Additional explanations and a numerical example for the Keynesian Cross In the Keynesian cross we draw the desired demand function (DD) and the total output (Y). In equilibrium DD has to be equal to Y. Definition of the desired demand: DD= C + G + I + PCA For illustration purpose, here focus on consumption (thus I=G=PCA=0) : DD = C Consumption is defined by the following function C= C (Wealth, disposable income) For the moment we don’t look at wealth but concentrate on the link between disposable income (Y) and desired consumption (note: since no taxes here since G = 0 total income equals disposable income). We can than write the consumption function also the following way: C = a + c*Y Where c = marginal propensity to consume and a = autonomous consumer expenditure. For finding the equilibrium between the demand and supply of goods, this autonomous consumption plays an important role. It explains why demand by consumers can lie above the actual income. What is autonomous consumer expenditure? The autonomous consumption is the amount of consumer expenditure that is independent of disposable income. It tells us how much consumers will spend when disposable income is 0. Since they still need to eat, buy clothes and pay rent when they have no income or very low income, they will always need at least this minimum amount. If a is 100 Euros for a disposable income of 0, then the consumer still wants to consume 100, even though he earns nothing. To this basic needs consumption, people then add always a fraction c of their actual disposable income. That’s why total consumption is described by C = a + c*Y. a can also be seen as the intercept of the DD demand (if I=G=PCA=0) c is the marginal propensity to consume and gives us the slope of the desired demand schedule. Equilibrium of supply and demand By fixing the parameters c and a, we can then find the equilibrium in the economy which is defined by Y = C = a + c*Y total output = actual consumption = desired consumption How do we find the level of output that equalizes supply and demand? Y = a + c*Y  Y – c*Y = a  Y (1‐c) = a  Y = a/(1‐c) Let’s assume a = 100 and c = 0,2 (I want to consume always 20% of my disposable income in addition to the 100 euros of autonomous consumption). We can the write the equilibrium condition: Y = a/(1‐c)  Y = 100/(1‐0,2)  Y = 125 In this case we see that total output equals total demand. Even though I only want to consume 20% of my disposable income, I first need to pay for my “autonomous consumption” (100 euros) and then I use 20% of my total disposable income (25 euros in this case) for additional consumption. Out of the equilibrium: If Y = 110: Demand is 100 + 0,2*110= 122. Here: Desired demand > actual output. People cannot consume as much as they want. If Y = 140 Demand = 128. Here: Desired demand < actual output. Firms are left with unsold goods and increase their unplanned investment. Adding Investment If we add investment, taxes, government expenditures and net exports, this will change of course the level of desired demand, but it will not change the logic. Here an example: When we change investments from I = 0 to I = 60 (we still keep G=T=PCA = 0 to keep thing easier). The equilibrium condition becomes: Y = C + I With I = 60 and C = 100 + 0,2*Y: Equilibrium output Y = 200. Y= 60 + (100+200*0.2) = 200 Reference: A good book for understanding the mechanisms behind the Keynesian cross is Frederic Mishkin, The Economics of Money, Banking and Financial Markets.