University of California, DavisECN 101 - FALL 2014NAME.........................................................................................................STUDENT ID.............................................................................................SECTION (and TA’s name)........................................................................This is a 70 minute examination. Please read the questions carefully before answeringthem. Part A consists of 10 multiple choice questions (40 points total). Part B consistsof 2 short questions (35 points total). Part C consists of 1 long question (25 points total).ALL pages are double-sided. Make sure you do not miss any questions. Write thecorrect answer for the multiple choice questions on your Scantron sheet. Answer all otherquestions in the space provided on your exam sheet.Good luck!1PART A: Multiple Choice questionsEach question is worth 4 points1. Consider the variables x, y, w. Assume that the growth rates of these variables aregiven by g(x) = 0.03, g(y) = 0.04, and g(w) = 0.01. Then the growth rate of the variablez =(xwy)1/4is approximately equal toa) -0.25 %b) 0 %c) 0.25 %d) 2.5 %2. Which of the following production functions exhibits Constant Returns to Scale (CRS)?a) Y =¯A + K1/3L2/3b) Y = K1/2+ L1/2c) Y =35K +45Ld) Y =¯AK3/10L4/53. The reason why the Romer model predicts sustained economic growth, unlike theSolow model, is thata) Ideas, unlike physical capital, are non-rivalrousb) Ideas, unlike physical capital, do not depreciatec) The accumulation of new ideas, unlike the accumulation of physical capital, doesnot run into diminishing returns to scaled) All of the above4. Which of the following statements is False regarding the Solow model:a) Countries with higher productivity levels have a higher level of consumption insteady state (all other things equal)b) Poor countries can increase the level of output per-capita in steady state by savingmore, i.e., increasing the savings rate ¯sc) An increase in the depreciation rate¯d implies a decrease in the steady state levelof capital.d) Poor countries will never reach rich countries since they have less capital stock andthat implies a lower growth rate of output per capita compared to rich countries.5. Consider a country where GDP = 100, Consumption = 20, Investment = Governmentexpenditure, and Net Exports = -50. Then, in this country the government expenditureequals:a) 60b) 65c) 70d) 8026. Which of the following will increase US GDP?a) an increase in stock market pricesb) an increase in social security paymentsc) a decrease in the foreign aid for developing countries by the US governmentd) an increase of projects to fix old roadse) none of the above7. If the US GDP doubles every 35 years, then the growth rate of the US GDP is:a) 0.002b) 0.02c) 0.2d) 0.0358. Consider the production function Yt= Kat(AtLt)1−a. In 2013, the capital stock (Kt)increased by 2%, the total factor productivity (At) increased by 1%, and the labor (Lt)decreased by 3%. What is the growth rate of output in 2013?a) (2a − 4)%b) (4a − 1)%c) (5a − 2)%d) (4a − 2)%9. According to the Solow growth model, output per person in the long-run is higher ina county witha) more export and fewer importsb) higher consumptionc) larger populationd) lower depreciation of capitale) both (c) and (d) are correct10. If the population of Romania was 25 millions in 1960 and the average populationgrowth rate wa 0.9 percent per year, then Romania’s population in 2000 would be ap-proximately equal to:a) 35.77 millions.b) 32.38 millions.c) 36.79 millions.d) 34.18 millions.3PART B: Short QuestionsShort Question 1: Consider the production model of Chapter 4. Final good is producedusing capital (K), skilled labor (Ls), and unskilled labor (Lu) according to the followingproduction function:Y =¯AK1/3L1/3sL1/3u. (1)The supply of all inputs is exogenous and equal to¯K = 100,¯Ls= 200, and¯Lu= 800. Thedemand for these inputs comes from firms that have access to the technology describedabove (the production function), and try to maximize their profits taking the prices of allfactors as given (in other words, the markets for those factors are perfectly competitive).Let wsdenote the price of one unit of skilled labor, wuthe price of one unit of unskilledlabor, and r the rental rate of one unit of capital.a) If¯A = 100, calculate the equilibrium quantities Y∗, K∗, L∗s, L∗u. (4 points)b) Assume again that¯A = 100. Calculate the equilibrium values of the prices of thevarious inputs, w∗s, w∗u, r∗. (5 points)4c) What fraction of the total payments to workers is allocated to skilled workers inthis economy? (5 points)d) Suppose you are a new worker thinking whether you should enter the unskilled orthe skilled labor force. To become a skilled worker you need to attend a series of intensiveseminars that require tuition payments. What is the highest price that you are willingto pay in order to attend these seminars? In this question you can safely assume thatwhatever choice you make will not affect market outcomes. (4 points)5Short Question 2: Consider the Romer model of Chapter 6. Final good is produced usingideas (or technology), At, and labor which is specifically assigned to final good production,Lyt, according to the following formula:Yt= AtLyt. (2)The stock of new ideas is given byAt+1− At= ¯zAtLat, (3)where Latis the amount of labor employed at the labs trying to come up with newtechnologies, and ¯z = 0.0025. Also, assume that in the initial period, A0= 1000. Thetotal supply of labor in this economy is fixed and given by¯L = 100. Finally, this economyallocates 70% of its labor force to the production of final good, that is: Lyt= 0.7¯L.a) What is the growth rate of technology (or the stock of ideas) in this economy?What is the growth rate of output per person? (5 points)b) What is the value of per person output in the economy in t = 20? How many years(from t = 0) will it take for output per person to double? (6 points)6c) Suppose that in t = 20, the portion of the labor force that is allocated to theproduction of new ideas becomes 0.15. Depict this situation in a graph with time in thehorizontal axis (ranging from t = 0 to, say, t = 40), and output per person in the verticalaxis (depicted in a ratio scale). (6 points)7PART C: Long QuestionThis question is based on the Solow growth model of Chapter 5. Consider an economywhere the period production function is given by Yt=¯AK1/3tL2/3t, where