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ECON60662
ECONOMIC GROWTH
SECTION A
1. The decision problem for an infinitely-lived agent is given as
(ρ, A, α > 0) where c denotes consumption, k denotes capital, 
denotes a proportional output tax, σ denotes a (constant) proportional consumption tax, and 
denotes a lump-sum subsidy.
(a) Solve the above problem to obtain the growth rate of consumption. [7.5 marks]
(b) What is the effect on the growth rate of (i) an increase in
, and (ii) an increase in σ? [5 marks]
2. In an overlapping generations economy, a two-period-lived agent born at time t faces the following decision problem:
where 
denotes consumption when young, 
denotes consumption when old, 
denotes labour when young, 
denotes labour when old, and At denotes the state of technology at time t.
(a) Solve the above problem to find the optimal labour supplies in the first and second periods of agent’s life. [7.5 marks]
(b) Suppose that technology evolves according to At+1 = (1+Lt)At, where Lt is total labour supply at time t. Assuming that the population of agents is N, derive an expression for the growth of technology. [5 marks]
3. Consider an economy in which monopolistically competitive firms produce differentiated intermediate goods that are used in the production of final output. The decision problem for a firm each period is given as follows:
(γ > 0, α > 1) where π denotes profits, x denotes output and p denotes the price of output. An intermediate input is created through research and development at a fixed cost of k. The total (discounted) payoff from innovation is
where r is the (constant) rate of interest.
(a) Solve the firm’s profit maximisation problem to determine the optimal price for its product. What is the implication for the time path of profits? [5.5 marks]
(b) Using the free-entry condition (V = 0), derive an expression for r in terms of π and k. If the Euler equation for households is 
, where c denotes consumption of final output, what is the effect on equilibrium consumption growth of an increase in the fixed cost of innovation? [7 marks]
4. In an overlapping generations economy a three-period-lived agent born at time t - 1 faces the following decision problem:
where 
denotes consumption during middle-age, 
denotes consumption during old-age, 1+nt denotes the number of children, et denotes time spent on education and ht denotes human capital.
(a) Solve the above problem to find the optimal amount of education and the optimal number of children. [8 marks]
(b) Compute the growth rate of human capital. What restriction on parameters is needed for growth to be positive (i.e., ht+1/ht>1)? [4.5 marks]
5. The decision problem facing a finitely-lived agent is given as
where 
denotes consumption when young, 
denotes consumption when old, st denotes savings, wt is the wage and rt+1 is the interest rate.
(a) Determine the agent’s optimal level of savings. [6.5 marks]
(b) Suppose that there is a unit population of agents who are divided into a fraction, μ, of low-skilled workers and a remaining fraction, 1-μ, of high-skilled workers. The wage of a low-skilled worker is fixed at wL, whilst the wage of a high-skilled worker is wHt = AKt with 
, where kt denotes capital. Using the capital market equilibrium condition (i.e., kt+1 = total savings), derive a dynamic equation for capital and illustrate this diagrammatically. [6 marks]
6. The decision problem for an infinitely-lived agent is given as follows:
where c denotes consumption, k denotes capital, 
denotes a (constant) proportional income tax, and G denotes government expenditures. The total population of agents is fixed and normalised to one.
(a) Solve the above problem to obtain the agent’s Euler equation. [7.5 marks]
(b) State the government’s budget constraint and use this to obtain an expression for the growth rate of consumption as a function of 
. [5 marks]
SECTION B
1. Outline a model of endogenous growth based on expanding product variety. What types of policy might influence growth in the model?
2. Outline a model of wealth distribution through investment in human capital and show that in the presence of credit markets’ imperfections and indivisibilities in investment in human capital, “an economy which is initially poor ends up poor in the long run, and an economy which is initially rich and its wealth is distributed among many ends up rich”.
3. In a model of corruption and growth, show why corruption persists in the long run.