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A Dynamic Macroeconomic Model Notes

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A Dynamic Macroeconomic Model Summary



Key Points

The Dynamic Macroeconomic Model The Representative Household The Representative Firm Government

The Dynamic Macroeconomic Model

• Putting together household consumption behaviour and firm behaviour to build a complete macroeconomic model

• Study the economy in general equilibrium

• General Equilibrium = Equilibrium in all markets

• We use the model as a benchmark for studying the effects of shocks

• We place an emphasis on expectations about the future

• Two time periods: the present and future
○ The length of time in each period may depend on the context
 For business cycles, the current period will be the current year or quarter
 For longer term issues, the current period may be the current decade or longer
□ i.e. productivity trends

• Closed economy = No international trade

• 3 agents in the economy: a. A representative household
 Makes a consumption vs. leisure decision, and a consumption now vs. saving decision b. A representative firm
 Makes a labour hiring decision, and an investment decision c. The government
 Consumes resources, levies taxes and issues debt

• 3 markets in the economy: a. Goods market
 Supply: output produced by firms
 Demand: consumption by households, investment (accumulation of capital) by firms, government spending b. Labour market
 Supply: work done by households
 Demand: hiring by firms c. Bond market
 Supply: debt issued by government
 Demand: household savings

The Representative Household

• Preferences over consumption and leisure, now and in the future
○ Assume that consumption and leisure are normal goods

• Income:
○ Labour income
○ Dividends (the representative household owns the firms)
○ Interest from bonds

• Must pay taxes to government

Household Preferences
○ Moving to a higher indifference curve but holding constant the slope (the MRS) implies that both consumption and leisure rise

Graph showing household preferences for consumption and leisure

○ Consumption in the current period and the future period are also assumed to be normal goods
 Same for leisure
○ Moving to a higher indifference curve (holding constant MRS)
 Implies more current and future consumption Graph showing household preferences for current and future consumption

Course Notes Page 14

Agents in the economy Markets in the economy Household preferences Household budget constraint Consumption/saving decision Consumption/leisure decision Intertemporal substitution: Labour Income and substitution effects Income effects in the closed economy Wealth effects Effects of changes in lifetime after-tax income Marginal propensity to consume

Household Budget Constraint
 Current Period:
 Future Period:
 Combined: Consumption/Saving Decision
 The optimality condition:
 Giving up one unit of consumption today yields an extra 1+r units in the future
 Households must be indifferent between doing this or not to maximize utility
 MRS is diminishing
□ ∴ higher interest rate encourages saving (substitution effect)

Graph of the consumption/saving decision

Consumption/Leisure Decision
 Optimality condition:
 Giving up an hour of leisure yields an extra w units of consumption now
 Households must be indifferent between doing this or not to maximize utility
 MRS is diminishing:
□ ∴ higher wage needed to work more (substitution effect) Graph of the consumption/leisure decision

 Where N = h - l = hours used for work Intertemporal Substitution: Labour
 There is also an intertemporal dimension to the labour supply decision
 Taking one more hour of leisure in the current period implies a reduction in income of w
 If consumption plans (now and in the future) are not to change, this income must be made up by working more in the future
 Each hour of future work pays wage
 So the household must work

in present value terms more hours in the future

 Optimality requires the household to be indifferent between working an hour now or in the future:

This can also be derived from the following 3 conditions:

Course Notes Page 15

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