goods market problem set

1/ false, the economy with the higher $c_1$ will have a higher drop. this is because of $c_1(Y-T)$, meaning $T$ is scaled by $c_1$, and thus is larger if $c_1$ is higher.

2/ false, as an increasing deficit means that $D=G-T$ increases. $I=S+T-G$, and by $D$, $I=S-D$. $I$ decreases since $\Delta I=\Delta S-\Delta D$, if $S$ is constant, $\Delta I=-\Delta D$. but $S=Y-T-C$, dependent on $\Delta T$, which is in $\Delta D$, so it cannot be assumed stable.

3/ false. all changes in taxes get canceled out in investment, $I=S+T-G=Y_D-C+T-G=Y-T-C+T-G=Y-C-G$. so $\Delta T$ does not create any $\Delta I$.

4/ same as 2/

5/ false. increasing budget deficit by 10%, deficit is $D=G-T$. by $Y=\frac{1}{1-c_1}[c_0+\bar{I}+G-c_{1}T]$, $\Delta Y=\frac{1}{1-c_1}[\Delta G]-\frac{1}{1-c_1}[c_1\Delta T]$. but the percentage change of $Y$ is dependent on the old $Y$—so even though $\Delta Y$ can end up being larger than $\Delta D$ because of the multipliers (when $G$ is shifting), it doesn’t prove that the percentage change of $Y$ is $>10\%$.

6a/

• $Y=\text{€150 B}$
• $T=0.25Y$
• $D=G-T=0.03Y$
• $G-0.25(\text{€150 B})=0.03(\text{€150 B})$
• $G=\text{€42 B}$

6b/

• $Y=\text{€157.5 B}$
• $D=0.035Y$
• $G-0.25(\text{€157.5 B})=0.035(\text{€157.5 B})$
• $G=\text{€44.8875 B}$
• increased by $\text{€2.8875 B}$

6c/ $\text{€157.5 B}-\text{€150 B}=\text{€7.5 B}$

6d/

• $Y=\frac{1}{1-c_1}[c_0+\bar{I}+G-c_{1}T]$
• $\Delta Y=\frac{1}{1-c_1}[\Delta G-c_1\Delta T]$
• $\text{€7.5 B}=\frac{1}{1-c_1}[\text{€2.8875 B}-c_1\text{€1.875 B}]$
• $\text{€7.5 B}\times (1-c_1)=\text{€2.8875 B}-c_1\text{€1.875 B}$
• $\text{€7.5 B}-c_1\text{€7.5 B}=\text{€2.8875 B}-c_1\text{€1.875 B}$
• $-c_1\text{€5.625 B}=\text{€2.8875 B}-\text{€7.5 B}$
• $c_1=0.82$
• $\frac{1}{1-c_1}=5.55$

6e/ $c_1=0.82$

6f/

• old $T-G=\text{€39.375 B}-\text{€44.8875 B}=\text{€5.5125 B}$
• new $T-G=\text{€6.06375 B}$
• $\text{€6.06375 B}-\text{€5.5125 B}=\text{€0.55125 B}$
• new $T=\text{€39.92625 B}$
• $T=rY=r(\text{€157.5 B})=\text{€39.92625 B}$
• $r=0.2535$