities are equal to each other. The third diagram shows a divergent fluctuation, given by the fact that the demand curve is steeper than the supply curve. Even though these three diagrams show very different results, the example explained above can result in any of these scenarios, depending on each curve’s elasticity. 

There is another possible scenario, which is given by changes in the steepness of curves: if near the point where the supply and demand curves cross demand is steeper than supply, but when we move far away from this point the supply curve gets steeper than the demand curve, we get a cobweb as the one in the figure below. At first, prices and quantities act as in a divergent fluctuation. However, as supply gets steeper than demand, a limit cycle may be reached, turning this divergent fluctuation into a continuous fluctuation.

Market clearing occurs in those market situations in which the amount demanded by consumers equals the amount supplied by firms. In market clearing the equilibrium point has its corresponding equilibrium quantity and an equilibrium price. Economic science has developed several adjustment models to reach this stable point. Léon Walras’ and Alfred Marshall’s models are those mostly studied.

Léon Walras’ model is based on price as the force that motivates the adjustment process towards equilibrium. In moments of an excessive demand, prices will rise and against an insufficient demand a decrease in price will take place. The process of tâtonnement or “groping” will happen until the equilibrium price is reached and then transactions will begin to take place.

On the contrary, Alfred Marshall’s model considers that adjustment occurs via quantity. If the demand price is lower than that of supply, the quantity will decrease. The available quantity will be sold at the different prices that consumers are willing to pay for, until the actual equilibrium is reached.

The walrasian approach makes sense when prices are easily observed (a market with perfect information) and modified, being auctions of almost any kind a good example. When prices can hardly be modified (let’s say, because of adjustment costs such as menu costs), and when it’s easier to modify quantities (when there are excessive inventories), the marshallian approach is more reliable.

Demand and supply are possibly the two most fundamental concepts used in economics. The concept of market is usually defined as a number of buyers and sellers of a given good or service that are willing to negotiate in order to exchange those goods. We will first explain them separately and then jointly to show their interaction.

Demand:

Demand is the global market value that expresses the purchasing intentions of consumers. The demand curve shows the quantity of a specific product that individuals or society are willing to buy according to its price and their income. This curve shows an inverse relationship between price and quantity demanded giving it a downward slope. The reason why this happens is known as the law of demand: ceteris paribus, and considering ordinary goods, the higher the price the lower the quantity demanded, and vice versa.

We can start by analysing demand from a purely microeconomic point of view: a single individual, let’s say her name is Joan. Joan’s demand for, let’s say, books, is such as shown in the adjacent graph. If the price of a book is $35 or more, Joan won’t demand any (point a), given her preferences (basically, she would rather spend her money on something else). However, if the price of books goes down to $30, she will want to buy one (point b). If it decreases to $20, Joan will buy two books (point c), and so on. By joining all the points (a-h), we’ll get Joan’s demand curve. It’s worth mentioning that, for simplicity’s sake (though violating monotonicity), we consider that the demand curve ends at the axes.

From a macroeconomic point of view, the demand curve is just the aggregation of all demand curves from all buyers in a particular market. Let’s say the market for books has only two buyers: Joan and her classmate Edward. The horizontal sum of Joan and Edward’s demand curves will give us the market demand: 

Supply:

On the other side, supply is the set of offers made in the market for the sale of goods and services. The supply curve records the location of the points corresponding to the amount offered for a particular good or service at the different prices. This curve shows a direct relationship between price and quantity supplied, giving it an upward slope. The reason why this happens is known as the law of supply: ceteris paribus, and considering ordinary goods, the higher the price the higher the quantity supplied, and vice versa.

Let’s see how the supply curve can be built, starting with an individual’s offer, let’s say his name is Robert. Robert is willing to supply books for $10 or more, this is, Robert won’t supply any books for $5 (point a). However, if the price of books goes up to $10, he will be willing to sell one book (point b). If it increases to $15, Robert will sell two books (point c), and so on. By joining all the points (a-g), we’ll get Robert’s supply curve. Notice that the supply curve goes up and seems not to have limits, an assumption made for simplicity’s sake. Of course Robert will have troubles to supply more than a certain amount of books, but let’s keep it simple and not think about the upper end of the supply curve.

Again, the market’s supply curve is just the aggregation of all supply curves from all sellers in a particular market. Let’s say the market for books has only two sellers: Robert and the librarian next door, Gregory. The horizontal sum of Robert and Gregory’s supply curves will give us the market supply:

Equilibrium and market clearing:

The demand and supply curves define the market clearing, that is, where the demand of the products meets its supply. At this point we have what is known as, an equilibrium point, with its corresponding price and quantity of equilibrium.

It is possible for disequilibrium to occur when the amount demanded does not equal the amount supplied. There are a series of scenarios in which this can happen. In situations in which the quantity demanded is higher than the quantity supplied, the market is suffering from an excess demand. When the opposite occurs we will be talking about an excess supply. Prices will have to gradually adjust through different market mechanisms until the equilibrium price is met.

Movements vs. shifts:

When analysing demand and supply and their respective curves, it is important to distinguish between two aspects: movements along curves and shifts in curves.

A movement refers to a change in either the demand or supply curve, which occurs when a change in the quantity is caused by a change in price and vice versa. An increase in the price of a good or service would cause a movement along its demand curve, decreasing the amount demanded. In the case of supply curves, as we previously saw, an increase in price would also increase quantity. It’s important to understand that movement along the curves does never actually change the equilibrium point, as movements along the curves do not affect it. In the adjacent figure we can see a price increase (let’s say, because an increase of VAT), which causes a movement along the demand curve.

Sometimes the market suffers from changes due to a displacement (shift) of the demand and/or the supply curve. This shift in curves will always result in a new market equilibrium. When a shift occurs, the curve moves, meaning that for each price there will be a new different quantity being demanded or offered. This curve shifts can occur in two directions, upwards and downwards, or if preferred, rightwards and leftwards. Depending in what curve we are considering one is equal to another one.

Demand curves may shift for multiple reasons, for example, an increase in the consumers’ level of income would increase the aggregate demand of a normal good for each price, and hence shift the demand curve to the right (left figure). Other examples would include changes in the price of competitors (substitute goods), changes in complementary goods, tastes, expectations, number of buyers, seasonality, etc.  Supply curve shifts may be also motivated by a variety of different reasons, such as input prices: an increase on the price of paper would shift the supply curve to the left, since the same quantity would be sold at a higher price (right figure). Other variables that can shift the supply curve include technological progress, expectations, number of sellers, etc.

Net exports (also known as balance of trade or commercial balance), are one of the components of the gross domestic product. Net exports of a country are the difference between that country’s exports and imports of goods and services. Exports are defined as the merchandise produced domestically and sold in the rest of the world, whereas imports is merchandise produced overseas and sold domestically:

Net exports = exports – imports

An equivalent denomination for net exports is the trade balance, a term that allows us to determine situations of surplus, deficit or equilibrium in a country’s relations with the rest of the world. When exports are greater than imports, there is an excess of exports and we talk about a trade surplus. In contrast, when imports are greater than exports, the country is said to run a trade deficit. In the case that the country’s exports and imports are identical, net exports are zero, and the country has a balanced trade.

Some of the factors that influence the trade balance are: the tastes and incomes of domestic and foreign consumers, the prices of the products in the country and abroad, the exchange rates, the associated costs to trade (e.g. transport costs), government policies, or international agreements.

Government spending, or government expenditure, is one of the components of a country’s gross domestic product. It includes all the spending on goods and services made by the government at all levels: local, regional, federal, national, etc. This component corresponds to the sum of government consumption and government gross investment.

Government consumption corresponds to the amount the government spends, subtracting the government’s revenue. On the one hand, government spending includes transfer payments made to households, such as unemployment benefits. On the other hand, government revenue includes taxes, which account for most of it.

As for investment, government spending has a multiplier effect. The reason is that government spending includes government investment. The multiplier effect makes that any amount spent in the present generates more than that amount in the future.

The level of government spending is one of the tools used in fiscal policy. An increase of public spending can be used to boost the economy, because the GDP increases as public spending does. On the other hand, a reduction of the public spending slows down the pace of GDP growing. The weight of government spending as a percentage of the GDP is considered as a measure of the importance of the public sector in a country.