Answer

Solution

1. 1

   $A$ spends $2/3$ of $pE_A$ on wheat $\Rightarrow$ wheat demand $=\dfrac{2pE_A/3}{p}=\dfrac{2E_A}{3}$. $B$ spends $1/3$ of $E_B$ (in TV) on wheat $\Rightarrow$ wheat demand $=\dfrac{E_B/3}{p}=\dfrac{E_B}{3p}$.

2. 2

   Wheat market clearing:

3. 3
   $$\frac{2E_A}{3}+\frac{E_B}{3p}=200. \quad (\star\star)$$
4. 4

   Combined with $200p+250=pE_A+E_B$:

5. 5

   Before ($E_A=100$): $(\star\star)\Rightarrow E_B=3p(200-200/3)=p(600-200)=400p$. Income identity: $200p+250=100p+400p=500p\Rightarrow p=\dfrac{5}{6}\approx 0.833$.

6. 6

   After ($E_A=70$): $(\star\star)\Rightarrow E_B=3p(200-140/3)=p(600-140)=460p$. Income identity: $200p+250=70p+460p=530p\Rightarrow p=\dfrac{250}{330}=\dfrac{25}{33}\approx 0.758$.

7. 7

   Thus $p$ decreases.

8. 8

   \textit{Intuition:} With home bias, $A$ spends more of its income at home (on wheat). When $A$ reduces total expenditure, the world demand for wheat falls disproportionately (since $A$'s marginal propensity to import is only $1/3$, while it was previously absorbing $2/3$ of its spending on wheat). Hence wheat becomes relatively cheaper.

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