NO.PZ2023010401000128
问题如下：
In a simple economy with no foreign sector, the following equations apply
If the real interest rate is 3% and government spending increases to 2,000, the increase in aggregate income will be closest to:
选项：
A.1,000.00 B.1,163. C.7,143.00解释：
Y = 4,200 + 0.86 × Y – 25 × r.
Y = 30,000 – 178.6 × r.
At 3%, Y = 30,000 – 178.6 × 3 = 29,464.
Alternatively, Y – 0.86Y = 4,200 – 25 × r
0.14Y = 4,200 – 256 × r.
If government spending increased by 1,000 to 2,000, then Y = 5,200 + 0.86 × Y – 25 × r.
Y = 37,142 – 178.6 × r, which at 3% would be Y = 37,142 – 178.6 × 3 = 36,607.
Representing an increase of 36,607 – 29,464 = 7,143.
Alternatively, at 5,200, Y – 0.86Y = 5,200 – 25 × r or 0.14 Y = 5,200 – 25 × r.
Or more simply, ∆G ÷ (1 – c) = 1,000/(1 – 0.86) = 7,143.
解题思路里面从联立方程得出0.14Y = 4,200 – 25 × r.，到增加政府支出1000变为Y = 5,200 – 25 × r.，这是不对的。因为0.14Y = 4,200 – 25 × r.这个公式是从Y=C+I+G三个函数合并项整理出来的。在Y=C+I+G这个线性方程中，在这个题里面G是与C和I的变化无关的独立常数=1000。那么现在常数增加1000，Y就是应该增加1000呀。
