| households | business | government | balance | |
|---|---|---|---|---|
| flows | ||||
| Government spending | G | -G | 0 | |
| Payment of taxes | -T | T | 0 | |
| Income (wages) | Y | -Y | 0 | |
| Consumption spending | -C | C | 0 | |
| stocks | ||||
| Change in household wealth | $\Delta H_h$ | |||
| Change in government balance | $\Delta H_g$ | |||
| balance | 0 | 0 | 0 | 0 |
production equation
$$G + C - Y = 0$$$$Y = G + C$$government budget equation
$$T - G = \Delta H_g$$household budget equation
$$Y - T - C = \Delta H_h$$Rearranging household budget equation
$$Y = T + C + \Delta H_h$$Equating $Y$'s
$$G + C = T + C + \Delta H_h$$Canceling $C$'s
$$G = T + \Delta H_h$$$$G - T= \Delta H_h$$$$-\Delta H_g= \Delta H_h$$Government budget deficit equation to household savings
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