Part A: Multiple Choice Question (5 marks)

1.   Assume we are in the basic Solow model. Two economies are in the transition to       their long-run equilibrium. Economy 1’s GDP per-capita is growing at 3% while           Economy 2’s GDP per-capita is growing at 2%. Both economies have: s = 0.2, α = 1/3, δ = 0.1, and a current level of capital per-capita of kt = 1. Using the lecture notes’      formula for the growth rate of y, what is the level of technology of Economy 1 (A1)    and Economy 2 (A2)?

A.   A1 = 1.1 and A2 = 1.

B.   A1 = 0.8 and A2 = 0.95.

C.   A1 = 0.95 and A2 = 0.8.

D.  A1 = 0.8 and A2 = 0.9

2.   What are predictions about the evolution of per-capita variables (k, y, c, i) and input  prices (w, r) in the basic Solow model when the economy is hit by a positive shock to technology A (assume Cobb- Douglas production function and the economy is initially at the steady state)?

A.   At the time of the shock, k, y, c, i, w, and r increase and then smoothly converge to the new higher steady state level.

B.   At the time of the shock, k, y, i, and w increase, while c and r decrease. They then converge to the new steady state with higher k ∗, y ∗, i ∗, w∗, and lower c∗ and r ∗ .

C.   At the time of the shock i, c, y, w, and r increase. In the next period, k, i, c, y, and w increase smoothly until they converge to a new higher equilibrium. In the next        period, r starts to decrease and it converges to initial long-run level.

D.  At the time of the shock i and c increase. In the next period, i, c, k, y, r, and w start to increase. Then, all variables converge to the new steady state with higher i ∗, c∗, k ∗, y ∗, w∗and r ∗ .

3.    Which of the following is false about the growth facts discussed in Lecture 1?

A.   Few percentage points difference in average growth can make an important difference in long-run GDP per-capita levels.

B.   Even though there are differences in the evolution of GDP per-capita, all countries appear to converge to the same level of GDP per-capita.

C.   The post-war growth rate of GDP per-capita in developed economies is steady and close to 2%.

D.  Growth miracles and growth disasters exist.

4. Which of the following production functions displays increasing marginal product of capital?

A. Y=AKα N1−α

B. Yt=logKt+logNt

C. Y=AK0.8 N

D. Y=AK1.8 N

5. Use the rule of 70 to predict in how many years Australian GDP per-capita will double. Assume the growth rate of GDP per-capita will be 2.7%.

A.   Australia will double its GDP per-capita in 20 years.

B.   Australia will double its GDP per-capita in 26 years.

C.   Australia will double its GDP per-capita in 24 years.

D.  Australia will double its GDP per-capita in 21 years.

Part B: Short-answer question (8 marks)

1.   (3 marks) Figure 1 shows the evolution of GDP per-capita and the saving rate of        Japan. Use the Augmented Solow model and the historical events affecting Japan to

describe the evolution of these variables, in isolation and together.

Figure 1:

2.   (3 marks) Evaluate the following statements as true/false/uncertain and explain your answer carefully. Please use diagrams and/or algebra when answering the question, when appropriate.

According to the Solow model, the only way to get sustained growth, in the long run, is through technological progress, not through capital accumulation. If we believe      this theory, then, savings behaviour is irrelevant to human welfare, and people           should simply consume all their income.

3.   (2 marks)

Suppose that we have a Solow model with one twist . The twist is that there is a government. Hence, the aggregate resource constraint is: Yt = Ct + It + Gt .

where Gt = Tt (public expenditure is financed by taxation) and Tt = Yt .

Define private output as  = Yt − Gt . Suppose that private investment is a constant fraction, s, of private output (consumption is then 1 − s times private output). A       fraction of sGGt is spent on public investment, which supplements the productive     capital stock. Otherwise the model is the same as in the lecture.

Derive the transition dynamic equation for this economy.

Part C: Problem-Solving question (17 marks)

Question 1: (5 marks) As an economic advisor to the Treasurer of country A, you are              required to provide some assessment of the likely impact of an increase in the tax rate from its current level of 40% percent to a new proposed level of 50 percent.

The first element of your analysis is the calibration of a theoretical model with the following elements:

Production Function:  =   1−  1−

Budget constraint:  =

Physical capital accumulation: ∆ =  −

Y is the level of total GDP, K is the stock of physical capital, N is the stock of labour, G is         government expenditure, A denotes the level of technological efficiency – which is assumed to be constant.

Your team of economic analysists provides the following information:

•   The rate of population growth in this country is zero and expected to remain at zero for the long-term

•   The saving rate (s) is 30%

•   The Labour stock is 300 units

•   The rate of capital depreciation () is 5%

•   The current level of technological efficiency is measured as 0.15

•   The production function is characterised by α = 0.65

Using this information, you prepare your analysis of the relationship between tax rate and growth rate of GDP per-capita:

a)   (2 marks) Present and briefly comment a diagram representing the relationship       between tax rate (displayed on the horizontal axis) and growth rate (displayed on   the vertical axis), using the theoretical model and the information provided by your team of economic analysts.

b)   (1 mark) Based on the results at point 1, predict the rate of growth of the economy if the tax rate is increased to 50%. Briefly explain the economics underlying your result.

c)   (1 mark) Based on your analysis, and assuming that the goal of the Treasurer is to maximise growth, what is your advice: should the tax rate be increased or not?

A member of your staff finds a very recent paper that present empirical estimates of the relationship between tax rate and growth rate based on a sample of countries similar to country A. The main result of the empirical estimates is reported in the following table

d)   (1 mark) Do the empirical findings of this paper make you change your advice as to

whether the tax rate should be increased or not? Briefly explain your why. Question 2: (6 marks)

We are in the basic endogenous growth model studied in class. Suppose that the quantity of output is produced according to

Y (t) = [A(t)(1 − aL)L(t)] . New ideas are produced in this economy according to ̇() = B[aL L(t)]γA(t)θ, B > 0,γ ≥ 1. Labor evolves according to ̇ () = nL(t).

a) (1 mark) Find an expression for the growth rate of the growth rate of knowledge (̇A (t)/gA (t)). Show your working (Hint: write the equation for gA (t) first) .

(2 marks) Assuming that θ = 1, find the long-run growth rate of knowledge ( ) and clearly explain its determinants

b) (3 marks) Explain the evolution of the economy when θ = 1 and there is a permanent     increase in B. In particular, what are the predictions about short-run and long-run growth? Consider the cases when n = 0 and n > 0.