Econ303 Homework 1B oints Find the derivatives of the following functions. (a) f(x) a + b (b) f(a) V5 +7 (c) f(x) (d) f(x) (x +3)(3-9x +11) 2. 3 p oints The following function describes how the value of import of country country j, Fiy is determined: In Fy 14.44+0.8521nG, +0.178 In G, -1.119 In Diy where Gi is GDP in country i, Gj GDP in country j, and D the two countries. ij the distance between Economists usually convert many aggregate measures of an economy in nature logs. According to the chain-rule din zz which measures the percentage change of Hence diny approximates the impact of 1% change of r on y, where the impact is also measured by percentage. dln For example, let y be student grade and z study time measured in hours. If y 0.5a, then dy 0.5 and one additional hours of study will increase grade by 0.5 point. It In y 0.5 Inx, then din 0.5 and 1% increase of study time will increase grade by 0.5%. Using derivatives to answer the following questions. (a) If country i’s GDP increases by 5% , what is the percentage change of its import from country j approximately? (b) If country j’s GDP decreases by 4% , what is the percentage change of country i’s import from country j approximately? is the percentage (c) If the distance between country i and j increases by 3% , what change of country i’s import from country j approximately? 3. 3 points Consider an economy with a corn producer, some households, and a gov- ernment. In a given year, the corn producer grows 30 million bushels of corn and the market price for corn is $5 per bushel. Of the 30 million bushels produced, 20 million are sold to households, 5 million are stored in inventory, and 5 million are sold to the government to feed the army. The corn producer pays $90 million in wages to households. Households pay $20 million in taxes to the government, receive the profits of the corn producer. Calculate GDP using (a) the product approach, (b) the expenditure approach, and (c) the income approach 59
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