Econ 208

Marek KapickaLecture 5

The Effects of Gov’t Spending

Announcements

Read Woodford, “Simple analytics..”, pages 1-9 (on the web)

PS2 will be posted today

B1) The Effects of Government Spending Equilibrium Conditions

The equilibrium condition (*)

Fiscal multiplier with and

𝑉 ′ (𝐻𝑡)𝑈 ′ ¿¿

𝑑𝑌 𝑡

𝑑𝐺𝑡

= 1

1+(𝜂+1−𝛼 )𝑌 𝑡❑− 1+𝜂

𝛼

B1) The Effects of Government Spending Equilibrium Conditions

𝑉 ′ (𝐻 𝑡)𝑈 ′ ( 𝑓 (𝐻𝑡 )−𝐺𝑡)𝑓 ′(𝐻𝑡)

𝐻𝑡𝐻𝑡∗

𝑤𝑡

B1) The Effects of Government Spending How big is the multiplier?

Rewrite, using :

is somewhere between 2 to 5 is around 0.6 is around 0.2

The fiscal multiplier is around 0.19 to 0.34. Very small!

𝑑𝑌 𝑡

𝑑𝐺𝑡

= 1

1+(𝜂+1−𝛼 )(1−𝐺𝑌

)

B1) The Effects of Government Spending Extension #1: Productive government spending

Assume now that government spending is productive:

Where measures the efficiency of government spending

Typically we would have Total production of the economy:

𝑌 𝑡𝐺=𝜙𝐺𝑡

𝑌 𝑡=𝑌 𝑡𝑃+𝑌 𝑡

𝐺=𝐻𝑡𝛼+𝜙𝐺𝑡

B1) The Effects of Government Spending Extension #1: Productive government spending

Planning problem:

subject to

Obtain

max𝐶 𝑡 ,𝐻𝑡

∑𝑡=0

∞

𝛽𝑡[ ln𝐶𝑡−11+𝜂

𝐻𝑡

1+𝜂

]

𝐶𝑡+𝐺𝑡=𝐻𝑡𝛼+𝜙𝐺𝑡

B1) The Effects of Government Spending Extension #1: Productive government spending

Putting together

The multiplier is now larger, but is still smaller than one

𝑑𝑌 𝑡

𝑑𝐺𝑡

=𝑑𝑌 𝑡

𝑃

𝑑𝐺𝑡

+𝑑𝑌 𝑡

𝐺

𝑑𝐺𝑡

<1

B2) The Effects of Government Spending Extension#2: Monopolistic Competition

Suppose that instead of competitive markets, there is monopolistic competition There is a final good producer that

demands the intermediate goods There are many small identical,

monopolistic firms producing intermediate goods

where is markup

𝑉 ′ (𝐻𝑡)𝑈 ′ ¿¿

B2) The Effects of Government Spending Extension#2: Monopolistic Competition

Since is constant, the frictionless economy with monopolistic producers behaves similarly as the competitive economy The fiscal multiplier is exactly the same

Note that the level of production is inefficiently low

B2) The Effects of Government Spending Frictions

Larger increase in would be possible if rises more than

Introduces a ‘’labor wedge’’ into the equilibrium condition:

Before we had . If then the fiscal multiplier is larger

1

𝛼𝑌 𝑡

𝛼− 1𝛼

𝑉 ′ (𝑌 𝑡❑1 /𝛼)

𝑈 ′ (𝑌 𝑡−𝐺𝑡 )=

𝑤𝑡

𝛼 𝑌 𝑡

𝛼−1𝛼

=Δ (𝐺)

B2) The Effects of Government Spending Frictions

How to justify increasing ? Assume sticky prices: some producers cannot change their nominal price

How much the labor wedge changes depends on How sticky prices are What the monetary policy does

B2) The Effects of Government Spending Frictions

Suppose that there is a nominal price of the final good . Each producer charges a nominal price for its product Before we had and, in equilibrium, .

Suppose that before an increase in government spending there is

Suppose that a fraction cannot change the output price

B2) The Effects of Government Spending Frictions

In equilibrium, obtain

Corresponds to If an increase in triggers an increase

in the price level then increases with A response of monetary policy

matters!

𝑤𝑡=𝜃−1𝜃 [ 1−𝛾

1−𝛾 𝑃 𝑡𝜃 −1 ]

11−𝜃𝛼𝑌 𝑡

❑𝛼−1𝛼

Δ= 𝜃𝜃−1 [ 1−𝛾

1−𝛾 𝑃 𝑡𝜃−1 ]

1𝜃 −1

Results from a world with frictions – a summary

If prices are sticky and the monetary policy reacts to increased government spending by producing some inflation, the fiscal multiplier is larger