Class 2: The determinants of National Income. Long Run

Transcription

1 Class 2: The determinants of National Income. Long Run 1. Aggregate economic profit ( π ) is defined as follows: π = Y [ ( W / P)* L] [( R/ P)* K] Show that if the production function of this economy displays constant returns to scale, then the economic profit must be zero. 2. From the basic equation that shows the uses of output Y = C+ I + G derive the definitions of Total (national) Saving (S), Private Saving (PrS) and Public Saving (PuS). Show also that in this economy Total Saving must always be equal to Investment (S=I). 3. Use the neoclassical theory of distribution to predict the impact on the real wage and the real rental price of capital of each of the following events: a) A wave of immigration increases the labour force. b) An earthquake destroys some of the capital stock, c) A technological advance improves the production function. 1

2 4. The government raises taxes by 100 billion. If the marginal propensity to consume is 0.6, what happens to the following? Do they rise or fall? By what amounts? a) Public saving. b) Private saving c) Total saving d) Investment 5. Suppose that an increase in consumer confidence raises consumer s expectations of future income and thus the amount they want to consume today. This may be interpreted as an upward shift in the consumption function. How does this shift affect investment and the interest rate? 6. Consider an economy described by the following equations: Y=C+I+G Y=5,000 G=1,000 T=1,000 C= (Y-T) I=1,000-50r a) Compute private saving, public saving and total saving. b) Find the equilibrium interest rate. 2

3 c) Suppose that G rises to 1,250. Answer again to question a). d) Find the new equilibrium interest rate. 7. Suppose the government increases taxes and government purchases by equal amounts. What happens to the interest rate and investment in response to this balanced budget change? Does your answer depend on the marginal propensity to consume? 8. Suppose the production function is Cobb-Douglas with α = 0.3. a) What fractions of income do capital and labour receive? b) Suppose that immigration raises the labour force by 10%. What happens to total output? The real rental price of capital? The real wage? Give all your answers in percentages. c) Suppose that a gift of capital from abroad raises the capital stock by 10%. Answer the same questions as in b). d) Suppose that a technological advance raises the value of the parameter A by 10%. Answer the same questions as in b). 3

4 Answers to Class If the production function has constant returns to scale, then by Euler s Theorem F(L,K)=Y=(MPL*L)+(MPK*K). On the other hand, in equilibrium of the capital and labour markets, the real prices of inputs must be equal to their marginal products. That is, MPL=(W/P) and MPK=(R/P) Substituting these two equalities in the definition of economic profit we have, ( * ) ( * ) π = Y MPL L + MPK K. Then, using Euler s Theorem we find, π = Y Y = 0 2. Y=C+I+G Y-C-G=I Y-C-G is the income in the economy that remains after paying for consumption and government purchases. We call this Total Saving (S) (also called National Saving). Thus,

5 5 S=I In a closed economy, total saving must always equal investment. From the definition of total saving we have, S=Y-C-G Adding and subtracting taxes (T) to this equation, we have Therefore, S=(Y-T-C)+(T-G) S=Private Saving+ Public Saving PrS=Y-T-C PuS=T-G 3. Suppose in general that the MP of both factors depends on K and L, and that they are cooperant factors. That is, that the increase in one factor increases the MP of the other. Then, the answers are: a) ( W P), and ( R P) b) ( W P), and ( R P) W P, and R P c) ( ) ( )

6 6 4. a) PuS = T G PuS = T G = = 100 b) Pr S = Y T C Pr S = Y T C = C C = α + β( Y T) = α + 0.6( Y T) C = 0.6( Y T) = 0.6(0 100) = 60 Therefore, Pr S = ( 60) = 40 c) S = PuS + Pr S S = PuS + Pr S = = 60 d) I = S I = S I = 60

7 5. S = I Y C G = I Y C G = I 7 Since Income and Government expenditures do not change, we have that I = C We therefore conclude that savings will change by C ; also, given the improvement in expectations, C > 0. Therefore savings will fall and thus investment will fall too. On the other hand, since nothing happens to the investment function, this fall in savings will elicit an increase in the rate of interest. I < r > a) PrS=Y-T-C C= (5,000-1,000)=3,250 PrS=5,000-1,000-3,250=750

8 PuS=T-G =1,000-1,000=0 8 S= PrS + PuS = = 750 b) S=I(r) 750=1,000-50r 50r=1, =250 r=250/50=5 c) PrS=5,000-1,000-3,250=750 (as in a) PuS=T-G=1,000-1,250= -250 S=PrS+PuS= = 500 Private saving is not affected by the increase in government expenditure ; public saving on the other hand, decreases : from an equilibrated public balance the economy goes into a public deficit. Total saving goes down from 750 to 500. e) S=I 500=1,000-50r r=10

9 9 7. Since S = I ( Y T C) + ( T G) = I ( Y T C) + ( T G) = I Y = 0 and T = G, we have that T C = I Suppose the consumption takes the form Then, if we take change, C = α + β ( Y T) α and β as parameters that do not C = β ( Y T) = β T So, T ( β T) = I I = T(1 β ) = ( )( + )( + ) < 0 Therefore investment falls because total savings falls by T(1 β ). For a given investment function, the fall in savings generates a rise in the interest rate. Clearly the marginal propensity to consume ( β ) plays a role since it determines the extent by which

10 10 consumption falls. The fall in consumption rises savings; but, given that β is less than 1, this rise in savings is not sufficient to compensate the fall in savings due to the increase in taxes. Thus, in net terms savings fall and so does investment. 8. Y = ( 1 ) α AK L α Check this useful arithmetical property, Y = A + α K + ( 1 α) L Y A K L Or, to make it more handy, ( α ) % Y = % A+ α% K + 1 % L a) Share of K=α =0.3 Share of L=(1 α) =0.7 b) Using the above equation in percentage rates of change, we have % Y = (1 0.3)10= 7

11 R αy = MPK = P K R % = % α + % Y % K = = 7 P 11 ( 1 α ) W Y = MPL = P L W % = % ( 1 α ) + % Y % L= = 3 P c) Following the same procedure you should be able to derive that the answers to this question are: % Y = 3 % ( R/ P) = 7 % ( W / P) = 3 d) % Y = 10 % ( R/ P) = 10 % ( W / P) = 10