Econ303 Homework 1B 1 1 4 points Find the derivatives of the following functions a f x a b b f x x5 7 c f x x2 e3x d f x x 3 3x3 9x 11 2 3 points The following function describes how the value of import of country i from country j Fij is determined ln Fij 14 44 0 852 ln Gi 0 178 ln Gj 1 119 ln Dij where Gi is GDP in country i Gj GDP in country j and Dij the distance between the two countries Economists usually convert many aggregate measures of an economy in nature logs which measures the percentage change of x According to the chain rule d ln x dx x d ln y Hence d ln x approximates the impact of 1 change of x on y where the impact is also measured by percentage For example let y be student grade and x study time measured in hours If y 0 5x dy 0 5 and one additional hours of study will increase grade by 0 5 point If then dx ln y ln y 0 5 ln x then dd ln 0 5 and 1 increase of study time will increase grade by x 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 c If the distance between country i and j increases by 3 what is the percentage change of country i s import from country j approximately 3 3 points Consider an economy with a corn producer some consumers and a government 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 consumers 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 consumers Consumers 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 Econ303 Homework 1B 2 4 10 points In year 1 and year 2 there are two products produced in a given economy cars and beef Suppose that there are no intermediate goods In year one 200 cars are produced and sold at 15 000 each and in year two 250 cars are sold at 16 000 each In year one 1 000 000 pounds of beef are sold for 7 00 each and in year two 1 000 000 pounds are sold for 8 00 each a Calculate nominal GDP in each year b Calculate real GDP in each year and the percentage increase in real GDP from year 1 to year 2 using year 1 as the base year Next do the same calculations using the chain weighting method c Calculate the implicit GDP price deflator and the percentage inflation rate from year 1 to year 2 using fixed price real GDP using year 1 as the base year Next do the same calculations using the chain weighting real GDP d Suppose that cars in year 2 are better than cars in year 1 That is cars are of higher quality in year 2 in the sense that one car in year 2 is equivalent to 1 2 cars in year 1 How does this change your calculations in parts a to c Explain any differences
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