National Income Study Notes PDF

# Chapter 3: National Income (where it comes from and where it goes) ## In the closed economy market: - Individuals, firms, and the government interact in three markets. - Three markets: - 1) Factor Markets - 2) Financial Markets - 3) Market for goods and services - Prices are flexible....

# Chapter 3: National Income (where it comes from and where it goes) ## In the closed economy market: - Individuals, firms, and the government interact in three markets. - Three markets: - 1) Factor Markets - 2) Financial Markets - 3) Market for goods and services - Prices are flexible. - Economy is at full employment. - QD = QS in each of the market: Labour market, asset market, and the goods market. - Longer term performance of the economy. ## Outline of the whole model: ### Supply side: - Factor markets (supply, demand, price) - Determination of output/income. ### Demand side: - Determinants of C, I and G ### Equilibrium: - Goods market - Loanable funds market ## What determines the Total Production of Goods and Services? Amount of GDP depends on: 1) Factors of production: - Capital (factories, machines) - Labour (workers) - Raw materials and energy - Technology and management 2) The Production Function. ### Assumptions: 1) The economy's factors of production is given and are fully utilized. $K = \overline{K}$ $L = \overline{L}$ (capital and labour are fixed). 2) Technology is fixed. ## ② The Production Function: - Mathematical expression relating the amount of output produced to quantities of capital and labour utilized. | number measuring overall productivity | Quantity of capital used (capital stock). | | ---------- | ---------- | | ↑ | ↑ | | Production Function: Y = AF(K,L) | | | real output produced. | Function relating Y to K and L. | Number of workers employed. | ## Total Factor Productivity (TFP): - How efficiently inputs are used in producing output or simply technology. - ie. Bakery 1: Production of cookies by manual labour = less production. - Bakery 2: Production of cookies by assembly line = more production. - Difference captured in TFP - For any values of K and L: Increase in TFP of say - 10% implies a 10% increase in the amount of output. ## Properties of production function: (Exist 4 assumptions) 1) **Capital and labour required for production** - without them will produce no output. $AF(K,0) = 0$ or $AF(0,L) = 0$ 2) **Output is increasing in both capital and labour:** - Holding TFP and capital fixed = bigger labour force increases output. - Holding TFP and labor fixed = more capital increases output. 3) **ΠΡΚ and ΠΡL are positive.** - Marginal product of labor (MPL) - Is the increase in output produced by each additional unit of labor. $MPL = \frac{ΔY}{ΔL}$ - Similarly $MPK = \frac{ΔY}{ΔK}$ 4) **There are diminishing marginal products of capital and labor.** - Holding the amount of capital fixed = MPL ↓ as the amount of labour increases. - When MPL is negative = Production function have diminishing marginal returns. ## ④ Production function exhibits constant returns to scale: - Has constant return to scale if an increase of an equal percentage in all factors of production causes an increase in output of the same percentage. ## Returns to scale: - How output changes when both inputs are scaled up by the same amount. - If % change in input = % change in output - Constant return to scale - If % change in input < % change in output - Increasing returns to scale - If % change in input > % change in output - Decreasing returns to scale ## Returns to scale: Mathematical review - Initially $Y_1 = F(K,L)$ - Multiplying capital and labor by a constant z (positive): - $Y_2 = F(zK,zL)$ - $= ZF(K,L)$ - $Y_2 = zY_1$ (Constant returns to scale means that if we double all inputs, the output is double). - **Increasing returns to scale:** Output will be more than doubled. $F(2K,2L) > 2F(K,L)$ - **Decreasing returns to scale:** Doubling the level of inputs yield less output. $f(2K,2L) < 2f(k,l)$ ## The Supply of Goods and Services - We assume that the supplies of capital and labor, and the technology are fixed. - **LABOR** - wages - labour fixed - labour - **Capital** - Capital supply - capital fixed - Capital - Rate - **Total output**: Determined by the fixed factor supplies and the fixed state of technology. $Y = F(\overline{K},\overline{L})$ ## How National Income Distributed to the factors of production? We know GDP = GDI - National Income flows from firms to households through the markets for the factors of production - will be applied Classical labour market along with Neoclassical theory. - Factor market: Helps distribution of income. - **Distribution of national income determine by factor prices**. The prices per unit firms pay for the factors of production. - wage = price of L - Rental rate = price of K ## How Factor prices are determined - Factor prices determined by supply and demand in factor markets - Supply of each factor is fixed. ## The Firm’s demand for Labour - Assume markets are competitive: - The competitive firm takes the prices of its output and inputs are given by market conditions - Profit = Revenue - Labour cost - Capital costs - P Y - W L - R K - Substituting: Y = F(K,L) - Profit = PF(K,L) - WL - RK - Since W, R and P are fixed, the firm chooses K and L that maximizes profit. ## Profit Maximising Quantities (ΠΡΙ, ΠΡΚ) - **MPL = The slope of the production function**. As the amount of labour increases, the production function becomes flatter indicating diminishing marginal product: As more labour, the marginal product of labour declines - If L increases while holding K fixed, machines per worker falls → worker productivity falls. ## From MPL to Labour Demand - Firm compare costs and benefits of hiring each additional worker. - **Cost of extra worker = w = Nominal Wage**. - **Benefit of extra worker = ΠΡΙ - the value of extra goods and services = Marginal Revenue Product of Labour = ΠΡ2 × P** - P = Product price - If benefit of additional worker: MRPL > W - Firm should increase employment. - If MRP2 < W - Firm should reduce employment. - **Firm’s demand of labour is: P × MPL = MRP2 = W** - **Profit maximizing level of labour is: ΠΡL = W = ε** - $MPL = W$ ## MPL and the demand of labour - MPL slopes downward - MPL declines if L increases. - Firm hires up to the point where MPL = real wages - **Example:** Pbread = $2; W = $20 per hour. - $\frac{W}{P}=\frac{20}{2} = $10. - Firm keeps hiring as long as MP2 = 10. ## MPK: Marginal product of Capital and Capital demand. - $MPK = \frac{ΔY}{ΔK}$ - **Diminishing returns to capital**: MPK falls as K rises. - The MPK curve is the firm’s demand curve for renting capital. - **Maximizes profit**: Marginal product of capita = real rental price of capital. ## The Division of National Income / How is Income distributed to L and K? - Since w = ΠΡL - **Total real wage paid to the labour are W × L = MPL × L** - **Total real return paid to the capital owner is r × K = MPK × K** - **Economic Profit = Y - (ΠΡ2 × L) - (ΠΡΚ × K)** - $Y = (MPL × L) + (MPK × K) + Economic Profit$ - **Total income is divided among the return to labour, return to capital and economic profit.** ## How is income distributed to L and K? - If production function has constant returns to scale, then economic profit = zero. - **Euler’s Theorem**: If factors are paid their marginal product, then the sum of these factor payments equals to total output. $MPL = (1-a)AK^{a}L^{1-a}$ $MPK= aAK^{a-1}L^{1-a}$ ## The exponent of each input variable indicates the relative share of that input in the total product. - **Cobb-Douglas Formula**: $Y = MPL × L + MPK × K$ - Capital's relative share of total product: $\frac{MPK × K}{Y}$ - Labour's relative share of total product: $\frac{MPL × L}{Y}$ - The ratio of the labor income to capital income is a constant $(\frac{1-a}{a})$, which is constant. ## - DEMAND SIDE - ## Demand for goods and services / How the production is used - Determinants: C, I, G(no nx) - Y = C + I + G - National Income Identity. ## Consumption(c): - $C = f(Y)$ - Income ↑, consumption ↑ - Disposable income: Total income - Total taxes - Y - T - Consumption Function: C = C(Y-T) - **Marginal propensity of consume (MPC)**: Change in C when disposable income increases by one dollar. ## Investment (I): - Investment depends upon interest rate. If revenue from a project is higher than the payments for borrower funds, the project is profitable. - **Real interest rate (i) = Nominal interest rate - inflation rate.** - Investment function: I = I(r) ## Government Spending (G): - Government spending on goods and services. - Excludes Transfer payments. - Saving - S = (Y - C - T) + (T - G) - S = Y - C - G - Public saving: (T-G) - Private saving: (Y-C-T) - 1) Budget deficit: T < G (negative public saving) - 2) Budget surplus: T > G (positive public saving) - 3) Balanced budget: T = G (public saving is zero). - Government spending and total taxes are exogenous : G = $\overline{G}$ and T = $\overline{T}$ ## Equilibrium in the Market (Supply and Demand in equilibrium) - In the classical model, the interest rate adjusts to equate demand with supply. - Y = C + I + G - C = C(Y-T) - I = I(r) - G = $\overline{G}$ T = $\overline{T}$ - Equilibrium in the market for goods and services, C + I + G. - ↓ I , Demand ↑ - ↑ r = ↓ I, Demand ↓ - The Goods market is in equilibrium when national savings equal investment. S = (y - T - C) + (T - G) = I - S = I(r) ## Supply - Demand model of the financial system - "Loanable funds" - Asset. - Demand for funds: Investment - Supply for funds: Saving - Price: Real interest rate. - Demand for Funds: Investment - Comes from investment - Depends negatively on r. - r is "price" of loanable funds - (cost of borrowing) - Supply for Funds: Saving - comes from saving - Government may contribute to saving, if it doesn't spend all tax revenue. ## Special role of “r” - Goods market equilibrium is equal to saving investment balance. - r adjusts market. - Loanable funds market in equilibrium: Y = C + I + G - Changes in Saving: The Effect of Fiscal Policy - Things that shift saving curve: Fiscal Policy - changes in G or T - ↑ G causes ↓ I and ↑ r - This is known as investment crowding out. - **Decrease in Taxes:** Taxes ↓ = Saving ↓ - Reduction in saving shifts saving line to the left, increasing interest rate and crowd out investment. - **An increase in Investment demand** - Shift Investment Curve: Technological innovations, advantage of some innovations, tax laws affect investment, Investment Tax Credit - ↑ Investment Demand ↑ r