Chapter 3 - Long Run Equilibrium in the Goods, Factor and Loanable Markets in Closed Economies (Classical View) Flashcards
Draw the Diagram for Long Run Equilibrium in the Goods, Factor and Loanable Markets For Closed Economies: Explain each concept.
Summary Flow
- Households provide resources to firms via the Factor Market and receive income.
- Households divide their income between consumption, private saving, and taxes.
Private saving flows into the Loanable Funds Market, where investors borrow for investment.
-Government collects taxes and may borrow from the Loanable Funds Market if there’s a budget deficit. - Investments, government spending, and consumption contribute to the Goods Market.
- Firms use revenue from the Goods Market to pay households, completing the cycle.
How are the aggregate supply and aggregate demand curves determined? Graph it and explain.
The Aggregate Supply and Demand Model
This question leads us to look at the two main curves in this model:
Aggregate Demand (AD)
Aggregate Supply (AS), which has both a Short-Run Aggregate Supply (SRAS) and a Long-Run Aggregate Supply (LRAS)
Let’s break down this slide on the Aggregate Supply and Demand Model to make it easier for you to understand.
Simplified Answer:
Axes of the AS-AD Model:
Y-axis: Price level in the economy.
X-axis: Real GDP (total output of goods and services).
Aggregate Demand (AD):
Shows total demand for goods and services at each price level.
Downward sloping: As prices fall, demand rises.
Short-Run Aggregate Supply (SRAS):
Shows total production by firms at each price level in the short run.
Upward sloping: Higher prices encourage more production short-term.
Long-Run Aggregate Supply (LRAS):
Shows maximum production when resources are used efficiently (full employment).
Vertical line: In the long run, output doesn’t depend on price but on resources and technology.
Equilibrium Point (O):
Where AD, SRAS, and LRAS intersect.
Economy is at full employment, with stable prices and output.
What is the supply side of the economy represented by? With this, suppose A = 2 K = 100 and L = 200, what happens to A if it doubles to 4?
Aggregate Supply and Production Function
Production Function Overview:
The formula Y= F(K , L) explains how output (Y) is created from capital (K) and labor (L) using available technology (F).
Y = Total output (all goods and services produced in the economy).
F = Technology factor, which determines efficiency in using resources.
K = Capital (like machinery, tools, buildings).
L = Labor force (workers or work hours).
Explanation of Capital and Labor:
Capital (K): Broad term for physical assets used in production.
Labor (L): Represents the workforce or hours worked, assuming workers are similar in skills and productivity.
Cobb-Douglas Production Function:
A common type of production function that uses specific exponents for capital and labor: Y = AKL 0<, <1
A = Technology multiplier (higher A means more output with the same inputs).
Examples:
Initial Scenario: With A = 2, K = 100, L = 200:
Y = 325 (output with this technology and resources).
Technological Progress: If A doubles to 4 (better technology), with the same K and L values:
Y = 650 (output doubles because of improved technology).
Key Takeaway:
The economy can produce more output with the same capital and labor if technology (A) improves.
Explain the concept of returns to scale, in the context of a production function, how does output change when all inputs (capital K and labor L) are scaled by the same factor, λ? Given the two production functions,Production function: Y = 2K^0.3L^0.7 and
Y = 2K^0.3L^0.6 what are their returns to scale?
Key Concept: Returns to Scale
Returns to scale describe how output changes when all inputs are increased by a certain factor, λ
If all inputs increase by a factor of λ > 1:
Three types of returns to scale are shown:
Constant Returns to Scale:
If increasing all inputs by λ causes output to increase exactly by λ, we have constant returns to scale.
Formula: F(λK,λL)=λY
Increasing Returns to Scale:
If increasing all inputs by λ causes output to increase by more than λ, we have increasing returns to scale.
Formula: F(λK,λL) > λY
Decreasing Returns to Scale:
If increasing all inputs by λ causes output to increase by less than λ, we have decreasing returns to scale.
Formula: F(λK,λL)<λY
Examples on the Slide
Example of Constant Returns to Scale:
Production function: Y = 2K0.3L0.7
Increase both K and L by a factor of λ, so the inputs become λK and λL
Plugging into the function:Y=2(λK)^0.3(λL)^0.7 = λ⋅2K^0.3L^0.7 = λY
Since the output Y scales exactly by λ, this shows constant returns to scale.
Example of Decreasing Returns to Scale:
Production function: Y = 2K^0.3L^0.6
Again, increase both K and L by λ
Plugging into the function: Y=2(λK)^0.3(λL)^0.6 =λ^0.9⋅2K^0.3L^0.6<λY
Here, the output increases by less than λ, indicating decreasing returns to scale.
What are all the Technology: Diminishing Returns To Factors:
Marginal Product of Labor (MPL):
The extra units of output due to increase in labor force by one unit, while keeping other factors fixed.
Diminishing Returns to Labor:
Given fixed capital, the output rises due to increase in labor force by one unit at a time, but in a decreasingly way.
➔ The marginal product of labor is diminishing in labor
Marginal Product of Capital (MPK):
The extra units of output due to increase in capital by one unit, while keeping other factors fixed.
Diminishing Returns to Capital:
Given fixed labor, the output rises due to increase in capital by one unit at a time, but in a decreasingly way.
➔ Marginal product of capital is diminishing in capital
What does W/P and R/P represent in terms of factor prices, list all factor prices?
Factor Prices:
W: Nominal Wage
R: Rental rate of capital
P: Price of output
Real Wage (W/P):
W/P represents the Real Wage.
This is the purchasing power of the wage, or the wage in terms of units of output.
Real Rental Rate of Capital (R/P):
R/P represents the Real Rental Rate of Capital.
This is the purchasing power of the rental rate, or the rental rate in terms of units of output.
What are Factor Prices and Demand for Labor and Capital in a Perfectly Competitive Market? What is the marginalism approach?
Perfect Competition in Markets:
When markets are perfectly competitive, firms make hiring decisions based on whether adding one more unit (e.g., a worker or machine) will add enough revenue to cover its cost.
Marginalism Approach:
This approach considers whether the additional cost of hiring one more worker or adding more capital is justified by the additional revenue generated.
For Labor:
Formula for Demand for Labor:
The demand for labor is determined by setting Marginal Revenue equal to Marginal Cost.
Marginal Revenue (MR) from labor = P × MPL
(where P is the price of output and MPL is the Marginal Product of Labor, or the additional output from one more worker).
Marginal Cost (MC) = W (Nominal Wage).
Equating Marginal Revenue and Marginal Cost:
In equilibrium, firms hire workers up to the point where: P × MPL=W
Rearranged, this gives: MPL = W/P
This relationship shows that the Marginal Product of Labor (MPL) should equal the Real Wage (W/P) to maximize profit, determining the Demand for Labor.
For Capital:
Formula for Demand for Capital:
Similarly, for capital, the firm will invest in capital up to the point where the Marginal Product of Capital (MPK) equals the Real Rental Rate of Capital (R/P).
In equilibrium: MPK = RP
This equation shows the demand for capital, where MPK (additional output from one more unit of capital) equals the real cost of capital.
Explain the concept of Diminishing MPK: If the production function is Y = 2K^0.3L^0.7, and L = 1 calculate the MPK, diminishing MPK and graph.
Key Concept:
Marginal Product of Capital (MPK): The additional output produced when one more unit of capital (K) is added, holding other inputs (like labor, L) constant.
Explanation of Diminishing MPK:
As capital (K) increases, the additional output (ΔY) gained from each additional unit of capital decreases.
This is seen in the values: as K goes from 1 to 4, the increase in output (ΔY) gets smaller (e.g., 2 → 0.46 → 0.32 → 0.25).
Equations:
Production Function: Y = 2K^0.3L^0.7
Here, L=1, simplifying to Y = 2K^0.3L^0.7
Calculating MPK:
The MPK formula is ∂Y/∂k = 0.6K^-0.7L^0.7
Diminishing MPL = ∂2Y/∂2k=-0.42K^-1.7L^0.7 < 0
This formula shows MPK decreases as K increases (since K has a negative exponent).
Explain the concept of Diminishing MPL: If the production function is Y = 2K^0.3L^0.7, and K = 1 calculate the MPL, and graph.
Key Concept:
Marginal Product of Labor (MPL): The additional output produced when one more unit of labor (L) is added, holding other inputs (like capital, K) constant.
Explanation of Diminishing MPL:
As labor (L) increases, the additional output (ΔY) from each additional unit of labor decreases.
This is observed in the values: as L goes from 1 to 4, the increase in output (ΔY) gets smaller (e.g., 2 → 1.25 → 1.07 → 0.96).
Equations:
Production Function: Y = 2K^0.3L^0.7
Here, K=1, so it simplifies to Y = 2K^0.3L^0.7
Calculating MPL:
The MPL formula is ∂Y/∂L =1.4K0.3L-0.3
∂2Y/∂2L = -0.42K^0.3L^-1.3 < 0
This formula shows MPL decreases as L increases (since L has a negative exponent)
Explain the concept of Diminishing MPL: If the production function is Y = 2K^0.3L^0.7, and K = 1 calculate the MPL, and graph.
Key Concept:
Marginal Product of Labor (MPL): The additional output produced when one more unit of labor (L) is added, holding other inputs (like capital, K) constant.
Explanation of Diminishing MPL:
As labor (L) increases, the additional output (ΔY) from each additional unit of labor decreases.
This is observed in the values: as L goes from 1 to 4, the increase in output (ΔY) gets smaller (e.g., 2 → 1.25 → 1.07 → 0.96).
Equations:
Production Function: Y = 2K^0.3L^0.7
Here, K=1, so it simplifies to Y = 2K^0.3L^0.7
Calculating MPL:
The MPL formula is ∂Y/∂L =1.4K^0.3L^-0.3
∂2Y/∂2L = -0.42K^0.3L^-1.3 < 0
This formula shows MPL decreases as L increases (since L has a negative exponent)
Explain the equilibrium in the Factor Markets and Factor Prices, draw the graphs out.
Key Concepts:
Fixed Capital and Labor:
Capital K and Labor L are fixed in quantity at K bar and L bar
This means the total amount of each factor available in the economy doesn’t change.
Factor Prices Determination:
Factor prices are determined by the equilibrium in each market, where the demand for each factor equals the fixed supply.
Supply of Labor (Left Graph):
MPL (Marginal Product of Labor) Curve: Shows the relationship between the quantity of labor L and its marginal product.
Supply of Labor: Vertical line at L bar since labor quantity is fixed.
Equilibrium Real Wage W/P
Determined where the MPL curve intersects the supply of labor line.
Formula: MPL= W/P, where W is the nominal wage and P is the price level.
Supply of Capital (Right Graph):
MPK (Marginal Product of Capital) Curve: Shows the relationship between capital K and its marginal product.
Supply of Capital: Vertical line at K bar due to the fixed capital amount.
Equilibrium Real Rental Rate R/P
Determined where the MPK curve intersects the supply of capital line.
Formula: MPK = R/P, where R is the nominal rental rate and P is the price level.
Explain all components of Factor Payments and the Distribution of National Income
Key Concepts:
Fixed Factors:
Capital (K) and Labor (L) are set at fixed levels K and L meaning they do not change.
Therefore, Output (Y ) is also fixed, determined by the function Y=F(K, L)
Competitive Markets and Constant Returns to Scale (CRTS):
In competitive markets with CRTS (constant returns to scale), the marginal products remain constant:
MPL (Marginal Product of Labor) is fixed at MPL
MPK (Marginal Product of Capital) is fixed at MPK
Real National Income ( Y):
Total income/output can be divided into:
Real Labor Income: MPL L (income from labor)
Real Capital Income: MPK K (income from capital)
Formula:Real National Income (output) Y = (MPL* L) + ( MPK * K) (including bar)
Economic Profit:
Economic Profit = Total Output minus the payments to labor and capital
In a competitive market with CRTS, Economic Profit is zero because all income is distributed as labor and capital income.
Formula: Economic Profit = Y - (MPL * L) + ( MPK ** K) = 0 (including bar)
Accounting Profit:
Defined as total output minus only labor income.
Formula: Accounting Profit = Y - (MPL * L) (including bar)
Explain the Cobb-Douglas Production Function under Constant Returns to Scale (CRTS) and how it changes with technology and factor productivity:
Key Points:
Cobb-Douglas Production Function:
Formula: Y = AK^αL^1-α
Y represents output.
A is Total Factor Productivity (TFP), which represents technological efficiency.
K is capital, L is labor.
α is a parameter (0 < α < 1) that affects the distribution of output between labor and capital.
Total Factor Productivity (TFP):
TFP increases the productivity of both capital and labor. An increase in A raises overall output.
Marginal Product of Labor (MPL):
Formula: ∂Y/∂L = A( 1-α)K^αL^-α
MPL is the additional output from increasing labor while keeping capital constant.
Behavior:
MPL is increasing in Capital: As capital K increases, MPL also increases.
MPL is decreasing in Labor: As more labor is added, each additional worker contributes less to output due to diminishing returns.
MPL is increasing in TFP: A higher A increases MPL.
Marginal Product of Capital (MPK):
Formula: ∂Y/∂K = AαK^α-1L^1-α
MPK is the additional output from increasing capital while keeping labor constant.
Behavior:
MPK is increasing in Labor: As labor L increases, MPK also rises.
MPK is decreasing in Capital: As more capital is added, each additional unit of capital contributes less to output due to diminishing returns.
MPK is increasing in TFP: A higher A increases MPK.
Summary of Relationships:
MPL and MPK are both positively influenced by TFP (A).
MPL increases with capital and decreases with labor, while MPK increases with labor and decreases with capital.
Explain how income distribution between labor and capital remains stable in economies that follow a CRTS Cobb-Douglas production model. Share of what?
Key Concept: Constant Returns to Scale (CRTS)
CRTS means that if we double both capital (K) and labor (L), output (Y) also doubles.
In a CRTS function, income can be split between labor and capital based on their respective contributions to production.
Income Shares
Share of Labor Income:
Formula: MPL * L / Y = 1- α
Formula: A(1-α)K^αL^-α * L / AK^α L^1- α = 1- α
MPL (Marginal Product of Labor): The additional output generated by an extra unit of labor.
Interpretation:
1−α represents the proportion of total income attributed to labor.
This means labor’s share of income remains constant at 1−α regardless of total output, due to CRTS.
Share of Capital Income:
Formula: MPK * K / Y = α
Formula: AαK^α-1L^1-α *K / AK^αL^1-α = α
MPK (Marginal Product of Capital): The additional output generated by an extra unit of capital.
Interpretation:
Α represents the proportion of total income attributed to capital.
Capital’s share of income remains constant at α due to CRTS.
Takeaway
In the CRTS Cobb-Douglas model:
Labor’s income share is 1−α constant over time.
Capital’s income share is α, also constant.
This stability in income distribution reflects that each factor of production (labor and capital) receives a consistent share of income based on its marginal productivity.
What is the relationship between Labour Productivity and Wages?
Real wages generally depend on labor productivity; higher productivity can lead to higher wages.
In a closed economy, what is the Aggregate Demand for goods formula, explain its components.
Key Concepts:
Aggregate Demand Formula:
Aggregate Demand = C + I +G+NX
Where:
C = Consumption
I = Investment
G = Government spending
NX= Net exports (Exports - Imports)
Closed Economy Assumption:
Since this is a closed economy (no trade with other countries), NX = 0. This simplifies aggregate demand to:
Aggregate Demand = C + I +G
Components of Aggregate Demand:
Consumption (C):
Function of Disposable Income (Y−T)): Disposable income is what’s left after income tax T is deducted from total income Y.
Formula: C = C(Y−T)
Income Tax (T): This is a policy variable set by the government, meaning it can change based on government policies. Here, it is shown as a fixed variable T = T.
Investment (I):
Depends on Real Interest Rate (r): Investment is negatively related to the real interest rate (r), meaning as interest rates go up, investment tends to go down, and vice versa.
Formula: I=I(r)
Government Spending (G):
Exogenous Policy Variable: Government spending is also set by policy and does not depend on income levels directly. Here, it is represented as G = G indicating it’s a fixed or externally set value.
