Part II Classical Theory: Long Run Chapter 3 National Income: Where It Comes From and Where It Goes

Part II Classical Theory: Long Run Chapter 3 National Income: Where It Comes From and Where It Goes Zhengyu Cai Ph.D. Institute of Development Southwestern University of Finance and Economics All rights reserved http://www.escience.cn/people/zhengyucai/index.html

Refresh your memory GDP GDP deflator CPI Unemployment rate Zhengyu Cai - 2017 Spring Macroeconomics Chapter 3 2/42

Long run Where is the long run? Zhengyu Cai - 2017 Spring Macroeconomics Chapter 3 3/42

How to explain what s happening We have known some important macro economic variables, how to explain their movements? Same way! Observe, build a model, and then let s see if it works! Zhengyu Cai - 2017 Spring Macroeconomics Chapter 3 4/42

Let s observe first: macro economy as a system Zhengyu Cai - 2017 Spring Macroeconomics Chapter 3 5/42

Macro economy as a system Macro economy is running like a machine. When it is newly built, it may have some glitches. However, as time goes, it will reach a smooth level. In terms of macroeconomics, we call it equilibrium. Equilibrium? How do we model equilibrium? Goods and service market Financial market Factor market Does this remind you Lego blocks? Zhengyu Cai - 2017 Spring Macroeconomics Chapter 3 6/42

Let s build the Lego blocks! Let s start from the production (supply side) Firms produce goods and services How does Starbucks produce a Frappuccino?( 星冰乐 ) We don t care how they make the drink! We only care what they use to make the product. What does Starbucks use to make a cup of coffee? Capital (K) Labor (L) Zhengyu Cai - 2017 Spring Macroeconomics Chapter 3 7/42

Factors of production Capital, labor, what else? Maybe human capital, entrepreneurship, For simplicity, we assume K and L is fixed. Reason? Simplicity We do not care K and L in a long run equilibrium To guarantee Y is at its natural level in long run (we will see this at Chapter 7) K = ഥK L = തL Zhengyu Cai - 2017 Spring Macroeconomics Chapter 3 8/42

Our very first model! The production function: tells us how much output is produced from given amounts of inputs. Inputs: K,L Output: Y The model: Somewhat full version: Y = F(K, L) Y = AF(K, L) Zhengyu Cai - 2017 Spring Macroeconomics Chapter 3 9/42

Constant returns to scale (CRS) For simplicity that make our life easier, we assume the production function is CRS. CRS? Mathematically, For δ if δy = F(δK, δl) We say F, is CRS Zhengyu Cai - 2017 Spring Macroeconomics Chapter 3 10/42

The supply of Goods and Services Y = F ഥK, തL = തY Done! Zhengyu Cai - 2017 Spring Macroeconomics Chapter 3 11/42

Who and how to share the bun? Output = Income, but how? Let s start from the factor market: supply and demand determine the factor prices. Capital: rent Labor: wage From our microeconomic point of view: in a perfect competition factor market, factor prices are given. Why? OK. But how is the equilibrium factor price determined? Zhengyu Cai - 2017 Spring Macroeconomics Chapter 3 12/42

Who and how to share the bun? The problem a typical firm facing: profit (π) maximizing How to solve this problem? Math! π = PY WL RK π = PF K, L WL RK max K,L π = PF K, L WL RK Zhengyu Cai - 2017 Spring Macroeconomics Chapter 3 13/42

Who and how to share the bun? Marginal Product of Labor (MPL): Δoutput when a firm employs 1 more unit of labor Math: first order derivative of a function. MPL =? Graph but wait how do you know the shape? Assumption: diminishing marginal product of labor given K, MPL with L Shape of production function: concave ( 凹 )? Zhengyu Cai - 2017 Spring Macroeconomics Chapter 3 14/42

Who and how to share the bun? Marginal Product of Capital (MPK):??? Math: MPK =? Diminishing marginal product of capital??? Graph Zhengyu Cai - 2017 Spring Macroeconomics Chapter 3 15/42

Who and how to share the bun? max K,L First order condition (FOC) of L: π = PF K, L WL RK MPL = W Real wage P WOW! But so what? How much is the real wage? How much labor a firm will employ? Let s back to the demand and supply analysis. Labor Demand: how to derive the labor demand function? Demand?: how much you will buy at a certain price level Labor demand?: how much labor a firm need at a certain (real) wage level Zhengyu Cai - 2017 Spring Macroeconomics Chapter 3 16/42

Who and how to share the bun? Consider this optimal employee condition: MPL = W P This equation tells us a firm will keep employing until its marginal product of labor reaches real wage. What does it mean? Y Y W/P MPL L1 L* L2 L MPL is our labor demand function! W/P W/P L L MPL L Zhengyu Cai - 2017 Spring Macroeconomics Chapter 3 17/42

Who and how to share the bun? Labor supply: in long run, we assume labor supply is fixed Y Labor supply W P തL MPL L Similarly, FOC of K: MPK = R P Zhengyu Cai - 2017 Spring Macroeconomics Chapter 3 18/42

Who and how to share the bun? π = PF K, L WL RK In a perfect competition market, economic profit π is 0. Why? 0 = PF K, L WL RK 0 = PF K, L P MPL L P MPK K F K, L = MPL L + MPK K Euler s theorem! Zhengyu Cai - 2017 Spring Macroeconomics Chapter 3 19/42

? Zhengyu Cai - 2017 Spring Macroeconomics Chapter 3 20/42 Who and how to share the bun? π = PF K, L WL RK In a perfect competition market, economic profit π is 0. Why? 0 = PF K, L WL RK 0 = PF K, L P MPL L P MPK K F K, L = MPL L + MPK K Output Income Euler s theorem!

Who and how to share the bun? π = PF K, L WL RK In a perfect competition market, economic profit π is 0. Why? 0 = PF K, L WL RK 0 = PF K, L P MPL L P MPK K F K, L = MPL L + MPK K This theorem is actually more general, which is true without perfect competition assumption. Proof Zhengyu Cai - 2017 Spring Macroeconomics Chapter 3 21/42

Implicit and explicit function Implicit: Explicit: Y = F(K, L) Y = F K, L = K + L Y = F K, L = KL What kind of production we want? CRS Diminishing marginal product of factor And Zhengyu Cai - 2017 Spring Macroeconomics Chapter 3 22/42

Implicit and explicit function What kind of production we want? CRS Diminishing marginal product of factor And the factor income share is relatively fixed. Zhengyu Cai - 2017 Spring Macroeconomics Chapter 3 23/42

Implicit and explicit function What kind of production we want? CRS Diminishing marginal product of factor And the factor income share is relatively fixed. Zhengyu Cai - 2017 Spring Macroeconomics Chapter 3 24/42

Cobb-Douglas Production Function Cobb-Douglas production function. Y = F K, L = AK α L 1 α A: technological production > 0 α: income share of capital (0,1) CRS. Proof. Diminishing marginal product of factor. Proof. α is a parameter indicating the contribution of a factor to income, and factor share is fixed over time. Proof. The marginal productivity of a factor is proportional to its average productivity. Proof. MPL = 1 α Y L MPK = α Y K Zhengyu Cai - 2017 Spring Macroeconomics Chapter 3 25/42

What determines the demand for goods and services? We have discussed the supply side of the goods market above. Now, we turn to the demand side. Output = Expenditure Where do we spend? Z = C + I + G We assume we do not trade here. Consumption spending Investment spending Government spending Zhengyu Cai - 2017 Spring Macroeconomics Chapter 3 26/42

Consumption Spending Reality: we earn income (Y), pay tax (T), then spend part of them, save the rest. Method: how do we model the consumption behavior? Consumption function: C = C(Y T) What properties this function should have? The more we earn, the more we spend. Marginal propensity to consume (MPC): Δconsumption when disposable income increase $1. MPC? Marginal propensity to save (MPS):? MPS? MPC + MPS =? Average propensity to consume C. We leave it here for now, will discuss it in a later chapter. Y Interest rate seems not to influence consumption. Zhengyu Cai - 2017 Spring Macroeconomics Chapter 3 27/42

Consumption Spending One way to model: a linear explicit form C = a Y T + b a is MPC. a (0,1) MPS? b is autonomous consumption. (?) b = a Zhengyu Cai - 2017 Spring Macroeconomics Chapter 3 28/42

Investment Spending Reality: our investment (I) depends on real interest rate (r). How? Method: investment function I = I(r) Nominal interest rate (i) r = i - π Zhengyu Cai - 2017 Spring Macroeconomics Chapter 3 29/42

ҧ Government Spending Government spending (G) is treated as an exogenous variable. G = G Where is the money from? Tax (T) is treated as an exogenous variable as well. T = തT Zhengyu Cai - 2017 Spring Macroeconomics Chapter 3 30/42

Demand for goods and services 1. Z = C + I + G 2. C = C(Y T) 3. I = I(r) 4. G = ഥG 5. T = ഥT From 1 5: Z = C Y തT + I r + ҧ G Zhengyu Cai - 2017 Spring Macroeconomics Chapter 3 31/42

ҧ The equilibrium of goods market Y = F ഥK, തL = തY supply side Z = C Y തT + I r + G demand side Y = Z equilibrium condition തY = C തY തT + I r + Exogenous variables? Endogenous variable? So how is the graph like? ҧ G Zhengyu Cai - 2017 Spring Macroeconomics Chapter 3 32/42

The equilibrium of goods market It seems a little bit hard to depict the equilibrium using the original equation. Let s look at the financial market, and revisit the national income account identity: Y = C + I + G Y C G = I (National) Saving S Y T C + T G = I Private Saving Public Saving Zhengyu Cai - 2017 Spring Macroeconomics Chapter 3 33/42

ҧ ҧ The equilibrium of goods market Now, we can draw a graph. Why equilibrium? Y C G = I തY C( തY തT) G = I(r) S = I(r) One equation, two unknowns!? Zhengyu Cai - 2017 Spring Macroeconomics Chapter 3 34/42

A summary: general equilibrium model Zhengyu Cai - 2017 Spring Macroeconomics Chapter 3 35/42

Implication How can we utilize the general equilibrium model? We have solved the model solve the endogenous variables. Now, we can play around with the model. We do not think about the exogenous variables yet. What are the exogenous variables in the general equilibrium model? How do the exogenous variables influence the model? In real life, we can only know what is happening (has happened). It is somewhat difficult to imagine what will happen if we make different choice. A model can help us to think about what happens in a parallel world. Exogenous variables are like the settings of a game, a fantasy fiction, a Si-Fi world, etc. We can change the exogenous variables to see how they affect the world, which could help people to make decisions. Zhengyu Cai - 2017 Spring Macroeconomics Chapter 3 36/42

Implication: for policy remarks Exogenous variables: G, T, K, L Although K and L is given in this model, they will be endogenous in very long run. They are just temporarily given as pseudo exogenous variables in this model. Also, K and L are not the choices made by the policy makers. Policy makers can only influence the economy by choosing the policyrelated variables (formulate and/or revise policies). Here in this model: G and T. Zhengyu Cai - 2017 Spring Macroeconomics Chapter 3 37/42

ҧ Implication: for policy remarks Fiscal policies policies related to the expenditure (G) and revenue (T) of government Government can choose G and T If government increase G, what will happen? (recall what should we do if we want to compare something) First approach: recall the national income identity തY = C തY തT + I r + G, then what? Decrease in investment: crowding out effect. The bun is produced, if the government spends more, it must crowd out investment with increased (real) interest rate. But this mechanism is not intuitive enough. G Zhengyu Cai - 2017 Spring Macroeconomics Chapter 3 38/42

Implication: for policy remarks Second perspective: investment saving analysis S തY തT C തY തT + (തT ҧ G) If G, S? Let s use the graph to help us. According to the graph, we find: G public saving S I r What does this model tell us? If government wants higher (real) interest rate, one way is to spend more. Zhengyu Cai - 2017 Spring Macroeconomics Chapter 3 39/42

Implication: for policy remarks If government decrease T, what will happen? First perspective: Second perspective: What we get? Same result But different mechanism Different effectiveness: which is more effective? Zhengyu Cai - 2017 Spring Macroeconomics Chapter 3 40/42

Implication: other exogenous variables Exogenous variables: G, T, K, L something else??? Change in investment demand. Technological improvement Policy influence Graph Implication: increased investment demand will raise the real interest rate. Zhengyu Cai - 2017 Spring Macroeconomics Chapter 3 41/42

Summary Long run Goods and services market Supply side how much to produce; Factor market who get the product, how much they get Demand side how are people willing to spend Equilibrium financial market, investment and saving relation Implications Zhengyu Cai - 2017 Spring Macroeconomics Chapter 3 42/42