Bewley Model

EC417_Macroeconomics

The key difference between Bewley Model, Aiyagari Model, and Huggett Model lies in the presence of Government bonds.

In Bewley Model, government isn’t invisible. It has following actions:

• $G$: Government buys Public Goods.
• $B$: Government issues bonds to finance its spending. And Households buy these bonds as a way of saving.
• $T$: Taxes collected from households to pay for government spending and interest on bonds.

The total tax revenues are:

$$T(r)=\sum _j{\int }_a\tau (a,y_j)g(a,y_j;r)da$$

It’s intuitive that the current statues $a$ and $y_j$ would lead to different tax payments $\tau (\cdot )$.

Thus government faces its own budget constraint:

$$G+rB=T(r)$$

where $rB$ would be the net borrowing cost on government bonds.

The market clearing condition thus is simply:

$$A(r)=B$$

meaning that all saving by households would be absurd by government bonds.