2. Consider now the single-good model. Let xt be the home endowment and x∗ t be the foreign endowment of the same good. The plannerís problem is to maximize φ ln ct + (1 − φ) ln c∗ t subject to ct + c∗ t = xt + x∗ t . Under zero capital mobility, the home agentís problem is to maximize ln(ct) subject to ct = xt. The foreign agent maximizes ln(c∗ t) subject to c∗ t = x∗ t . Show that asset trade is necessary in this case to achieve efficient risk sharing.