[2022] Describe and discuss the main assumptions relating to technology and preferences in the
standard Real Business Cycle (RBC) model. The standard RBC model assumes that technological shocks
are persistent but temporary. Discuss the effects on key macroeconomic variables (such as
consumption, investment, labour supply, real wages and the real interest rate) of a positive
productivity shock that is permanent rather than temporary
Assumptions
Students should start with a discussion of the key assumption of the model: neoclassical
production function (in fact Cobb-Douglas), modelling of technology shocks (see slides).
Students should note implications for factor prices (which will be useful in the following
discussion).
Competitive factor markets and Cobb-Douglass production function
o
o
W increase with (K/L), r decrease with (K/L)
Agents are assumed rational and forward looking; preferences are such that agents prefer
smooth paths for consumption and labour supply.
o Subject to
o consumption Euler equation
When r is above steady state, consumers desire an upward-sloping path of
consumption and vice versa.
o intratemporal labour supply equation
o labour supply Euler equation
Preferences are over paths for consumption and leisure.
o The lectures also remarked that “preferences are chosen so that a permanent increase
in the real wage (such as the one associated with the trend in technical progress)
generates exactly offsetting income and substitution effects so that labour and leisure
are left unchanged (to match the empirical fact that despite a positive trend in labour
productivity, hours worked have not changed much over many decades).”
Temporary but persistent technology shock: Students may start out reviewing the case of a temporary
shock to technology. One can refer to lecture slides' “response to a shock when ρ>0” part.
, Para: model of shock and ↑MPL=w, ↑MPK=r
(↑A0 > 1) Initial shock: u0 > 0, z0 > 0, ↑A0 > 1
o
o zt = ρzt−1 + ut, 0 ≤ ρ ≤ 1
(↑MPL=w, ↑MPK=r) The increase in productivity increases w and r temporarily
This triggers a chain of shifts in macroeconomic factors shown below, which we would explain in
later paragraphs
Para: ↑L from higher w (substitution effects dominate) and r
(↑L, from higher w) For the effect of wages on labour supply, the contrasting income (richer,
afford more leisure) and substitution (substitute from expensive leisure to consumption) effects
should be noted.
o But for a temporary shock the substitution effect dominates and labour supply increases
(this is a consequence of the point about preferences noted below: if the effects cancel
out exactly for a permanent shock, the substitution effect must dominate for a
temporary one, which increases “human wealth” less).
(↑L, from higher r) Candidates might note that the higher r reinforces the effect of the higher w
by encouraging postponement of enjoyment of leisure (Euler equation for labour supply)
o
Work harder if they expect wt > wt+1.
Work harder if r is high since extra income earned now can be invested to
capital stock that earns high r
Para: Y, I, C, K rise
(↑Y) ↑Y (from ↑A and ↑L)
(↑C but less than Y) The higher interest incentivises postponement of consumption too.
Consumption goes up but significantly less than ↑Y. (The rest of the ↑Y goes to ↑I).
o consumption Euler equation
standard Real Business Cycle (RBC) model. The standard RBC model assumes that technological shocks
are persistent but temporary. Discuss the effects on key macroeconomic variables (such as
consumption, investment, labour supply, real wages and the real interest rate) of a positive
productivity shock that is permanent rather than temporary
Assumptions
Students should start with a discussion of the key assumption of the model: neoclassical
production function (in fact Cobb-Douglas), modelling of technology shocks (see slides).
Students should note implications for factor prices (which will be useful in the following
discussion).
Competitive factor markets and Cobb-Douglass production function
o
o
W increase with (K/L), r decrease with (K/L)
Agents are assumed rational and forward looking; preferences are such that agents prefer
smooth paths for consumption and labour supply.
o Subject to
o consumption Euler equation
When r is above steady state, consumers desire an upward-sloping path of
consumption and vice versa.
o intratemporal labour supply equation
o labour supply Euler equation
Preferences are over paths for consumption and leisure.
o The lectures also remarked that “preferences are chosen so that a permanent increase
in the real wage (such as the one associated with the trend in technical progress)
generates exactly offsetting income and substitution effects so that labour and leisure
are left unchanged (to match the empirical fact that despite a positive trend in labour
productivity, hours worked have not changed much over many decades).”
Temporary but persistent technology shock: Students may start out reviewing the case of a temporary
shock to technology. One can refer to lecture slides' “response to a shock when ρ>0” part.
, Para: model of shock and ↑MPL=w, ↑MPK=r
(↑A0 > 1) Initial shock: u0 > 0, z0 > 0, ↑A0 > 1
o
o zt = ρzt−1 + ut, 0 ≤ ρ ≤ 1
(↑MPL=w, ↑MPK=r) The increase in productivity increases w and r temporarily
This triggers a chain of shifts in macroeconomic factors shown below, which we would explain in
later paragraphs
Para: ↑L from higher w (substitution effects dominate) and r
(↑L, from higher w) For the effect of wages on labour supply, the contrasting income (richer,
afford more leisure) and substitution (substitute from expensive leisure to consumption) effects
should be noted.
o But for a temporary shock the substitution effect dominates and labour supply increases
(this is a consequence of the point about preferences noted below: if the effects cancel
out exactly for a permanent shock, the substitution effect must dominate for a
temporary one, which increases “human wealth” less).
(↑L, from higher r) Candidates might note that the higher r reinforces the effect of the higher w
by encouraging postponement of enjoyment of leisure (Euler equation for labour supply)
o
Work harder if they expect wt > wt+1.
Work harder if r is high since extra income earned now can be invested to
capital stock that earns high r
Para: Y, I, C, K rise
(↑Y) ↑Y (from ↑A and ↑L)
(↑C but less than Y) The higher interest incentivises postponement of consumption too.
Consumption goes up but significantly less than ↑Y. (The rest of the ↑Y goes to ↑I).
o consumption Euler equation
