econ exam 2

problem set and poll everywhere questions

What is the Solor Model Golden Rule Condition?

MPK − δ = n

(marginal product of capital - depreciation rate = labor force growth rate)

what if MPK − δ > n

• Capital is very productive

• you should increase the savings rate

what if MPK − δ = n

• you are at the optimum

• consumption per person is maximized

what if MPK − δ < n

• Capital is not productive enough

• you should decrease the savings rate

How do the Solow growth model and the endogenous growth model view the marginal product of capital?

The Solow model assumes diminishing returns, and the endogenous growth model assumes constant returns to capital.

What is the key equation of growth accounting?

∆Y/Y = α∆K/K + (1 − α)∆L/L + ∆A/A

OR

GDP growth rate = share of income to capital*(capital growth rate) - share of income to labor(labor growth rate) + technology growth rate

names for ∆A/A

• solow residual

• the change in output not explained by the change in inputs

• change in output measured indirectly

If the net marginal return to capital (MPK − δ) is above the economy’s average growth rate (n +g )…

there is an opportunity to increase future consumption per capita

A comparison of these two countries most clearly demonstrates the importance of institutions to economic development.

North Korea and South Korea

A static decision is one that…

involves planing over one time period

it is useful to assum that there is a single representative consumer because…

this is a useful abstraction if we are interested in problems where distribution effects are not important.

a utility function

needs to measure relative amounts of happiness for a single individual

why do we use indifference curves?

they help represent preferences

what is a numeraire?

a good used as a unit of account

A consumer’s real disposable income equals

wage income plus profit income minus taxes

(wxL) + π dividends - T

With consumption on the vertical axis and leisure on the horizontal axis, the slope of the budget line is equal to

-w

If dividend income increases…

• the consumer chooses to consume more leisure. 

• the consumer chooses to consume more consumption goods. 

• the budget constraint shifts to the right.

The household budget constraint may have a kink because

leisure is limited by the number of available hours

theoretically, an increase in the real wage

has an ambiguous effect on leisure

In an economic model, an endogenous variable is…

determined by the model itself

(endogenous - inside the model)

relationships in the one period model:

• G=T 

• Y=C+G 

• Y=zF(K,N)

In the one-period competitive model we have been studying…

consumption is endogenous, and total factor productivity is exogenous

The PPF determines…

the set of feasible outcomes

A competitive equilibrium 

is economically efficient only given some special conditions

conditions for competitive equilibrium:

• Households optimize (work vs leisure)

• Firms optimize (w = MPL , r = MPK)

• Markets clear (L supply = L demand , Y=C+I+G, savings = investment)

Why may a competitive equilibrium fail to be Pareto optimal?

• externalities. 

• distorting taxes. 

• non-price-taking firms (imperfect competition)

• incomplete markets

Does inequality prevent competitive equilibriums from being pareto optimal?

No

• Pareto optimal can’t make someone better off while making someone worse off; inequality itself doesn’t necessarily make someone worse off

An increase in government spending shifts the PPF

downward, but does not change its slope

 Real business cycle theory argues that the primary cause of business cycles is fluctuations in

total factor productivity

At the competitive equilibrium with a positive proportional labor income tax

 the real wage after tax is lower than the marginal product of labor

When the tax rate increases, the tax revenue

• may increase or decrease depending on what side of the laffer curve it is on

in the solow growth model, which variable is endogenous?

• the capital stock

Solow growth equation

Δk= sf(k) − (n+δ)k

In the Solow model, which two variables have similar effects on the capital stock per worker?

• the savings rate and depreciation rate

if population grows at rate n and workers become more effective at rate g, which variable grows at rate (n+g)?

• output

  • Y=A⋅F(K,L)

  • Depends on both A andL

  • In general growth:

    • Y grows at n+g  (plus capital accumulation effects in transition)

What might Joseph Schumpteter have called the rise of online retailing at the expense of brick-and mortar retail outlets?

• creative destruction

Which statement is suorted by research?

Nations with high levels of physical and human capital tend to use those factors more efficiently

what would NOT change the total factor productivity?

• an increase in capital, labor, or both

  • adding more inputs increases output, but TFP specifically measures efficiency independent of input quantities

what is a possible explanation of the productivity slowdown in the 1970s?

• worker quality declined

  • large Baby Boomer generation entered the labor force, bringing many inexperienced workers that temporarily dragged down average productivity

the utility function captures:

How an individual consumer ranks consumption bundles

the fact that indifference curves are downward sloping…

follows the fact that more is preferred to less

the real wage denotes…

The number of units of consumption goods that can be exchanged for one unit of labor time

a positive, pure income effect can be obtained by:

Increasing the dividend.

• A pure income effect means the consumer's purchasing power changes without any change in relative prices (i.e., the real wage stays the same, so the budget constraint shifts parallel).

• In the static macro model (ECON304), the consumer's budget constraint is;

  • C = w(h - l) + π - T

the substitution effect measures:

The responses of quantities to changes in the relative prices of goods.

a production function describes the:

• Technological possibilities for converting factor inputs into outputs

• Production function

  • Y = zF(K, N)

the assumption that the marginal product of labor decreases as the labor input increases implies…

• The production function is concave.

  • the marginal product of labor (MPN) is the slope of the production function. If MPN is decreasing as labor increases, that means the slope is getting flatter and flatter as you move right — which is precisely the definition of a concave function

when the representative firm maximizes profits…

The marginal product of labor equals the wage

• π = zF(K, N) − wN

• MPN = w

a competitive equilibrium is a state of affairs in which…

• markets clear and economic agents are price takers

in a competitve equilibrium, which relationships are true?

• labor demand = labor supply

  • labor clearing

• Y = G + C

  • goods market clearing

  • output = gov. spending + private consumption

• C (G = T)

  • government budget constraint

  • gov. spending = tax revenue

an increase in government spending…

reduces private consumption, increases hours worked, and reduces the real wage

• higher G = higher T

• higher T = reduced consumption and leisure = more hours worked

• more hours worked = increased labor supply = lower real wage

In response to an increase in total labor productivity…

The substitution effect suggests hours worked should increase, while the income effect suggests hours worked should decrease

An increase in TFP (z) raises the real wage (w = MPN↑), which triggers two opposing effects on labor supply:

Substitution Effect:

• Leisure becomes relatively more expensive (higher opportunity cost)

• Consumer substitutes away from leisure → works more (N↑)

Income Effect:

• Higher wage means greater real income/wealth

• Consumer buys more of all normal goods, including leisure → works less (N↓)

These two effects pull in opposite directions, making the net effect on hours worked theoretically ambiguous

Proportional income tax is distorting because…

• The competitive equilibrium is not Pareto optimal

• a tax is distorting when it drives a wedge between the consumer's and firm's optimality conditions, causing the equilibrium to be inefficient.

  Here's the mechanism with a proportional income tax (rate t):

  • Firm's condition: MPN = w (firm pays the full wage)

  • Consumer's condition: MRS = w(1−t) (consumer only keeps the after-tax wage)

  This creates a wedge: MPN ≠ MRS, meaning the social value of an extra unit of labor differs from the consumer's private valuation. The result is that the competitive equilibrium is not Pareto optimal — you could reallocate resources to make someone better off without hurting anyone else.

Indifference Curve

connects a set of points representing consumption bundles among which the consumer is indifferent

MRS l,c

• Marginal Rate of Substitution of leisure for consumption

• the rate at which the consumer is willing to substitute leisure for consumption goods

indifference curve properties

• slopes downward

• convex (the consumer has a preference for

  diversity in his or her consumption bundle).

properties of firm’s production function

• Constant returns to scale.

• Output increases with increases in either the labor input or the capital input.

• The marginal product of labor decreases as the labor input increases.

• The marginal product of capital decreases as the capital input increases.

• The marginal product of labor increases as the quantity of the capital input increases.

• The marginal product of capital increases as the quantity of the labor input increases.

adding capital _________ the marginal product of labor, and ______ the TFP

• increases

• increases

static model exogenous variables:

G, K, A

Production Possibilities Frontier

set of all feasible bundles of consumption and leisure that can be produced.

slope of the PPF

• MRT (L,C) = -w

• Marginal Rate of Transformation of Leisure

  into Consumption

the competitive equilibrium is constructed by…

• superimposing the consumer’s indifference curves on the diagram that includes the PPF.

• competitive equilibrium is where the indifference curve is tangent to the

  PPF

Pareto Optimal

• there is no way to rearrange production or to reallocate goods so that someone is made better off without making someone else worse off

Pareto Improvement

• makes at least one agent better off without making any other agents worse off.

Properties of a Pareto Optimal Equilibrium

MRS(L,C) = MRT(L,C) = MPn = w

First wellfare theorem

Under certain conditions, a competitive equilibrium is Pareto optimal

Second wellfare theorem

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