Question 1: Working with growth rates Suppose k, l and m grow at constant rates given by 5k, 5; and gm. Using the rules in Table 3.1 of the textbook (and that we saw in class), what is the growth rate of y in each of the following cases? (a) y = 161/3 (my=wea (c) y = mk1/3lz/3 (d) y = mk1/4l3/4 (e) y = mk3/4ll/4 my=wmw mymmwmm Question 2: Using FRED and macro data In class we saw some charts using the FRED database (https : //fred. stlouisfed. org/). This is an easy-to-use online database containing a large amount of macroe- conomic data. You should read the case study "The FRED Database" at the end of chapter 2, page 34 (4th Edition of the textbook) for further information about FRED. Using the FRED database, locate the data on real and nominal GDP for the U.S. economy. You may notice that there are both annual and quarterly data (i.e., measures of production every 3 months) available. For the purpose of this question, lets stick with the annual data. The easy way to find this is to type "annual nominal GDP" and "annual real GDP" into the FRED search box. (a) What is the value of real GDP and nominal GDP for the most recent year available? Explain why these numbers are different. (b) What was the value of real GDP and nominal GDP in 1970? (c) By what factor (e.g. a number like 2.0 if it doubled) did real GDP increase between 1970 and the most recent year? What about nominal GDP? (d) What explains the difference between the two number in part (c)?Question 3: Returns to scale in production Do the following production functions exhibit increasing, constant or decreasing returns to scale in K and L? (Assume A is some fixed positive number.) a ) Y = K1/2[1/2 b ) Y = K2/3 [2/3 c) Y = K1/3[1/2 d) Y = K +L e) Y =K + K1/3[1/3