Assignment 5.1: Homework – Marginal Propensity to Consume and the Multiplier

A study in Italy by Jappelli and Pistaferri (2014) showed the following the average marginal propensity to consume (MPC) is c_{1} = .52.

They then looked at how different groups had different marginal propensities to consume. In particular:

- For Group 1 of Italians, their MPC is c
_{1}= .3 - For Group 2 of Italians, their MPC is c
_{1}= .65

Now, take the following hypothetical situation about the Italian economy:

M = X = 0

G = 500, T_{p}=500

C = 1000 + c_{1}(Y-T_{p})

I = 200

Round to two decimal places in answers below:

- First let’s imagine all Italians have the average MPC of c
_{1}= .52- What is the equilibrium level income?
- If the gov’t increases spending by 200, what is the new equilibrium level of income?
- What is the multiplier on government spending?
- If government spending stays at 500, and instead they lower personal taxes by 200, why is the new equilibrium level of income?
- What is the multiplier on the tax reduction (in absolute value)?
- Which multiplier is larger (in absolute value)?
- Why are they different?

- Now, let’s look at the effect of difference in MPC.
- Fill out the following table (your answer for all Italians should come from question 1)

**Effect of Difference in MPC**

Marginal propensity to consume | Multiplier on government spending | |

All Italians | .52 | |

Group 1 | .3 | |

Group 2 | .65 |

- Discuss the differences in multipliers. In words (not math!), how does the MPC relate to the multiplier?
- Group 1 and Group 2 are two mutually exclusive collections of people in the Italian economy that have different consumption habits (this could be based on geography, age, income level, education, etc.) Make an educated guess (or read the paper itself!) about who belongs to each group. Then explain your reasoning.

**References: **

Jappelli, T., & Pistaferri, L. (2014). Fiscal Policy and MPC Heterogeneity. *American Economic Journal: Macroeconomics*, 6(4), 107–136. http://dx.doi.org/10.1257/mac.6.4.107

QUESTION ONE

M = X = 0

G = 500 T p = 500

C = 1000 + C_{1}(Y – T p)

I = 200

C_{1}= 0.52

- Equilibrium level of Income

Y = C + I + G

Therefore,

C = 1000 + C_{1}(Y – T p)

= 1000 + 0.52 (Y- 500)

= 1000 + 0.52Y – 260

= 740 + 0.52Y

Therefore, Equilibrium level of income is

Y = C + I + G

Y = 740 + 0.52Y + 200 + 500

Y = 1440 + 0.52Y

Y- 0.52Y = 1440

0.48Y = 1440

Y= 3000

- New equilibrium if government spending increases by 200

Initial government spending = 500

After increase = 500 + 200

= 700

Y = C + I + G

Y = 740 + 0.52Y + 200 + 700

Y = 1,640 + 0.52Y

Y-0.52Y = 1,640

0.48Y=1,640

Y= 3,416.67

- Multiplier of Government spending

Government Multiplier = 1

____________

1 – MPC

= 1

_________

1 – 0.52

= 2.08

- New equilibrium if taxes are lowered by 200 and government spending remains the same

Initial Taxes is =500

After decrease = 500 -200 = 300

C = 1000 + C_{1}(Y- T p)

= 1000 + 0.52(Y – 300)

= 1000 + 0.52Y – 156

= 844 + 0.52Y

Therefore, new equilibrium

Y = C + I + G

Y = 844 + 0.52Y + 200 + 500

Y = 1,544 + 0.52Y

Y – 0.52Y= 1,544

0.48Y = 1,544

Y = 3,216.67

- Tax Multiplier

Tax Multiplier = – MPC

___________

1 – MPC

= – 0.52

___________

1 – 0.52

= 1. 08

- Which Multiplier is larger?

Government Multiplier Is greater than Tax Multiplier

- Why are they different

Government affects expenditure choice directly while tax affects outlay decision through consumption and consumption is dependent on the MPC

QUESTION TWO (2a)

a) | b) Marginal propensity to consume | c) Multiplier on government spending |

All Italians |
.52 |
2.08 |

Group 1 |
.0.3 |
1.43 |

Group 2 |
0.65 |
2.85 |

2 a) Government spending Multiplier

Government spending Multiplier = 1

Italian __________

1 – MPC

= 1

______________

1 – 0.52

= 2.08

Group One Government Spending Multiplier = 1

______________

1 – 0.3

= 1.43

Group two Government Spending Multiplier = 1

____________

1 – 0.65

= 2.86

2b) Discuss the difference in the Multipliers

The larger Marginal Propensity to Consume the Larger multiplier effect. Therefore, Group two has greater Multiplier effect since it has higher Marginal propensity to consume. While Group one has a lower multiplier effect since it has lower Marginal Propensity to consume

2c) Consumption habits of both groups are influenced by income level. The higher the income the higher marginal propensity to consume and lower the income lower marginal propensity to consume

[1] Much of this data comes from Jappelli and Pistaferri (2014). However, some of the numbers were altered slightly for pedagogical reasons.