Economics

Department of Economics

ECON200 – 06B

Macroeconomics and the Global Economy

Assignment 1

Due: August, Wednesday the 16th, 2006 at 11:59.

Please:

1. Answer the questions in the spaces provided on these sheets.

2. Read the section on Internal Assessment and Honesty in the Course Handbook

3. Add your completed Management Student Centre (MSC) cover sheet to the front of this assignment. Check that you have your correct tutorial number on the cover sheet.

4. Submit your assignments to the MSC.

5. Keep a copy of your assignment in case the original goes astray.

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Questions: [25 marks]

Question 1: Do some research on value theory in economics and define the labour theory of value. Explain the interest of this theory and its failures. Which theory does a better job? [4 marks]

There are two kind of value theory of economics. One is labour theory of value. It defines as the value of one good is the amount of human labour expended in producing it. Most classical economists like Smith, Ricardo and Marx subscribed to it. The other one is price theory of value, it defines as the value of one good is measured by its price which reflects demand and supply (Marshall, Allais, Debreu, most modern economists)

The interest of the labour threory value is it can be used to measure how productivity of the labour to do the job. Also, it can measure how well or bad the workers are doing this job. It could increase the workers’ competitive. The company will not only focus on the cheaper resource and the materials, but pay more attention to train the employees.

The failure of labour theory of value is there are many critics of it. The labour theory of value is no longer satisfying the specific requirement of the consumers. There are different requirement for the consumers, the labour theory of value cannot resolve everyone’s requirement. So, it is not useful for some of the customers.

Actually, every value theory has it own strengths. However, in the economics, the price theory of value would be better, because the market prices are used to measure the value of very different things. The company set up the price is usually thinking about the cost of the material, resources, workers, and the competition of the market. Therefore, the price theory of value is doing the better job.

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Question 2: Explain the trade-off behind every investment decision. [2 marks] Explain the similarities and differences between Robinson Crusoe and a country’s economy with regards to this trade-off. [2 marks] Using the Golden rule, explain why trying to reach the highest possible stock of capital may not be a good idea. [2 marks]

Trade-off behind every investment decision means that you need to do a alternative choise. That is a constant of money, if you decise to use it to do consumption. It means you cannot do the investment by the same money. However, if you choose to do the investment, then you cannot do the consumption.

In the case of the Robinson Crusoe, the similarities are: The investment and the consumption cannot happen in the same time. He either catches the fish in one day to ensure his survival or productivity after the investment. It will increase the level of consumption.

The differences: In economic, the resource can be managed to investment and consumption. For example, the amount of money can be divided to two parties. One part can be used to investment and other part can be used to consumption. However, in the case of Robinson, it cannot do that, because he spend the whole day only can make sure it is survival. In addition, in economics, to do the investment can maxim the consumption. In the case of Robison, in the island that is no other person to do the consumption but himself. Therefore, to do the production to increase the productivity to catch more fish may be not that necessary for him.

It is not necessary to try to reach the highest possible stock of capital, because in the situation of better technology, A2>A1. It will help the Y to reach the higher output than just increase the number of stock of capital.

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Question 3: The market for loanable funds

a) Explain why the savings curve is an increasing function of the interest rate. [1 mark]

As the interest rate increase, more people will save their money to gain more money by the better interest rate. Therefore, the saving curve is an increasing function of the interest rate.

b) Explain why the investment curve is a decreasing function of the interest rate. [1 mark]

To invest, you must first borrow the funs. And the higher interest rate means the higher cost of borrowing. Therefore, the investment will decrease as the higher cost of investment.

c) Assume the only available saving products are bonds. Explain why the savings curve can be considered as the supply of loanable funds and also the demand for bonds? [2 marks] Explain why the investment curve can be considered as the demand for loanable funds and the supply of bonds? [2 marks]

Households save the money on hand or on banks, that means the households got those money available to lend (Supply of loanable). And the amount of saving could use for the demand for bonds too. To invest you money to borrow the fund, in this reason, investment curve can be considered as the demand for loanable funds an the companies may selling bonds to collec money for the investment. So, the investment curve can be considered as the demand for loanable funds and the supply of bonds.

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d) Represent a market for loanable funds in equilibrium. Represent and comment on the consequences for the economy of the government running a budget surplus. [3 marks]

The government is running surplus. Any change in the level of the government budget affect total saving in the economy. So, only total saving affected. Budget surplus: T-G>0, the amount of total saving is increased by T-G. total saving for any given interest rate has increased. Total saving curve shifts to the right. The equilibrium quantity of loanable funds is higher.

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Question 4: Explain in detail what the four components of the GDP are and their importance for the economy. [2 marks]

Y = C+ I + G + NX

Consumption C is spending by households on goods and services. It is influenced by the revenue Y (the more you earn the more you spend on consumption goods). C is usually stable. C is an increasing function of Y.

Investment I is the purchase of goods that will be used in the future to produce more goods and services. I is driven by business confidence. Therefore, it is volatile erratic. It strongly influences the level of current output and employment.

Government Spending G includes spending in goods and services by local, state, and federal government. G is driven by politics rather than by economics. G is usually stable.

Net exports: NX= X-M. We consider them as given as a first approach. In reality many variable like the exchange rate impact NX. NX is depends on the world economic situation and the firms’ competitiveness within the country.

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Question 5: Making an analogy with physics (or any other relevant science) and using examples, explain to what extent models are necessary for the study of macroeconomics. [4 marks]

Medico is the question of nature. It questions “ What is the human’s apparatus do in the body?” The doctors study human’s body. It is only analysis the single apparatus in the human body but also analysis the whole body. For example, the doctors study how is the cerebra woke in the body, and hwo the nerve effect the cerebra. It analyse the individual apprartus and the whole body, because it not onlu woke bu itself but affect each other.

The Macroeconomic is similar as the Medico study. It need to deal with the individual decision and aggregate the results. And the relationships between them.

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Problem: The Solow model [25 marks]

1. Noting F the production function, A the level of technology, L the number of workers, K, H and N the stocks of physical capital, human capital and natural resources respectively, give the equation that relates all these elemenrs to total GDP noted Y. [1 mark]

Y = A.F (L, K, H, N)

2. How do you explain that A is usually not an argument of the production function? [1 mark] A represents the level of technology. Output per worker can increase by the better technologies, even for a constant stock of capital per worker. Better technologies delay the effect of diminishing returns on capital by driving up the production function.

Technological knowledge increases with time and can not be destroyed. Therefore, A is usually not an argument of the production function.

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3. Give all the hypotheses that are needed to move from the relationship in question 1 to the following, y=f(k), where k stands for physical capital per worker and y for GDP per worker. [2 marks]

Y = A. F (L, K, H,N)

First, we restrict out attention to the role played by labour, L, and capital, K, only. And neglect for a while the other factors. Then we have Y = F (L, K)

Second, we suppose that this production function F has “constant returns to scale”, which means that if both labour and capital are multiplied by a number B, the production is in crease by Bas well.

Analytically, F (B.L, B.K) = B. F (L, K). We will then write

Y = F (L, K) = F (L.1, L. K/L) = L. F (1, K.L) = L. f(K/L) Where f (K/L) = F (1, K/L) then Y/L = f(K/L)

If we note y=Y/L and k=K/L. We have then y=f(k)

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4. Assuming diminishing marginal returns, draw in a k-f(k) diagram the y=f(k) relationship. [1 mark]

That is as k increases, the marginal production of an additional unit of k will be less than the marginal product of the pervious unit.

5. Noting s the savings rate, n the growth rate of workers and d the depreciation rate of capital, explain in details why investment per worker can be summarized by s.f(k) in the Solow model? [1 mark]

 The revenue can be consumed or saved:

Y = C+ S

 The revenue can be spent on consumption or investment goods: Y = C+I. Then

S = I

Thus, in this situation, saving is used to finance investment. In this reason, investment per worker can be summarized by s.f(x).

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6. Explain similarly why (n+d).k corresponds to the required capital per worker. [1 mark]

n: the growth rate of labour, that is the arrival rate of new workers. d: the depreciation rate of existing capital k The capital devoted to  New workers: n.k

 Replace depreciation capital: d.k So, the required capital per worker is: (n+d).k

7. Represent the long-run equilibrium k* of the economy [1 mark] and explain in details why an economy starting with k1At k1, the level of consumption and investment atill get plenty of room to increase. The consumption is not satisfied by the investment. Therefore, households will contine to invest to the market to gain profit from the investment. So, in k1, it will converged towards k*. Until k*, the consumption is maxima. In this level, the investment is maixma by the investment.

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Economic growth is mainly a question of labour productivity. Accumulating capital, whether physical or human (even though both are complementary) enables to increase this productivity. Assume the government decides to boost investment by decreasing taxes on interests paid on savings.

8. Using the market for loanable funds, show and comment on the new equilibrium that follows from this policy. [2 marks]

The government decrease the taxes on interest paid on saving, means people will get more return from saving. So, the supply curve is affected. Saving would be less taxed, household would increase their savings, at any given interest rate. S shifts to the right.

 The equilibrium interest rate is lower  The equilibrium of loadable fund is higher

A lower tax rate on financial earnings would lead to a lower interest rate and greater investment and saving.

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9. We assume that this policy translates into a rise of the savings rate from s to s1>s in the Solow model. Explain in detail, with the help of a diagram, the process by which the economy moves to the new equilibrium that will result from this rise. [2 marks]

As the saving rate increases from S to S1, there will be more money to invest to the new machines and new stock to the business. Therefore, it will increase the stock of capital/worker. The (n+d).k increases as well. Thus, the s.f(x) and (n+d).k have the new equilibrium at B, and the capital per worker at k1*.

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The Solow residual

We assume that GDP has increased by $10,000 in 2005 in this representative economy. We assume that the marginal productivity of labour is equal to $10 per unit of labour, and that the marginal productivity of capital is equal to $20 per unit of capital. We assume that labour has increased by 100 units and capital by 200 units in 2005.

10. Explain what the Solow residual corresponds to and give its value for the economy described in the above paragraph. [2 marks]

GDP: $10,000

Labour: $10*100=$1,000 Capital: $20* 200=$4,000 $5,000

A occupied 50% of GDP, therefore, A equal $5,000 Value for the economy is $5,000

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Technology and the Solow residual

According to your answer from question 10, our starting model does a correct job at the most. It is suggested that technology should be taken into account. From now on, you will be working with the following model: Y=A.F(K,L).

11. Represent on the diagram from question 4 the new production function given by y=A.f(k) in case A>1. [1 mark]

12. Using the formula Δ(C.D)= ΔC.D+C.ΔD where ΔC and ΔD represent finite increments of C and D, show how you get 1 YAF 

YAF

from Y=A.F(K,L), and therefore how you get: AYmpk.K mpl.LA AYY

where mpk=F’K and mpl=F’L stand for the marginal productivity of capital and labour respectively. [2 marks]

Y=A.F(L,K)

△Y=△A.F(L,K)+A.△F(L,K) △ Y=△A.F(L,K) + A.△F(L,K)

△Y/Y=△A.F(L,K)/Y + A.△F(L,K)/Y △Y/Y=△A/A +△F/F

Y=A.F(K,L)

△ Y/Y=△A/A + A.△F(L,K)/Y

△ Y/Y=△A/A + A(F’△L.K +F’△K.L)/Y As mpk=F’k and mpl= F’l Then:

△ Y/Y=△A/A + A.(mpl△L + mpk△K)/Y △ A/A=△Y/Y – A.(mpl△L + mpk△K)/Y

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13. Assume that in year 2004 A was equal to 1 (A2004=1) and Y to $200,000 (Y2004=$200,000). Using the above formula and your answer from question 10, determine the value of A in 2005? [2 marks] Then verify that

YAA.F 5%YAY [1 mark]

Y in 2004=200,000

Y in 2005=200,000 + 10,000=210,000

The increase rate of 2005: (210,000-2000,000)/200,000=0.05

A occupied 50%, then the value of A in 2005 equal to 1+0.05/2= 1.025.

△Y= 10,000 Y=200,000 A=1 △A=O.O25 △F=5,000 Then:

△Y/Y= 10,000/200,000=5% △A/A + A△F/Y= 0.025/1 + 1*5000/200,000=5%

So, △Y/Y=△A/A +A.△F/Y=5%

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14. Look on the internet and find recent figures for the Solow residual in New Zealand. [1.5 marks] What do you conclude from these figures? [1.5 marks] Note: if your figures come from a different version of the Solow model than that used here, it is fine.

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Richard Dutu

Economics Departmen

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Note: In calculus, the Leibniz notation, named in honour of the 17th century German philosopher and mathematician Gottfried Wilhelm Leibniz was originally the use of dx and dy and so forth to represent \"infinitely small\" increments of quantities x and y, just as Δx and Δy represent finite increments of x and y respectively. For instance if x increased from x1 in 2004 to x2 in 2005, then Δx=x2-x1. Source: Wikipedia.

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