final2009fall

# final2009fall - UNIVERSITY OF TORONTO Faculty of Arts and...

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Faculty of Arts and Science DECEMBER EXAMINATIONS 2009 ECO 325H1 F Duration: 2 hours NO AIDS ALLOWED NOTE TO STUDENT: Enter your name and student number on each examination book that you use. There are four questions on this test for a TOTAL OF 200 MARKS . Count the exam pages to ensure you have all 4 pages. Read each question carefully and note the number of points allocated to each part. Good Luck. 1. (Total 40 points) Assume that Y t K t A t L t  1 ,where 0 1, Y t is total output at time t , K t is total capital at time t , A t is the amount of knowledge at time t ,and L t is the amount of labour at time t . Use the Solow model to answer the following questions. a. (8 points)Using the Solow model find the steady state values for k , y and c (i.e., k , y and c ) as functions of the savings rate, s , the growth rate of labour, n , the rate of depreciation, , the growth rate of knowledge, g ,and .What is the golden rule level of capital, k G as a function of s , n , , g and ? b. (8 points) Prove that the elasticity of total output with respect to total capital is equal to the elasticity of output per unit of effective labour with respect to capital per unit of effective labour. c. Assume that there is a permanent increase in s . i. (8 points) Show what happens to the steady state levels of k , c ,and y , and the level of k G using a diagram. ii. (8 points) Find and determine the signs of: k s , c s , y s ,and k G s d. (8 points) If s 0.6, decreases from 1% to 2%, a decreases from 1 2 to 1 3 , n 1% and g 1%, how much time will it take for k and y to move half way to their new balanced growth path? (Note: You only need to provide the final equation for each variable. You do not need to evaluate it.) (Continued on next page)

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final2009fall - UNIVERSITY OF TORONTO Faculty of Arts and...

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