ECMB06 Assignment 1 Solution Fall 2011.docx

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Department
Economics for Management Studies
Course
MGEB06H3
Professor
Jack Parkinson
Semester
Fall

Description
ECMB06 Assignment 1 Answer Key – Fall 2011 Question 1 (25 points) Part (a) (5 points) (Must show work for credit)  Output, Y: Y = AK L1/4 3/= 2(10000) (50625) 3/= 67500  Taxes, T: T = 0.1Y = 0.1(67500) = 6750  Government spending, G: G = T + 0.15Y = 6750 + 0.15(67500) = 16875  Equilibrium of the long-run classical model is given by: S = Y – C – G = I (1 pt) 67500 – [30000 + 0.5(67500 – 6750) – 1500r] – 16875 = 16500 – 1000r – 9750 + 1500r = 16500 – 1000r r = 10.5 (10.5%)  Consumption, C: (1 pt) C = 30000 + 0.5(67500 – 6750) – 1500(10.5) C = 44625  Investment, I: (1 pt) I = 16500 – 1000(10.5) I = S = Y – C - G I = 6000 I = 67500 – 44625 – 16875 = 6000  Real wage for labour, W/P: (1 pt) W/P = MPL = (3/4)[2K L 1/4 –1] = (3/4)[2(10000) (50525) –1/] W/P = 1  Real rental price for capital, R/P: (1 pt) R/P = MPK = (1/4)[2K –3/L ] = (1/4)[2(10000) –3/(50625) ]/4 R/P = 1.6875 Part (b) (5 points)  The level of total factor productivity increases by 50%, the new production function: Y = 3(10000) (50625) 3/= 101250  Taxes, T: T = 0.1Y = 0.1(101250) = 10125  Government spending, G: G = T + 0.15Y = 10125 + 0.15(101250) = 25312.5  Equilibrium of the long-run classical model is given by: S = Y – C – G = I (1 pt) 101250 – [30000 + 0.5(101250 – 10125) – 1500r] – 25312.5 = 16500 – 1000r 375 + 1500r = 16500 – 1000r r = 6.45 (6.45%)  Consumption, C: (1 pt) C = 30000 + 0.5(101250 – 10125) – 1500(6.45) C = 65887.5  Investment, I: (1 pt) I = 16500 – 1000(6.45) I = S = Y – C - G I = 10050 I = 101250 – 65887.5 – 25312.5 = 10050  Real wage for labour, W/P: (1 pt) W/P = MPL = (3/4)[3K L 1/4 –1] = (3/4)[3(10000) (50525) –1/] ECMB06 Assignment 1 Answer Key (Fall 2011) 1 W/P = 1.5  Real rental price for capital, R/P: (1 pt) –3/4 3/4 –3/4 3/4 R/P = MPK = (1/4)[3K L ] = (1/4)[3(10000) (50625) ] R/P = 2.53125 Part (c) (10 points)  By comparing the answers in parts (a) and (b), when the level of total factor of productivity rises:  Y, C, I, G, T, W/P, and R/P rise.  r falls. FYI: Output, Y = F(A, K, L):  In the long run, output is determined by the state of technology (TFP), capital stock and labour force.  When A rises, the economy can make use of its production factors more effectively, so the level of output rises. FYI: Taxes, T, & Government spending, G:  Taxes = 10% of Y  When Y , T  by 3375.  Government spending = 25% of Y (as the size of the budget deficit is 15% of Y)  When Y , G  by 8437.5. Equilibrium real interest rate, r (2 pts – must mention  in Y, C & G affect S for full credit)  Real interest rate is determined by the demand for and supply of funds in the loanable funds market.  Supply of funds = National saving, S = Y – C – G:  Y , S  by 33750.  C = C(Y – T, r)  (Y – T)  by 30375  C  by (MPC  (Y – T)) = 0.5  30375 = 15187.5  S  by 15187.5  G  by 8437.5  S  by 8437.5  Overall, S  by 10125.  Given S , the supply of funds  to S .  At the initial real interest rater (r= 10.5%), there is an excess supply of loanable funds.  Point B is the new equilibrium: r  to r (r = 6.45%). Consumption, C: (1 pt)  When the economy reaches its new equilibrium, the  in (Y – T) and the  in r (as the cost of borrowing falls) lead to higher level of consumption.  At point B, C = 0.5  (Y – T) – 1500  r = 0.5(30375) – 1500  (6.45 – 10.5) = 21262.5 Investment, I: (1 pt)  When the equilibrium real interest rate falls to 6.45%, the cost of borrowing  and I  by (1000  r ) = [1000  6.45 – 10.5] = 4050. ECMB06 Assignment 1 Answer Key (Fall 2011) 2 Alternatively,  For a closed economy, equilibrium in the market for loanable funds requires S = I.  When the level of total factor productivity increases by 50%, the (equilibrium) level of national saving  by 4050.  When the (equilibrium) level of national saving , so does the (equilibrium) level of I. Real wage, W/P: (1 pt)  When the level of total factor productivity , labour becomes more productive  MPL   demand for labour  to LD = MPL . 1 0  At the initial real wage, (W/P) , there is excess demand for labour.  Point B’ is the new equilibrium in the labour market: (W/P)  to (W/P) 1 Real rental price of capital, R/P: (1 pt)  When the level of total factor productivity , capital becomes more productive  MPK   1 1 demand for (rental) capital  to KD = MPK . 0  At the initial real rental price of capital, (R/P) , there is excess demand for (rental) capital.  Point B” is the new equilibrium in the labour market: 1 (R/P)  to (R/P) Market for loanable funds (2 pts) r S 0 1 S A Graph: 2 pts will be subtracted if the 0 r = 10.5% supply of funds curve is not upward sloping. r = 6.45% B 0 I (r) I, S I* =S* ,0 I* =S* ,1 = 6000 = 10050 Labour Market (1 pt) Rental Market for Capital (1 pt) W/P LS R/P KS 1.5 B’ 2.53125 B” 1.0 A’ 1.6875 A” LD = MPL 1 KD = MPK 1 0 0 0 0 LD = MPL KD = MPK L* = 50625 L K* = 10000 K ECMB06 Assignment 1 Answer Key (Fall 2011) 3 Part (d) (5 points) Suppose the government wants to lower the level of interest rate to 5%:  Using the investment function to find the level of investment when r = 5%: (1 pt) I = 16500 – 1000(5) I = 11500  The level of government spending that will keep r at 5%:(2 pts) In equilibrium, S = I and the equilibrium level of investment = 11500 11500 = 101250 – [30000 + 0.5(101250 – 10125) – 1500(5)] – G G = 21687.5  Government budget balance, GBB: (2 pts – must discuss what happens to GBB) GBB = T – G = 10125 – 21687.5 = – 11562.5  Since G  and there is no change in taxes, GBB improves (i.e., the government runs a smaller budget deficit, GBB = – 11562.5 – (– 15187.5) = 3625. Question 2 (25 points) Part (a) (10 points) Suppose the level of the capital stock falls by 10% and the size of the labour force falls by 25%:  Output, Y: (1 pt) Y = F(A, K, L)  K  & L , Y .  National saving, S = Y – C – G 3 pts  Y , S  by Y.  C = C(Y – T)  when Y , C  by (MPC  Y)  S  by (MPC  Y).  Overall, S  by (1 – MPC) 1 Y.  S , supply of funds  to S .  At r , there is excess demand for funds  r  to r . (1 pt) Note: you must mention there is a  in C and there are 2 forces causing a  in S for full credit.  Point B is the new equilibrium: r  to r . I*  by (1 – MPC)  Y to I* . (1 pt) C*  by (MPC  Y). (1 pt) r S 1 S 0 r1 B Graph: 3 pts 0 r A I(r) S, I I* =S* ,1 I* =S* ,0 ECMB06 Assignment 1 Answer Key (Fall 2011) 4 Part (b) (15 points) Suppose the level of the capital stock falls by 10% and the size of the labour force falls by 25%: K K   Given k  L , K  by 10% and L  by 25%, then  k  L  . (1 pt) ,0 1  k  f1om k* to k . 3 pts  At k , sy < (n + )k  k < 0.  k begins to decrease.  k continues to decreases until k = k* .  Point A is,0he new steady state: k = k* (no change) Growth rate of output per worker, y/y:  FYI: Immediately after the rise in capital-labour ratio:  When k , y  because  y = Af(k).  Since y , y/y > 0.  During transition to steady state: (4 pts)  sy < (n + )k  k < 0  k .  Since y = Af(k), y  when k .  When y , y/y turns negative.  As k approaches its steady-state value, k is decreasing at a slower rate, so does y  y/y slows down.  In steady state: (3 pts) ,0  In steady state, k = k* and does not change.  Since k does not change, so does y.  y/y = 0. y, sy, (n + )k (n + )k ,0 y y* k < 0 sy A Graph: 4pts No credit if you shift any curve k = K/L k* ,0 k1 ECMB06 Assignment 1 Answer Key (Fall 2011) 5 Question 3 (25 points) Part (a) (4 points) (1 pt for showing work)  Production function: Y = AK L 1 –   Per worker production function, y = Y/L  1 –  Y/L = y = (AK L )/L
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