l. (50 points) Suppose the aggregate consumption of a country, is dened as the following constant elasticity of substitution (CES) aggregator: 1 c = [ag'2' + (1 wagg (Utility) where C h, C f are total consumptions on the home (exportable) and foreign (importable) goods of the country. 0.5 S a S 1 is the home bias factor. The representative consumer maximize the aggregate consumption (Utility) subject to the following budget constraint: PhCh + Pfo = 1 (Budget Constraint) where Ph, Pf are the prices of the home (exportable) and foreign (importable) goods, respectively. I IS the 1ncome of the representative consumer. i. Suppose a 0.75, (2): 0. 5, Ph= 2, Pf 1, I 300. Calculate C}: and Cf. (Keep 2 decimals.) Show your work clearly. ii. Suppose a = 0.8,(2) = 0.5, Ph = 2, Pf = 1,1 = 300. Calculate C}: and C}. (Keep2l decimals.) Show your work clearly. iii. Comparing answers in (i) and (ii), what are the impacts of home bias on the consumptions? iv. Suppose a = 0.8,(2) = 0.5, Ph = 2, Pf = 1.5,! = 300. Calculate C}; and C}. KeepZ decimals.) Show your work clearly. v. Are C h, C f gross substitutes or gross complements when (2) = 0.5? Use the answers in (ii) and (iv) to answer this question? Show your work clearly. 2. (50 points) Suppose f (x; a) = 2x2 + 2ax + 4a2. i. Draw a 3D graph to show that f (x; a) has a global minimum point. The domain in this graph is -4