# Keynesian cross model

## Introduction

### The Keynesian model

In this chapter we will look at the Keynesian cross model. This model is a simple version of what we call the "complete Keynesian model" or simply the Keynesian model. The Keynesian model has as its origin the writings of John Maynard Keynes in the 1930s, particularly the book "The general theory of Employment, Interest, and Money". Although this book was written as a criticism of the classical model, the similarities between the Keynesian model and the classical model are definitely greater than the differences. Lets point out the three most important differences directly:

• Say’s Law does not apply in the Keynesian model.

• The quantity theory of money does not apply in the Keynesian model.

• The nominal wage level * W *is an exogenous variable in the Keynesian model.

Remember that * W *being exogenous means that it is pre-determined outside the model. It does not necessarily mean that it is constant over time - even though this is a common assumption. However, the nominal wage must be known at any point in time in this model. To simplify our description of the Keynesian model, we will begin by assuming that

*is constant.*

**W**The Keynesian model is slightly more complicated than the classic model, and it is developed in four stages by analyzing four separate models. Each model has, however, a value in itself. The models we will consider and the major characteristics of each are:

• * Cross model: W, P and R *are constant (and exogenous).

• * IS-LM model: W, P *are constant and

*is endogenous.*

**R**• * AS-AD model: W *is constant,

*and*

**P***are endogenous.*

**R**• * The full Keynesian model: W *is exogenous (but not constant),

*and*

**P***are endogenous.*

**R**Once we have developed the full Keynesian model, we will combine it with the clasmodel which will lead to the neoclassical synthesis. The final chapter covers the Mundell-Fleming model - an extension of the neoclassical synthesis to an open economy where we also analyze the exchange rate.

### Summary of the cross model

The following list summarizes the cross model and relates it to the classical model:

• * Labor Market: *The real wages

*is exogenous in the cross model (*

**W/P***is exogenous in all the Keynesian models and*

**W***is exogenous in cross model). The determination of*

**P***is very different from the classical model, see Section 11.4.4.*

**L**• * Aggregate supply Ys *is determined by the production function

*=*

**Ys***Again, we always remove any trend in GDP and its components.*

**f(L, K).**• * Aggregate demand *is not always equal to the aggregate supply. Say’s Law does not apply in any of the Keynesian models. Therefore, we must describe how aggregate demand and GDP is determined in the cross model. This can be found in Section 11.3.

• * The Quantity theory of money *does not apply anymore. Fortunately, we don’t need it since

*is given in the cross model.*

**P**• * Consumption *was a function of the real interest rate in the classical model. In the cross model it is a function of

**Y.**• * Investment *was also a function of

*in the classical model. In the Keynesian model it is exogenous.*

**r**• Government spending (G) is exogenous but the net tax * NX *is endogenous (in the classical model, they were both exogenous). Net tax is assumed to be a function of

*which means that government savings will be endogenous (SG(Y)=*

**Y***- G).*

**NT(Y)**• Exports (X) is exogenous, as it is in the classical model, but imports (Im) is endogenous. Imports will also be a function of * Y. *Net imports and external savings will therefore also be endogenous variables (NX(Y) =

*-*

**X***and*

**Im(Y)***=*

**SR(Y)***- X).*

**Im(Y)**• Household savings and total savings were functions of the real interest rate in the classical model. In the cross model they are functions of **Y.**

• The real interest rate is exogenous in cross model. This follows by the fact that the nominal interest rate is exogenous and prices are constant (7re must be zero, and * r *= R).

We can divide our analysis of the cross model into three parts:

• * Aggregate demand. *Aggregate demand is a major component of the cross model. The main purpose of this section is to arrive at the conclusion that aggregate demand depends on real GDP.

• * Determination of GDP. *GDP is determined very differently in the cross model compared to the classical model.

• * Labor market. *One of the main points of the Keynesian model is to allow for involuntary unemployment. In the classical model of the labor market, we are always in equilibrium and there is no involuntary unemployment.