The basic macro model In this lecture, we will cover the fundamental macro model (also known as the IS-LM model). Developed in the 1950s/60s, economists at the time believed that through this model they had “solved” macroeconomics. This model was the basis of government policy in Australia, the US and the UK up to the mid 1970s, when facts showed that macroeconomic problems were not a thing of the past.

The goods market Our accounting identity from Macro 120 says that demand for goods and services: Z ≡ C + I + G + (X – IM) –Normally we just use “goods” as short-hand for “goods and services”. –Where C is private consumption of households and firms, I is investment by households and firms, G is government consumption of goods and services, X is exports and IM is imports.

Deriving the IS equation Assume we are in a “closed” economy (that does not trade with the outside world), so X = IM = 0. we will deal with open economies in a later lecture. Assume consumption is a function of disposable income so C(Y – T). Equilibrium in the goods market requires goods demand, Z, is equal to goods supply, Y. Y = C(Y – T) + I + G Is called the IS equation.

Linearizing consumption If we “linearize” consumption, we assume consumption to be given by: C = c 0 + c 1 (Y – T) Where c 1 is our marginal propensity to consume (MPC). We assume 0 < c 1 < 1. Our IS equation becomes: Y = c 0 + c 1 Y – c 1 T + I + G

The multiplier Rearranging we get: Where our equilibrium level of Y will be a function of parameters (c 0 and c 1 ) and our exogenous variables (I, G and T). Equilibrium Y is increasing in c 0 and c 1 (for sensible ranges). Equilibrium Y increases by for a change in I and G and by for a change in T.

Equilibrium in the goods market The value is called the “multiplier”. Is there a role for the government in this model? Yes, through manipulating G and T. Raise G and lower T in a recession, while lower G and raise T in a boom. If the government raises G in a recession, by how much will output rise? Which is why we call it the multiplier.

Variant: Balanced budget multiplier The government above was free to set G and T however it wished. What if the government had to control the budget deficit, so that G = T at all times? If we put the G = T requirement into the IS equation, we get the balanced budget multiplier: So our new multiplier is 1.

Balanced budget multiplier Intuition: Why is the balanced budget multiplier less than the multiplier without balancing the budget? Answer: In the balanced budget case, the government has to raise T by $1 when it raises G by $1. Raising T will lower output but by less than G raises output. The net result is a higher level of output, but less than if the government did not have to simultaneously raise taxes.

Investment The goods market model assumed that investment was exogenous- that changes in Y did not impact investment. Assume investment is a function of production and interest rates: I = I(Y, i) We assume that investment and production are positively-related and that investment and interest rates are negatively-related. Intuition: As interest rates rise, the cost of capital to firms rises, so fewer new projects are profitable.

New IS equation Our new IS equation is: Y = C(Y-T) + I(Y, i) + G Since C(.) and I(.) are functions, G and T are the only exogenous variables. The new IS equation represents the equilibrium combinations of (Y, i) given the values of (G, T). Since we have two variables (Y, i) but only one equation to determine them, the new IS equation expresses a relationship between Y and i.

Linearizing investment Assume investment is linear in Y and i: Plugging this into the IS equation we get: Can we talk about a new multiplier?

New IS equation Answer: Not yet! As if we changed G, we will affect Y and also i. What we have is a relationship between the equilibrium values of (Y, i) and the exogenous variables (G, T). How are the equilibrium values of Y and I related? As long as c 1 + b 1 < 1, we have Y negatively-related to i. So if we graphed the IS curve, it would be down-ward- sloping.

We need another equation! The new IS curve shows us possible equilibrium values of (Y, i), but it does not determine a unique value. There are an infinite number of solutions for one equation and two variables. We need another equation to have a solvable problem: two equations, two variables.

The money market Demand for money (M d ) is increasing in the money value of output and decreasing in the interest rate. Intuition: If the economy produces more goods, the economy will require more money to exchange for those goods. Interest rates are the time opportunity cost of holding money. If an individual were not holding cash, that wealth would be accumulating value in a bank or investment at the rate of interest.

Demand for money M d = L(Y, i) Assume that doubling output, doubles the demand for money for any interest rate, then this equation becomes: M d = Y L(i) We have assumed that L(i) is decreasing in i as above. Money supply (M s ) is exogenous and is determined by the government.

Equilibrium in the money market Equilibrium in the money market requires that money supply is equal to money demand. M s = Y L(i) This is called the “LM” equation. The exogenous variable is M s and the endogenous variables are (Y, i). This is another relationship in (Y, i). So the LM curve is upward-sloping in (Y, i).

Combining the IS and LM equations IS: Y = C(Y – T) + I + G LM: M s = Y L(i) We have two equations in two variables (Y, i), and so this equation is (generally) solvable for a unique solution (Y*, i*) that satisfies both equations. Only one set of values (Y*, i*) will simultaneously solve both the IS and LM equations. So only one set of values will lead to equilibrium in both the goods and money markets.

Role of the government? Combining the IS and LM equations means that we have two variables which are jointly determined by the three exogenous variables (M s, G, T). We call policies involving M s “monetary policy” and policies involving G and T “fiscal policy”. This was the dominant macro model of the 1950s and 1960s.

The IS-LM framework Fiscal policy (G, T) shifts the IS curve, while monetary policy shifts the LM curve. An increase in G shifts IS to the right. An increase in T shifts IS to the left. An increase in M s shifts LM to the right. i Y IS(G,T) LM(M s ) i* Y*

Experiments with IS-LM Show what happens in the IS-LM graph if you –Increase G or T or M s –Have a reduction in C or I –Have a decrease in M d For Thursday: Do Problem 4 and 5 in Chapter 5.