Econ303 Homework 1B 11. 4 points Find the derivatives of the following functions.(a) f(x) = a + b.(b) f(x) =√x5+ 7.(c) f(x) = x2e3x.(d) f(x) = (x + 3)(3x3− 9x + 11).2. 3 points The following function describes how the value of import of country i fromcountry j, Fijis determined:ln Fij= −14.44 + 0.852 ln Gi+ 0.178 ln Gj− 1.119 ln Dij,where Giis GDP in country i, GjGDP in country j, and Dijthe distance betweenthe two countries.Economists usually convert many aggregate measures of an economy in nature logs.According to the chain-rule d ln x =dxx, which measures the percentage change of x.Henced ln yd ln xapproximates the impact of 1% change of x on y, where the impact is alsomeasured by percentage.For example, let y be student grade and x study time measured in hours. If y = 0.5x,thendydx= 0.5 and one additional hours of study will increase grade by 0.5 point. Ifln y = 0.5 ln x, thend ln yd ln x= 0.5 and 1% increase of study time will increase grade by0.5%.Using derivatives to answer the following questions.(a) If country i’s GDP increases by 5% , what is the percentage change of its importfrom country j approximately?(b) If country j’s GDP decreases by 4% , what is the percentage change of countryi’s import from country j approximately?(c) If the distance between country i and j increases by 3% , what is the percentagechange of country i’s import from country j approximately?3. 3 points Consider an economy with a corn producer, some consumers, and a govern-ment. In a given year, the corn producer grows 30 million bushels of corn and themarket price for corn is $5 per bushel. Of the 30 million bushels produced, 20 millionare sold to consumers, 5 million are stored in inventory, and 5 million are sold to thegovernment to feed the army.The corn producer pays $90 million in wages to consumers. Consumers pay $20 millionin 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 24. 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 carsare produced and sold at $15,000 each, and in year two, 250 cars are sold at $16,000each. 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 fromyear 1 to year 2 using year 1 as the base year. Next, do the same calculationsusing the chain-weighting method.(c) Calculate the implicit GDP price deflator and the percentage inflation rate fromyear 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 ofhigher quality in year 2 in the sense that one car in year 2 is equivalent to 1.2 carsin year 1. How does this change your calculations in parts (a) to (c)? Explainany
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