Consider our general equilibrium trade model with perfect competition. $We$ discussed

how this model could $be$ extended $to$ multiple countries and multiple products. This

question wants $to$ demonstrate that with trade there should $be$ a positive correlation between

net exports and the difference $in$ free trade and autarky prices. $In$ equation form:

${}_i(p_i^F-p_i^A)T_{i}0$

Where $T_l$ denotes net exports $of$ good $i{Q}_i^F,$ minus consumption $in$ free trade, $C_i^{F}i=1,$dots,$N.$

$p_i^{g_i}is$ the price $of$ good i with free trade and $p_i^{A}is$ the price $of$ good $iin$ autarky.

$a{Q}_k^A=C_k^A$ and $Q_D^A=C_{bj}^A.$

$b{p}_k^A{Q}_K^A+p_D^A{Q}_b^A=p_k^A{C}_k^A+p_0^A{C}_D^A$

$c{T}_{K}tobe$ positive $or$ negative?

What about $T_D?$

$d(p_D^F-p_D^A)T_D+(p_K^F-p_K^A)T_{K}0$

$e,,$ and $,in$

equation $[3].$ Show how $to$ derive equation $[3]$ from equation $[2].$

$[p_K^F{T}_K+p_D^F{T}_D]-[(p_K^A{Q}_K^F+p_D^A{Q}_D^F)-(p_K^A{c}_K^F+p_D^A{C}_D^F)]0(),$ why would you expect this term $tobe$ equal $to$ zero? Explain

your intuition.

$g{p}_K^A{Q}_K^F+p_D^A{Q}_D^F{p}_K^A{Q}_K^A+p_D^A{Q}_D^A$

$h{p}_K^A{C}_K^F+p_D^A{C}_D^F{p}_K^A{C}_K^A+p_D^A{C}_D^A$

$i[(p_K^A{Q}_{}^F+p_D^A{Q}_D^F)-(p_K^A{C}_{}^F+p_D^A{C}_D^F)]$

$[(p_K^A{Q}_K^A+p_D^A{Q}_D^A)-(p_{}^A{C}_{}^A+p_D^A{C}_D^A)]$

$0$

$ky-$axis below plots the change $in$

prices from autarky $to$ free trade. The $x-$axis shows net exports under free

trade $in1869.$ Discuss $if$ the graph $is$ consistent with the theory $we$ are trying

$to$ demonstrate?