課程名稱︰總體經濟學（上） 課程性質︰英文授課 課程教師︰蔡宜展 開課學院：社會科學院 開課系所︰經濟學系 考試日期（年月日）2017/10/27︰ 考試時限（分鐘）：3小時 試題 : 1. Nominal GDP vs Real GDP Think about a simple economy that produces only 2 goods in the economy (denoted by A and B).The table shows the hypothetical prices(p) and quantities(q) of these good in 2005, 2006, and 2007. ======================================== | T| P_A| Q_A| P_B| Q_B| |======================================| | 2005| 1| 100| 2| 50| |======================================| | 2006| 1| 200| 2| 100| |======================================| | 2007| 2| 200| 4| 100| ======================================== 1. Compute the nominal GDP and constant price real GDP for each year using 2005 as the base year 2. Compute the implicit price deflator for each year using constant price real GDP. 3. Compute the growth rate of nominal GDP, constant price real GDP and the GDP deflator in 2006 and 2007. For each year indentify the variable that does not change, explain why your answer makes sense. 4. Compute the value of the chain-weighted GDP using 2005 as the base year. 5. Compute the implicit price deflator for each year using chain- weighted real GDP. 6. Compute the growth rate of chain-weighted real GDP and its associated GDP defaltor in 2006 and 2007. Compare these numbers with the ones computed using constant price GDP. Is there any difference between these numbers realtive to their constant price GDP counterpart? 2. Who is who in 2017 1. Who is the chairman of the Federal Reserve Bank? 2. Who was awarded the Nobel Prize in Economics in 2017? He/She was awarded for his contribution in which area of Economics? 3. Solow Model Let L_t denote the number of total population in period t, which is constant over time. Each person has one unit of time that they supply as labor in each period. Therefore, total labor supply is L_t. In addition each person consumes a constant fraction, 1-s, of its income. Therefore the aggregate consumption C_t equals the constant fraction of aggregate income Y_t, i.e. C_t=(1-s) * Y_t. Furthermore, the aggregate saving in period t is S_t=s * Y_t. Suppose that output is produced according to the constant returns to scale production function Y_t=z * F(K_t,L_t)=z * K_t^a * L_t^(1-a) where K_t and L_t represent the capital and labor input respectively. In addition, the law of motion for capital stock evolves according to K_t+1=(1-δ)K_t+I_t. Finally, the equilibrium condition required I_t=S_t. 1. Does this production functio satisfy consant returns to scale? Explain. 2. Define y as output per worker, and k as captal per worker. Express the relation between y and k. 3. Derive the law of motion for capital per capita, express the relation in terms of saving rate and depreciation rate. In this economy, what is break-even investment(the amount of investment needed to keep capital per worker constant)? 4. Compute the steady-state quantity of capital per worker as a function of the saving rate, the depreciation rate and total factor productivity. 5. Use a diagram to show the effect of an increase in saving rate, s, in the Solow Growth Model. In particular, please show both the original and new steady state quantity of capital per capita in the diagram, and explain dynamic adjustment of capital per worker over time. 6. Now consider the economy with population growth and suppose its growth is L_t+1=L_t(1+n). Derive the law of motion for capital per worker. In this economy, what is break-even investment (the amount of investment needed to keep capital per worker constant)? 7. Compute the steady-state quantity of capital per worker as a function of the saving rate, population rate, the depreciation rate and total factor productivity. Is the new steady state capital per capita higher or lower relative to its constant population counterpart? 8. Now suppose that there are two countries in the world. Assume that country A and country B have the same production function, population growth rate, depreciation rate and saving rate. Assume further that country A have lower output per capita, which country has higher growth rate in output per capita during the transitional dynamics? Which country has higher growth rate in output per capita when r eaching the steady state ?Explain? 9. Now consider the following production function Y= F(K,E,L) = K^α*(EL)^(1-α). Where E denotes the efficiency of labor . Suppose that labor efficiency improves over time where E_t+1 = E_t(1 + g).Derive the relationship between output per effective labor and capital per effective labor. 10. Derive the law of motion for capital per effective labor. What is break-even investment (the amount of investment needed to keep capital per worker constant) in this economy? 11. In the economy with population growth and labor efficiency improvement, what would the steady state growth rate you predict for the following variables? --

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