Growth Flashcards
What is Eulers Theorem?
Euler’s theorem implies that the production function is equal to the marginal product of labor multiplied by labor plus the marginal product of capital multiplied with capital.
Y = MP_L L + MP_K K
How will variables like output, consumption and investment grow at the balanced growth path?
They will grow at constant rates, and the same rates given the linearity of the recourse constraint. Then g_c, g_i and g_y = g
This is due to the Uzawa’s theorem.
Vad är derivatan av den andra controll variablen. T.ex a
H_a = βμ - μ´
Där β är raten som äexponenten gäller. Text exp(-g(t)); så är β = g
Explain how income and substitution effects are at play when there is balanced growth.
Growing wages render the same level of consumption feasible with fewer hours worked, i.e. they make leisure more affordable. This incentivizes households to supply fewer hours; this is the income effect. Note that in this setting, rising non-labor income will have a similar effect. On the other hand, higher wages increase the return from each hour of work supplied, thereby rendering work more attractive - this is the substitution effect.
The result from the exercise we did with labor supply shows that on the BGP, the income effect from both rising wages and non-labor income - and the substitution effect from rising wages must exactly offset each other.
What is the free entry condition in the Romer (1990) model?
1 = 𝜂𝑉 (𝜈, 𝑡).
Which is equal to
MC = MB
A unit of final good spent on research generates 𝜂 new ideas. Then the free entry condition ensures that the marginal benefit of expending resources on research must equal the marginal cost if research takes place (i.e. 𝑍(𝑡) > 0).
𝜈 = machine type
𝑍 = expenditure on R&D
What is the no-arbitrage condition used in the expanding varieties (lab-equipment model)?
𝑟(𝑡) 𝑉 (𝜈, 𝑡) = π (𝜈, 𝑡) + 𝑉 ˙(𝜈, 𝑡)
Explain why the BGP in the Romer (lab-equipment) model is the unique equilibrium, and why there are no transitional dynamics.
- If there is positive research so that 𝑍(𝑡) > 0, then by the free entry and no arbitrage conditions the interest rate must be constant (nbl-p). This implies that the consumption, and all other aggregate variables, grow at the same rate at all time periods. The economy hits the BGP immediately if research takes place.
- We could have 1 > 𝜂𝑉 (𝑡), so no research takes place (i.e. 𝑍(𝑡) = 0), then there is no growth. Thus all aggregate variables are constant at all times and 𝑟(𝑡) = 𝜌.
What expression for z(t) do we derive in the dynamic part of the social planner problem of the Romer model?
Z(t) = (1-B)^{-1/B)BN(t)L - C(t)
How do we write the growth rate g = x’/x in terms of X(0) ?
X(t) = X(0)exp(gt)
What does the consumption Euler equation
c’/c = (r(t) - p)
State?
it states that consumption will grow over time when the discount rate is less than the rate of return on assets.
It also specifies the speed at which consumption will grow in response to a gap between this rate of return and the discount rate, which is related to the elasticity of marginal utility of consumption (= inverse of the intertemporal elasticity of substitution).
Why do incumbents have incentive to innovate in our last growth model but not the quantitive latter?
In the Quantity ladders model, it is never profitable for the incumbents to innovate, since they would replace their own profits (Arrow’s replacement effect).
In the last model, firms can have more product lines, and they it is harder for them to exit the more product lines they have, thus they are incentivised to keep inventing stuff.
When do we hit BGP immediately?
The only model for which you are supposed to know how to analyze transitional dynamics is the neoclassical growth model (phase plane analysis).
For Romer, quality ladders, and Klette & Kortum you just remember that the BGP is hit immediately.
Is the decentralized EQ inefficient in the QL model?
Yes - In general
Monopolisti power creates “static inefficiency”
Standing on the sholder of giants - externality creates “dynamic inefficiency”
Buessnies stealing effect creates dynamic inefficiency.
Buessnines stealing:
When a firm does more R&D and reduces its cost, it generates a business stealing effect by reducing the profit of other firms. Part of this effect will be due to changes in the output levels of other firms, and part to the change in equilibrium price.
What is the scalar effect?
Most baseline models of endogenous technological change predict that the growth rate should increase linearly with the size of the workforce (or the number of people capable of research)
▶ not true in cross-section of countries
▶ not true in time series for rich economies
▶ although in the very long run and at a global scale, growth has sped up as population has increased
