KYAMBOGO UNIVERSITY FACULTY OF SOCIAL SCIENCES DEPARTMENT OF ECONOMICS BACHELOR OF ARTS IN ECONOMICS BACHELOR OF ECONOMICS AND STATISTICS YEAR III SEMESTER II EXAMINATIONS 2020/2021 AEC 3202 INTERMEDIATE MACROECONOMICS Time: 9:00 – 12.00noon Date: Wednesday 30th March, 2022 Instructions: • Answer any FOUR questions. • Begin each question on a fresh page. Question One (a) An economy is described by the following equations: Y = AK t L1t− K = sYt − K t L = nLt Production function: Capital accumulation: Labor force: Where Y = output, K = capital, L = labor, A = total factor productivity and α = 1/4. (i) Show that this production function exhibits constant returns to scale. (2 marks) Yt = AK t L1t− zYt = F ( zK t , zLt ) = A(zK t ) (zLt ) 1− where z 0 = z +1− AK t L1t− = zAK t L1t− …………………….2mks Since the production function is of degree one, it exhibits constant returns to scale. 1 (ii) Find expressions for the stable steady state values of the input ratio and per capita output as functions of the propensity to save, s , and the other exogenous parameters of the model. (5 marks) Yt = AK t L1t− Yt AK t L1t− = Lt Lt Yt AK = t Lt Lt K Yt = A t Lt Lt Let Yt and Lt Therefore yt = kt = Kt Lt y t = Ak t ……………….. 1mk But k = i − d , where d = k , i = sy , i = sAk Therefore; k = sAk − k At steady state; k = 0, sAk = k sAk k = ………………………………. 1mk k k k sA = k sA k 1− = 1 / 1− sA Therefore; k* = as the steady state per worker (input ratio) ………1mk From yt = Ak y * = A(k *) ……………………………………….. 1mk 2 1 1− sA * y =A 1− y = A. A * 1 1− y* = A (iii) s 1− s 1− As the steady state per capita output …………. 1mk Given that the savings rate in this economy is 25% of GDP, the depreciation rate of capital is 10% per year and the index of technological level is 1. Evaluate the per capita steady state of physical capital and final product. (4 marks) S=25% = 0.25, A = 1, = 1/ 4 = 10% = 0.10 ➢ Per Capita steady state of physical capital 1 / 1− sA From k* = 4 3 0.25 ✓ k* = 0.10 ✓ = 3.393 ➢ Per Capita steady state final product 1 1− From y = A * ……………………… 2mks s 1− 1 1−0.25 * ✓ y =1 0.25 0.25 1−0.25 0.10 4 3 1 0.25 3 * ✓ y =1 0.10 4 3 1 0.25 3 * ✓ y =1 0.10 ✓ y * = 1.357 ✓ 3 2mks (iv) Suppose there are two identical countries except for difference in the savings rate. The savings rate for country i is 25% while for country j it is 10%. Predict and comment on their differences in GDP per worker. (4 marks) si = 25% = 0.25 , s j = 10% = 0.1 1 1− ✓ For country i , yi = A * ✓ For country j, yj = A * si 1− yi 1 1− sj 1− 1 1 − s A1− i * yi = ✓ * There fore ; y j 1 s j 1− A1− si 1− yi = * s yj j * ✓ ✓ yi 0.25 = * yj 0 .1 ✓ yi 0.25 3 = * y j 0 .1 ✓ yi = 1.356 * yj * * 1mk 0.25 1−0.25 1 * 2mk ➢ Comment; The model predicts that country i’s income per capita will be 1.36…times that of country j’s. 1mk 4 (b) Using the Solow Growth Model, graphically illustrate and explain the effect of an increase in the savings rate on the economic growth of a country. (7 marks) ➢ An increase in the saving rate implies that the amount of investment for any given capital stock is higher. It therefore, shifts the saving function upward. S2f(k) Investment Depreciation S1f(k) s 1 f (k ) ……02mks s s 1 2 K1* k2* capital per worker Explanation 2mks ➢ At the steady state K1*, investment now exceeds depreciation. The capital stock rises until the economy reaches a new steady state k2* with more capital and output. Thus, if the saving rate is high, the economy will have a large capital stock and a higher level of output. According to the Solow model, higher saving leads to faster growth. (c) Suggest any three ways through which the savings rate can be raised in an economy like Uganda. (3 marks) ✓ Reducing the government budget deficit ✓ Increasing incentives for private saving, e.g reducing capital gain tax, corporate income tax , estate tax ✓ Expanding tax incentives for IRAs (Individual Retirement Accounts) and other retirement savings accounts. Any 3points*2mks = 6mks 5 Question Two After graduating with an economics degree, you have been appointed as an Economist in the Ministry of Finance of a small open economy with a floating exchange rate. The President of this country asks for “An evaluation of the impact of a reduction in import tariffs on the economy”. (a) With an aid of a graphical illustration, explain the impact of this policy change on the economy with reference to aggregate income, the exchange rate, and the trade balance. (9 marks) (b) Now suppose this economy was operating a fixed exchange rate regime, how would such a policy change affect the economy’s aggregate income, the exchange rate, and the trade balance? (8 marks) (c) Explain how the following policies affect a country’s trade balance: (i) Currency devaluation (4 marks) (ii) Currency revaluation (4marks) ANSWER: (a) When a tariff is reduced on imports it shifts the net exports schedule in wards. For any given exchange rate, net exports fall. This is because it now becomes possible for Uganda to get more imports. 1mk Exchange rate 1mk e Nx1 (e) Nx2 (e) NX2 NX1 Net export ➢ The inward shift in the next exports schedule causes the IS* schedule to shift in ward as well. 6 e Exchange rate LM* e1 e2 4mks IS1* IS2* Y income, output ➢ From the diagram above exchange rate falls, income and trade balance remain unchanged since NX (e) = Y-C(Y-T) -I(r) –G. Reducing the tariff has no effect on Y, C, I and G. Therefore, it has also no effect on the trade balance. 3mks (b) If it is a fixed exchange rate. Then the shift in IS* curve puts down pressure on the exchange rate. In order to keep the exchange rate fixed, the central bank is forced to buy dollars and sell foreign exchange. This shifts the LM* curve to the left as shown below. 2mk LM2* LM1* Exchange rate 5mks e B A IS1* Y1 IS2* Y2 Y1 Income, output ➢ From the graph above, at equilibrium income is lower and exchange rate is unchanged. The trade balance fall because net exports are lower at any level of the exchange rate. 3mks (c) (i) Currency devaluation is the deliberate downward adjustment of the value of a country’s currency relative to another currency. Countries that have a fixed 7 exchange rate or semi-fixed exchange rate use this monetary policy tool to stabilize the economy 3mks (ii) Currency revaluation is the upward adjustment to a country’s official exchange rate relative to a chosen baseline. The baseline can be anything from wage rates to the price of gold to a foreign currency. In a fixed exchange rate regime, only a decision by a country’s government such as its central bank can alter the official value of the currency. 3mks Question Three (a) Explain the term “balanced budget”. (2 marks) (b) What happens to the domestic interest rate, income, consumption, and investment if government increases expenditure and taxes by equal amounts? Be sure to use an appropriate graph and calculus to illustrate your answer. (13 marks) (c) An economy is described by the following equations: Y = C + I + G , C = C (Y − T ) , M I = I ,T = T , = L( r , Y ) , and P = P . Examine the effect of a decrease in the P money supply on domestic income and interest rate in this economy, clearly explaining the monetary transmission mechanism. (10 marks) ANSWER: (a)Government increases expenditure and taxes by equal amount (b) Y = C(Y-T) +I+G dy/dT = C’dy/dt –C’ dy/dt - C’dy/dt = –C’ :. dY/dt = –C’/1–C’ Bt C’= mpc dY/dT= -MPC/1-MPC ∆Y = ∆T *-MPC/1-MPC ……………………. 01MK Government purchases multiplier Y = C(Y-T) +I+G dy/dG = C’dy/dt +1 dy/dG- C’dy/dt = 1 :. dY/dG = 1/1–C’ Bt C’= mpc From Y / T =1/ 1− MPC Y =G /1−MPC …………………………………….01MK 8 Tax multipliers =ΔY/ΔT = - MPC/1-MPC ΔY = ΔT * -MPC/1-MPC ΔY = (ΔG/1-MPC) – (ΔT*MPC/1-MPC) But ΔG =ΔT ΔY = (ΔG/1-MPC) – (ΔG*MPC/1-MPC)……………………01MK ΔY = ΔG(1-MPC/1-MPC) ΔY=ΔG…………………………………………………………………………………01MK This expression tells us how output change holding the interest rate constant. It says that an equal increase in government expenditure and taxes shifts the IS curve to the right by the amount that G increases. 01mk LM r2 B r2 Interest rate A IS2 r1 2mks IS1 Y1 Y2 OUTPUT Output increases, but by less than that of G and T increases. This means that disposable income Y-T falls. As a result, consumption also falls. The interest rate rises, causing investment to fall. 1mk 9 (c) Effect of a monetary contraction LM2 Interest rate r2 LM1 r1 5 marks IS Y2 Y1 Income, Output Well detailed Explanation 5mks When the central bank reduces money supply people have less money than they want to hold. As a result, they start borrowing extra money from banks. The interest rate then rises. The higher interest rate discourages investment, which reduces planned expenditure, production and income. Question Four Consider the Solow growth model with no technological progress. The production function in intensive form is given by y = f (k ) = k and the capital stock motion equation is k = sy − (n + )k , where s is the saving rate, n is the population growth rate, is the depreciation rate, and 1 . (a) Derive expressions for the steady state values of per capita capital stock and production. (10 marks) (b) Given that the saving rate in this economy is 20% of GDP each year. It is also known that the population growth rate and the depreciation rate of capital are 2% and 4% per year, respectively. Assume α = 0.6 and β = 0.4. Compute the per capita steady state of physical capital and final product. (6 marks) (c) Political leaders in Uganda have argued before that high population growth accelerates the economic growth and development of the country. As an 10 economist/statistician in the Ministry of Finance, Planning and Economic Development, you have been invited to present a paper on “The effect of an increase in population growth rate on economic growth of Uganda” at a political leaders meeting at Kyankwanzi. Using the Solow Growth Model, prepare a paper that you would present to the meeting. (9 marks) ANSWER: (a) Derive expressions for the steady state values of per capita capital stock and production. (10 marks) (a) y = f (k ) = k Using k = sy − (n + )k = 0, where sy = (n + )k But y = k sk = (n + )k Divide both sides by k sk (n + )k = k k (n + )k s = k s k = (n + ) k s k 1− = (n + ) s Therefore; k * = n + 1/1− as the steady state value of per capita capital stock. From yt = k y* = (k *) 1 1− s * y = n + y = . * 1− y* = s 1− n + 1 1− s 1− As the steady state value of production n + 11 (b) Given that the saving rate in this economy is 20% of GDP each year. It is also known that the population growth rate and the depreciation rate of capital are 2% and 4% per year, respectively. Assume α = 0.6 and β = 0.4. Compute the per capita steady state of physical capital and final product. (6 marks) = 4% = 0.04 n=0.02 (b) S=20% = 0.2, = 0.6 , = 0.4 ➢ Per Capita steady state of physical capital s From k * = n + ✓ 1/1− 1mk 0.2 * 0.4 k* = 0.02 + 0.04 k* = 1.33 to get the value) ➢ Per Capita steady state final product ✓ ➢ 1.3 = y = * 1 1− 1 0.76 = ?? (use a scientific calculator s 1− n + y * = (0.4) 1 1− ( 0.6*0.4 ) 1mk 0.6*0.4 0.2 1−( 0.6*0.4 ) 0.02 + 0.04 ✓ y * = ?? (use a scientific calculator to get the value) ✓ y* = 2mks (c) Political leaders in Uganda have argued before that high population growth accelerates the economic growth and development of the country. As an economist/ statistician in the Ministry of Finance, Planning and Economic Development, you have been invited to present a paper on “The effect of an increase in population growth rate on economic growth of Uganda” at a political leader’s meeting at Kyankwanzi. Using the Solow Growth Model, prepare a paper that you would present to the meeting. (9 marks) 12 As shown in the figure below, an increase in the rate of population growth from n1 to n2 shifts the line representing population growth and depreciation upward reducing the steady state level of capital per worker from k1* to k2* . This is because higher population growth rate reduces capital stock per worker by spreading the capital stock more thinly among a larger population 1mk (n2+δ)k (n1+δ)k Investment Break even s Investment 1 f (k ) ……05mks n n 2 k2* k1* 1 capital per worker Since k* is lower, and because y*=f(k*), the level of output per worker y* is also lower. Thus, the Solow model predicts that countries with higher rates of population growth will have lower levels of capital per worker and therefore lower levels of GDP per person. Question Five (a) Explain the term “crowding out” of investment. (2 marks) (b) Consider an increase in government purchases of G . Using the closed economy model, illustrate graphically and explain the effects of such a policy on domestic interest rate (r), domestic income (Y), national saving (S), and investment (I), clearly pointing out the crowding out effect. (8 marks) 13 (c) Now use the open economy model and illustrate graphically how the model predicts the exchange rate (e), domestic income (Y), and net export (NX) in response to such an economic policy: (i) Under a floating exchange rate regime (7 marks) (ii) Under a fixed exchange rate regime (8 marks) ANSWER: (a) A situation when increased interest rates lead to a reduction in private investment such that it dampens the initial increase of total investment and incomes. (b) Closed economy LM Interest rate r2 r1 B 4MKS A A* IS2 IS1 YI Y2 y3 OUTPUT An increase in government expenditure shifts the IS curve to the right, moving the equilibrium from point A to point B Increase in government expenditure stimulates the production of goods and services which causes total income Y to rise y2 The rise in income increases the quantity of money demanded, causing the interest rate r to rise. When the interest rate rises, investment (I) falls, and savings (S) fall……….4MKS 14 (c)Small open economy model (i)Under a floating exchange rate regime LM* 4MKS exchange rate e2 e1 IS2* IS1* Y OUTPUT An increase in government expenditure shifts the IS* curve to the right. As soon as the interest rate tries to rise above, world interest rate, capital flows in from abroad. This capital inflow increases the demand for domestic currency, causing currency appreciation. Currency appreciation makes domestic goods expensive relative to foreign goods, reduces next exports. The fall in net exports of the effects of the expansionary fiscal policy leaving income constant ……………………………………………………….. 3MKS 15 (ii)Fixed exchange rate regime LM1* LM2* Exchange rate 4mks e IS 2* IS1* Y1* Y2* Income A fiscal expansion shifts the IS* curve to right. To maintain the fixed exchange rate, the central bank must increase money supply thereby shifting the LM* curve to the right. Hence, under fixed exchange rates, fiscal expansion raises income. ……Detailed explanation 4mks Question Six (a) Show that, according to the Phillips curve, inflation results from three sources: expected inflation ( e ) , cyclical unemployment (u − u n ) , and supply shocks (v ) (8 marks) (b)Can an economic policymaker achieve low inflation and low unemployment in an economy at the same time? Use an appropriate illustration to explain your answer. (8 marks) (c)The Phillips curve is given by = e − 3(u − 0.06) . Given that actual inflation is 8% and expected inflation is 5%, find the unemployment rate. (5 marks) 16 (d)Do you think the Phillips curve is a useful tool for analyzing the economy today? Why or why not? (4 marks) ANSWER: (a) From the short run aggregate supply curve _ Y =Y + ( P − P e ) ………………………………… 1mk Making P the subject; P= P + 1/ e _ (Y − Y ) ……………………1mk Add to the right-hand side of the equation as shock V to represent exogenous events. P= P + 1/ e _ (Y − Y ) + V To go from the price level to inflation rates, last year’s price level p −1 both sides of equation. − (P − P −1 ) = ( P − P−1 ) + 1 / + (Y −Y ) e …………………………1mk But p- p −1 = π, which is inflation _ = + 1 / (Y − Y ) + V e ……………………………………………….1mk To go from output to employment, use Okuns law 1/ :. = Where _ (Y − Y ) = e e − (u −u n ) …………. 1mk − (u −u n ) +V ………………….2mks = inflation = expected inflation …………………….1mk 17 from (u −u n ) = cyclical unemployment, V = Supply shocks (b) Price AS2 P3 C AS1 B P2 A P1 AD2 04mks AD1 Y1 Y2 Y output When policy makers move the economy up along the short run aggregate supply curve (using monetary or fiscal policy), they reduce the unemployment rate and raises inflation rate. ………………………………………… 2mks Conversely, when they contract aggregate demand and more the economy down. The short run aggregate supply curve, un employment rises and inflation falls. Thus, a policy maker cannot achieve both low inflation and low unemployment in an economy at the same time. This trade off is called the Phillips curve……2mks (c) Given = But π= 0.08, e − 3(u − 0.06) e = 0.05, find u? − 3(u − 0.06) ……………………………….1mk Using = 0.08=0.05-3(u-0.06)………………………………… 1mk 0.08- 0.05 = -3u +0.18………………………………… 1mk 3u =0.15………………………………………………… 1mk U = 0.05 or 5% ……………………………………………1mk e 18 (d) Yes , Useful because both inflation and unemployment are key measures of economic performance…………………………………………. 2mks Used by monetary policy makers ……………………………….1mk Used in forecasting ………………………………………………1mk 19