# s6ex1365 - Econ 365 M Muniagurria Spring 2006 Exam 1(I...

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Unformatted text preview: Econ 365 M. Muniagurria Spring 2006 Exam 1 (I) Basic Solow Model with population growth (without technological change) Answer the following questions using the model presented in class. (1) (12 PtS) Draw a diagram to identify the level of capital per worker at the Balanced Growth Path (BGP). What is the growth rate of output per worker at the BGP? What is the growth rate of consumption per worker at the BGP? What is the growth rate total output at the BGP? (2) (12 pts) Suppose the economy is at the BGP and unexpectedly receives a large gift of capital. What will happen to the growth rate of capital per worker in the periods immediately following the gift? What will happen to the level of capital per worker at the BGP? Justify. What will happen to the growth rate of output per worker at the BGP? (II) Basic Solow Model (without population growth and without technological change) Consider a particular example of the Solow Model Economy: Output per worker as a function of capital per worker: y = k” 3 Depreciation rate: 5 = 0.10 Population Growth: n=0 Savings rate: s = 0.333 I calculated that in this case, the level of capital per worker at the BGP is 6.08. Answer the following questions : (l) (6 pts) Suppose the initial level of capital per worker (k 0) is 4. Do you think that the growth rate of capital per worker in period zero will be positive, negative or zero? Justify (no ' calculations needed). (2) (12 pts) Assume that the savings rate decreases. What will happen to the level of output per worker along the BGP? What will happen to the level of consumption per worker along the BGP? Justify using a diagram and a clear explanations. (III) Solow Model With Labor Augmenting Technological Change and Population Growth Answer the following question using the model presented in class. ‘ (10 pts) Consider the case of two countries (Country A and Country B) that are identical in every respect except that the rate of population growth is higher in country A than in country B (i.e., nA > r1B ). Compare the output per effective unit of labor (Y/AL) at the BGP in both countries. Compare the growth rate of output per worker at the BGP in both countries. (IV) Growth Accounting/ Catching up The table below present estimates of the growth of output, capital and labor during roughly 20 years for Hong Kong (i.e. it presents Y, K and L for the period). Assume as always that the production function for each country can be written as: Y = A K a L 1' a . We also know that the capital shares (on ) is: ocHK = 0.38 Estimates of Growth of Country/Time Period Output Labor Capital Hong Kong 1971-1990 1.47 0.55 1.6 Remark: Notice that these are large numbers because we are talking about growth in a 20 year period. Answer the following questions: (1) (6 pts) Calculate TFP growth. (2) (4 pts) How important was the contribution of : ( a) inputs (i.e. capital and labor together) and (b) total factor productivity to the growth of output. (3) (4 pts) Look now at Figure 1.1 1 where the data for Hong Kong was deleted, but where other ﬁve High Performing Asian Economies are clearly marked. Divide these economies in two groups. One of the groups should have strong similarities with Hong Kong . Justify clearly the grouping you chose. Remark: Notice that you do not have enough data to precisely add Hong Kong to Fig. 1.11. This ﬁgure presents growth per year in percentages over almost 30 years. Your data from the table presents growth over 20 years . (4) (6 pts) Assume that the TFP growth of the “technological leader” in the period 1971—1990 /\ was 0.45 (i.e. A' = 0.45). Explain whether Heng Kong is “catching Up” or “Falling Behind”. (V) (6 pts) Income Inequality The table below gives information about the income distribution in Mexico, Japan and Hong Kong (the information was collected in the eighties and early nineties). Country % of income received by Lowest 40% Highest 20% Hong Kong 16.2 47.0 Japan 21.9 37.5 Mexico 11.9 55.9 Which of the three countries will have the highest Gini coefﬁcient? Which of the three countries will have the lowest Gini coefﬁcient? Justify brieﬂy. (V I) E. Asia (8 pts)Consider the case of a country that maintains a ﬁxed exchange rate. Explain why a devaluation of the currency (i.e . more local currency is needed tobuy a dollar) can become a “self fulﬁlling prophecy”. (VII) Romer (1) (4 pts )State the main assumptions of the model used by Romer to analyze the case of Mauritius. ( 2) (10 pts) Use a diagram to show that although workers are “exploited” by foreign entrepreneurs, they are better off than when the country did not have a garment industry. Econ 365. Maria Muniagurria Solow Model Equations (1) Solow with population growth and no technological change. (population = # of workers) (1) Y=.K“L"“ /\ (2) L=n,S=sY, C=(1—s)Y (3) AK=SY -6K /\ (4) K=s(Y/K) —5 Y= output, K= capital, L= labor Deﬁne new variables : y = Y/L (output per worker) , k= K/L (capital per worker) (5) Ak=Sy —(6+n)k (II) Solow with technological change and population growth (population = # of workers) (1) Y = K“ (AL)'-“ /\ /\ (2) L=n , A=g S=sY, C=(1-s)Y (3) AK=sY -6K Deﬁne new variables : k = K /- L A (capital per effective unit of labor), y = Y / L A (output per effective unit of labor) ~ (4) Ak=sy -(6+n+g)k Figure 1.11 Total Factor Productivity Growth and Part a! Growth Due to Growth of Factor Inputs, 1960—89 11’? Growth 1960-69019le W Va") Nighhcome' economies * “PIES O Oiher developing :conomies 4 ‘2 0 2 4 G 8 You! laclot ham grow“! (percent per year) Nate: Dashed lines rcprzscnt total average cor growth rates, 196049. Solid rays rcprcscnr Eh: contribution to total growth by "P growth. Saturn: Nchru and Dharcsh\\1r(l993): World Bank data. ...
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