# 21.1: Aggregate Output and Keynesian Cross Diagrams

- Page ID
- 32280

learning objectives

- What does this equation mean: Y = Y
_{ad}= C + I + G + NX? - Why is this equation important?
- What is the equation for C and why is it important?
- What is the Keynesian cross diagram and what does it help us to do?

*Developed in 1937 by economist and
Keynes disciple John Hicks, the IS-LM model is still used today to
model aggregate output (gross domestic product [GDP], gross
national product [GNP], etc.) and interest rates in the short
run*.__en.Wikipedia.org/wiki/John_Hicks__
It begins with John Maynard Keynes’s recognition that

Y = Y a d = C + I + G + N X

where:

Y = aggregate output (supplied)

Y_{ad} = aggregate demand

C = consumer expenditure

I = investment (on new physical capital like computers and factories, and planned inventory)

G = government spending

NX = net exports (exports minus imports)

*Keynes further explained that C = a
+ (mpc × Y _{d})*

where:

Y_{d} = disposable income, all
that income above a

a = autonomous consumer expenditure (food, clothing, shelter, and other necessaries)

mpc = marginal propensity to consume (change in consumer expenditure from an extra dollar of income or “disposable income;” it is a constant bounded by 0 and 1)

Practice calculating C in Exercise 1.

exercise

1. Calculate consumer expenditure using the formula C = a + (mpc
× Y_{d}).

Autonomous Consumer Expenditure | Marginal Propensity to Consume | Disposable Income | Answer: C |
---|---|---|---|

200 | 0.5 | 0 | 200 |

400 | 0.5 | 0 | 400 |

200 | 0.5 | 200 | 300 |

200 | 0.5 | 300 | 350 |

300 | 0.5 | 300 | 450 |

300 | 0.75 | 300 | 525 |

300 | 0.25 | 300 | 375 |

300 | 0.01 | 300 | 303 |

300 | 1 | 300 | 600 |

100 | 0.5 | 1000 | 600 |

100 | 0.75 | 1000 | 850 |

*You can plot a* **consumption function**
*by drawing a graph*, as in Figure 21.1 *, with consumer
expenditure on the vertical axis and disposable income on the
horizontal*. (Autonomous consumer expenditure a will be the
intercept and mpc × Y_{d} will be the slope.)

*Investment is composed of so-called fixed investment on
equipment and structures and planned inventory investment in raw
materials, parts, or finished goods*.

For the present, we will ignore G and NX and, following Keynes,
changes in the price level. (Remember, we are talking about the
short term here. Remember, too, that Keynes wrote in the context of
the gold standard, not an inflationary free floating regime, so he
was not concerned with price level changes.) *The simple model
that results, called a Keynesian cross diagram, looks like the
diagram in* Figure 21.2 .

The 45-degree line simply represents the equilibrium Y =
Y_{ad}. *The other line, the aggregate demand function,
is the consumption function line plus planned investment spending
I*. Equilibrium is reached via inventories (part of I). If Y
> Y_{ad}, inventory levels will be higher than firms
want, so they’ll cut production. If Y < Y_{ad},
inventories will shrink below desired levels and firms will
increase production. We can now predict changes in aggregate output
given changes in the level of I and C and the marginal propensity
to consume (the slope of the C component of Y_{ad}).

Suppose I increases. Due to the upward
slope of Y_{ad}, aggregate output will increase more than
the increase in I. *This is called the expenditure multiplier
and it is summed up by the following equation*:

Y = ( a + I ) × 1 / ( 1 - m p c )

So if *a* is 200 billion,
*I* is 400 billion, and *mpc* is .5, *Y* will
be

Y = 600 × 1 / .5 = 600 × 2 = $ 1,200 billion

If I increases to 600 billion, Y = 800 × 2 = $1,600 billion.

If the marginal propensity to consume were to increase to .75, Y would increase to

Y = 800 × 1/.25 = 800 × 4 = $3,200
billion because Y_{ad} would have a much steeper slope. A
decline in mpc to .25, by contrast, would flatten Y_{ad}
and lead to a lower equilibrium:

Y = 800 × 1 / .75 = 800 × 1.333 = $ 1,066.67 billion

Practice calculating aggregate output in Exercise 2.

exercise

1. Calculate aggregate output with the formula: Y = (a + I) × 1/(1 ? mpc)

Autonomous Spending | Marginal Propensity to Consume | Investment | Answer: Aggregate Output |
---|---|---|---|

200 | 0.5 | 500 | 1400 |

300 | 0.5 | 500 | 1600 |

400 | 0.5 | 500 | 1800 |

500 | 0.5 | 500 | 2000 |

500 | 0.6 | 500 | 2500 |

200 | 0.7 | 500 | 2333.33 |

200 | 0.8 | 500 | 3500 |

200 | 0.4 | 500 | 1166.67 |

200 | 0.3 | 500 | 1000 |

200 | 0.5 | 600 | 1600 |

200 | 0.5 | 700 | 1800 |

200 | 0.5 | 800 | 2000 |

200 | 0.5 | 400 | 1200 |

200 | 0.5 | 300 | 1000 |

200 | 0.5 | 200 | 800 |

## Stop and Think Box

During the Great Depression, investment (I) fell from $232 billion to $38 billion (in 2000 USD). What happened to aggregate output? How do you know?

Aggregate output fell by more than $232 billion − $38 billion = $194 billion. We know that because investment fell and the marginal propensity to consume was > 0, so the fall was more than $194 billion, as expressed by the equation Y = (a + I) × 1/(1 − mpc).

*To make the model more realistic, we can easily add NX to
the equation*. An increase in exports over imports will
increase aggregate output Y by the increase in NX times the
expenditure multiplier. Likewise, an increase in imports over
exports (a decrease in NX) will decrease Y by the decrease in NX
times the multiplier.

*Government spending (G) also
increases Y*. We must realize, however, that some government
spending comes from taxes, which consumers view as a reduction in
income. With taxation, the consumption function becomes the
following:

C = a + m p c × ( Y d - T )

T means taxes. The effect of G is always larger than that of T
because G expands by the multiplier, which is always > 1, while
T is multiplied by MPC, which never exceeds 1. So increasing G,
even if it is totally funded by T, will increase Y. (Remember, this
is a short-run analysis.) *Nevertheless, Keynes argued that, to
help a country out of recession, government should cut taxes
because that will cause Y _{d} to rise, ceteris paribus. Or,
in more extreme cases, it should borrow and spend (rather than tax
and spend) so that it can increase G without increasing T and thus
decreasing C*.

## Stop and Think Box

Many governments, including that of the United States, responded to the Great Depression by increasing tariffs in what was called a beggar-thy-neighbor policy. Today we know that such policies beggared everyone. What were policymakers thinking?

They were thinking that tariffs would decrease imports and thereby increase NX (exports minus imports) and Y. That would make their trading partner’s NX decrease, thus beggaring them by decreasing their Y. It was a simple idea on paper, but in reality it was dead wrong. For starters, other countries retaliated with tariffs of their own. But even if they did not, it was a losing strategy because by making neighbors (trading partners) poorer, the policy limited their ability to import (i.e., decreased the first country’s exports) and thus led to no significant long-term change in NX.

Figure 21.3 *sums up the discussion
of aggregate demand*.

key takeaways

- The equation Y = Y
_{ad}= C + I + G + NX tells us that aggregate output (or aggregate income) is equal to aggregate demand, which in turn is equal to consumer expenditure plus investment (planned, physical stuff) plus government spending plus net exports (exports – imports). - It is important because it allows economists to model aggregate output (to discern why, for example, GDP changes).
- In a taxless Eden, like the Gulf Cooperation Council countries,
consumer expenditure equals autonomous consumer expenditure
(spending on necessaries) (a) plus the marginal propensity to
consume (mpc) times disposable income (Y
_{d}), income above a. - In the rest of the world, C = a + mpc × (Y
_{d}− T), where T = taxes. - C, particularly the marginal propensity to consume variable, is important because it gives the aggregate demand curve in a Keynesian cross diagram its upward slope.
- A Keynesian cross diagram is a graph with aggregate demand
(Y
_{ad}) on the vertical axis and aggregate output (Y) on the horizontal. - It consists of a 45-degree line where Y = Y
_{ad}and a Y_{ad}curve, which plots C + I + G + NX with the slope given by the expenditure multiplier, which is the reciprocal of 1 minus the marginal propensity to consume: Y = (a + I + NX + G) × 1/(1 − mpc). - The diagram helps us to see that aggregate output is directly related to a, I, exports, G, and mpc and indirectly related to T and imports.