Closed-Economy One-Period Model

Question 1

Closed-Economy

Answer 1

• A single country that is no interaction with the rest of the world

Question 2

Closed-Economy One-Period Macro Model

Answer 2

• Representative Consumer
• Representative Firm
• Government
• Competitive Equilibrium (everyone is price takers, Qs = Qd)

Question 3

Government

Answer 3

• Wishes to purchase a given quantity of consumption goods and finances these purchases by taxing the representative consumers
• Governments provide public gods, which are difficult or impossible for the private sector to provide (eg national defence), because it is difficult to get individuals to pay according to how much each one receives
• Output is produced in the private sector, and the government purchases an exogenous amount G of this input, with the remainder consumed by the representative consumer

Question 4

A model takes exogenous variables and determines endogenous variables

Answer 4

• The model will take exogenous variables – determined outside the model – and will determine the endogenous variables
• Government spending is exogeneous as we are assuming that government spending is independent of what happens in the rest of the economy.
• The government must abide by the government budget constraint which we write as G = T
• Economic experiments involve showing how the endogenous variables depend on the exogenous variables.

Question 5

Fiscal Policy

Answer 5

• Refers to the government’s choices over its expenditures, taxes, transfers and borrowing

Question 6

Competitive Equilibrium

Answer 6

• Representative consumer optimizes given market prices
• Representative firm optimizes given market prices
• The labour market clears (S = D)
• The government budget constraint is satisfied, or G = T In a static model (one period), there is no credit, and so the government does not borrow or lend. The government balances its budget. We assume that the goods acquired by the government are just thrown away

Question 7

Income-Expenditure Equilibrium

Answer 7

• In a competitive equilibrium, the income-expenditure identity is satisfied, so Y = C + G (No I or NX)
• p 166

Question 8

The production function

Answer 8

• Y = zF(K,N)
• Output is of course produced according to the production function in equilibrium, where K is the exogenous capital stock and N is the equilibrium quantity of labor.

Question 9

The Production Function and the Production Possibilities Frontier

Answer 9

• There are two goods in this economy, consumption and leisure, and the PPF describes the technological possibilities for producing consumption and leisure in this economy, after the government takes out G units of consumption goods
• Graphs p 168

Question 10

Competitive Equilibrium graph

Answer 10

• The competitive equilibrium is constructed by superimposing the consumer’s indifference curves on the diagram that includes the PPF
• The marginal product of labor, equal to minus the slope of the PPF, is equal to minus the real wage w
• In a competitive equilibrium the marginal rate of substitution is equal to the marginal transformation, which is equal to the marginal product of labor.
• MPS l,C = MRT l,C = MPn
  Etc p170 / slide 10

Question 11

Marginal Rate of Transformation

Answer 11

• The rate of which one good can be converted technologically into another (In this case the rate at which leisure can be converted in the economy into consumption goods through work.
• MRT l,C = MPn = -(slope of the PPF)

Question 12

Pareto Optimality

Answer 12

• A competitive equilibrium is pareto optimal if there is no way to rearrange production or to reallocate goods so that someone is made better off without making someone else worse off
• The Pareto optimum is the allocation that is chosen to make the representative consumer as well off as possible given what is feasible in this economy.
• Note that in this model, the Pareto optimum and the competitive equilibrium are the same thing. - - The competitive equilibrium is in this sense economically efficient.

Question 13

The first fundamental theorem of welfare economics

Answer 13

• Under certain conditions, a competitive equilibrium is Pareto optimal.

Question 14

The second fundamental theorem of welfare economics

Answer 14

• Under certain conditions, a Pareto optimum is a competitive equilibrium.

Question 15

Using the Second Welfare Theorem to Determine a Competitive Equilibrium

Answer 15

• The second welfare theorem in this case tells us that we don’t need to worry about prices in solving for a competitive equilibrium.
• Just solve the social planner’s problem, and then determine the real wage from the slope of the PPF at the tangency with the indifference curve.

Question 16

Sources of Social Inefficiencies

Answer 16

• Externalities - Any activity for which an individual firm or consumer does not take account of all associated costs and benefits - can be positive or negative
• Distorting taxes - Tax which is not a lump sum - eq if wages are taxed the effective wage becomes w(1-t)
• Firms may not be price takers ege Monopoly

Question 17

Effects of in increase in G

Answer 17

• An increase in G shifts the PPF down by a constant amount for each value of leisure
• C decreases, l decreases, Y increases, w falls.

The pure income effect causes a decline in consumption and leisure, and therefore an increase in labor supplied.

• For the representative firm, output rises, and the marginal product of labor falls, which implies that the real wage must be lower in equilibrium.
• The consumer works harder to provide for the government, and government spending crowds out some private consumption.

p 178

Question 18

Effects of an Increase in z (or an increase in K)

Answer 18

• The increase in z is analogous to an increase in the real wage for an individual consumer.
• It will shift the PPF up, and make it steeper, so that there are income and substitution effects to contend with.
• The shift out in the PPF – the income effect – will tend to increase consumption and leisure.
• But the steepening in the PPF causes substitution from leisure to consumption. Thus, consumption must increase, but leisure could rise or fall.
• Therefore, labor supply could rise or fall.

Question 19

Solow Residual

Answer 19

• Measure of Total factor productivity (TFP)
• TFP procyclical with real GDP
• Basis for business cycle theory
• There must be a large substitution effect relative to the income effect, otherwise the labor input will not be procycliclical

Slide 24 Page 186

Question 20

Real business cycle theory

Answer 20

• View Total Factor productivity shocks as the most important cause of business cycles
• Argue that much of the short-run variation in the labor supply is the result of intertemporal substitution of labor, which is the substitution of labor over time in response to real wage movements

Question 21

Production Function (A Simplified Model with a Proportional Income Tax)

Answer 21

• Labor is the only input, but there is still constant returns to scale (linear production function).
• No capital
• 𝑌=𝑧𝑁

Question 22

Production possibilities frontier (A Simplified Model with a Proportional Income Tax)

Answer 22

• The production possibilities frontier is now linear.
• C = z(h−l)−G

Profits are proportional to productivity minus the real wage. But in equilibrium z = w, so profits are zero.

Question 23

Consumer’s Budget Constraint (A Simplified Model with a Proportional Income Tax)

Answer 23

• Note that dividend income will be zero. All of the firm’s revenue goes to paying wages to workers, and the firm’s profits are zero in equilibrium
• C =𝑤(1−𝑡)(ℎ−𝑙)+ π

Question 24

Profits for the firm (A Simplified Model with a Proportional Income Tax)

Answer 24

• Profits are proportional to productivity minus the real wage. But in equilibrium z = w, so profits are zero.
• π = Y - wN^d = (z-w) N^d

Question 25

Consumer’s Budget Constraint in equilibrium (A Simplified Model with a Proportional Income Tax)

Answer 25

• In equilibrium dividend income is zero and w = z.

- C = z(1 − t)(h − l).

Question 26

Labor Demand Curve (A Simplified Model with a Proportional Income Tax)

Answer 26

• The labor demand curve is perfectly elastic at w = z.

- Thus, labor demand determines the equilibrium real wage.

Question 27

Revenue for the Government Given the Tax Rate t (A Simplified Model with a Proportional Income Tax)

Answer 27

• REV= tz[h − l(t)]
• In equilibrium, revenue collected by the government is the tax rate multiplied by the tax base, where the tax base is the quantity of labor income, which is equal to total output. Note that leisure depends on the tax rate, because the after tax wage is w(1-t).

Question 28

Competitive equilibrium (A Simplified Model with a Proportional Income Tax)

Answer 28

• In a competitive equilibrium the marginal rate of substitution is less than the marginal rate of transformation, so the competitive equilibrium is not Pareto optimal.
• p 194 graph

Question 29

Laffer curve

Answer 29

• The Laffer curve depicts the equilibrium quantity of tax revenue the government collects for each tax rate t.
• If t = 0, then the government collects no revenue, and if t =1 the government collects no revenue because no one will work.
• The maximum quantity of revenue, REV, is collected when t = t.
• In general, for a given G, there are two tax rates that will generate the required amount of revenue.
• Thus there Can Be Two Competitive Equilibria
• G = t z [ h - l(t) ]

Question 30

Representative consumer’s budget constraint: (A Model of Public Goods)

Answer 30

C + T = Y

Question 31

Production possibilities frontier (A Model of Public Goods)

Answer 31

C = Y −𝐺/𝑞

q ~ efficiency of the government relative to the private sector

Suppose that income is exogenous, and the consumer must pay taxes T. Therefore, he or she does not have any choice, except through the political process, to choose G, and therefore T. Assume the government produces public goods from private consumption goods according to G = qT.

Question 32

The Optimal Choice of Government Spending

Answer 32

• The government chooses G to make the representative consumer as well off as possible.
• G chosen so that the marginal rate of substitution of private for public goods equals the marginal rate of transformation.
• Assume that G is chosen optimally, which implies that Y is split between C and G so as to make the consumer as well off as possible.

Question 33

What Happens to the Optimal Choice of G when Y increases

Answer 33

• This works like a pure income effect.
• Private consumption and government spending both increase.
• Wealthier countries choose to have larger governments – but not clear whether G/Y increases or decreases. This depends on whether public goods are luxury goods or inferior goods.

Question 34

The Effects of an Increase in Government Efficiency

Answer 34

• If government efficiency increases, i.e. q rises (can produce more G for a given input of private goods), then there are income and substitution effects.
• The consumer would substitute G for C, so G increases, but C could increase or decrease.
• A more efficient government is therefore a larger government.
• p 201