real business cycles - primative RBC model Flashcards
how do you model the economy in the primative RBC model?
two discrete time periods 1 and 2
a representative household solving intertemporal consumption leisure problem
a representative producer solving profit maximisation problem each period and choosing the optimal level of investment
competitive market for inputs and final output <-> both the household and the firms are price takers
how do we deal with dividends in the RBC model?
from the households standpoint, the flow of dividends is exogenous ie depends on the firms business decisions so should not affect the optimal choice between Consumption and leisure. moreover the equillibrium profits in the competitive economy are zero and so we can exclude dividends income from the households optimization problem
what is the intratemporal optimization condition for a household>
[v’*(l_t)]/[u’(C_t)]=w_t for t=1,2
the household optimises by choosing leisure and consumption in every period so that the marginal rate of substitution of leisure for consumption is equal to the real wage. in each period, the household must be indifferent at the margin between dedicating a unit of time to leisure or to market work
higher real wage makes leisure less attractive relative to consumption
what is the intertemporal optimisation condition for a household?
[u’(C1)]/[Bu’(C2)] = 1+r
the marginal rate of substitution of current consumption for future consumption equals the relative price of current consumption in terms of future consumption
no matter how the household obtains its income, it distributes its consumption over time in accordance with the real interest rate
higher r makes current consumption less attractive relative to future consumption
what is the combined optimisation condition?
v’(l1)/v’(l2) = w1/w2 *B(1+r)
the ratio of marginal utilities of current and future leisure depends on the wage ratio if w1 rises relative to w2 the ratio of marginal utilities rises, the houshold will decrease first period leisure relative to second period leisure and the first period labour supply increases relative to second period labour supply
a rise in the interest rate increases the attractiveness of working today and saving relative to working tommorow. it is worht working more in the present under the highest interest rate as it provides a larger reture in terms of future leisure
what is the optimisation condition for the firm?
dΠ/dl = A1F’(L) - w=0 or A1F’(L) =w so the marginal product of labour equal real wage
and
dΠ/dK = -1 + [A2F’(K) + 1 - δ ]/ (1+r) =0 or r+ δ =A2F’(K)
the marginal product of capital after taking account of the depreciation of the capital stock should equal the real interest rate
what is the resource constraint for goods in period 1?
C1+ I1 =Y1 or C1 +K =Y1
what is the resource constraint for goods in period 2?
Y2= C2
what is the resource constraint for time in period 1?
L + leisure =1
what is the law of motion of capital?
I1=K
what is the general equillibrium condition for how the economy will allocate the use of time?
v’(l)/u’(C1) = w = A1F’(L)
on the LHS : how the representative household is willing to trade off leisure against consumption
on the RHS : how the available technology is able at the margin to convert time into output
what is the general equillibrium condition for how the economy will allocate output between the present and the future
u’(C1)/bu’(C2) = 1+r = A2F’(K)
on the LHS: how the representative household is willing to trade off present consumption against future consumption
on the RHS : how the available technology is able to convert current output into future output by building an extra unit of capital
what is the first welfare theorem?
even if all agents delegate their consumption and investment decisions to a benevolent social planner, the allocation of resources would coincide with the outcome of competitive markets
what is pareto efficiency?
there is no technologically feasible way to make someone better off without making someone else worse off
what are examples of productivity shocks?
unfavourable developments in the physical enviroment which adversely affect output
significant changes in energy prices
war, political upheavel or labour unrest which disrupts the existing performance and structure of the economy
government regulations which damage incentives
TFP shocks in a narrow sense
