midterm solution Recent site activity Vu, Tuan Khai's personal website

1 ICU winter 2011, Principles of Macroeconomics February 4, 2012

Answers to Midterm Examination

Problem 1 (4pts^×5) (References: topic 2 and chapter 2)

(a) Since the PC is capital (i.e. it is used for the production of education service) of ICU, the purchase of it by ICU is investment (business fixed investment).

(b) In this case, the PC is used for consumption (as a durable good) so the purchase of it by the Japanese student in ICU is consumption.

(c) In this case the purchase of the PC is consumption. This is because the Canadian student in ICU is staying in Japan with a student visa. If instead, he/she has a tourist visa, the purchase is export.

(d) Since Mitaka Municipal Office is a local government, its purchase of the PC is government spending.

(e) The branch of Gucci in Japan must register as a firm operating in Japan, so its purchase of the PC is investment (business fixed investment).

Problem 2 (10pts^×2) (References: topic 4 and chapter 6)

We learned that the steady state unemployment rate is /U L_s s/( _ f) 1/(1_{ } f s/ ). 1. Suppose that the unemployment rate does not begin at its steady state level, but at a level at which the unemployment rate is above the natural rate (fU>sE) (the converse case is similar). We show that the unemployment rate falls over time. Refer to slide #7 of the lecture note and note that fU is the outflow of, and sE is the inflow of the unemployment pool. Because fU > sE, in the unemployment pool (U): outflow > inflow _ U^↓ _{ (}U/L)^↓ (because L is constant), thus the unemployment rate falls over time and converges to the steady state level at which fU = sE.

2. Suppose that the government implements a law that makes it more difficult for firms to fire workers.

(a) If the law reduces the rate of job separations without affecting the rate of job finding

 ^{s↓& f} unchanged _ f/s↑ _{ (1 +} f/s)^↑_{ 1/(1 +} f/s) = (U/L)^↓, i.e. the natural rate of unemployment falls. In this case, the government achieves its goal by using the law: unemployment is reduced.

(b) Is is plausible that the law would not affect the rate of job finding?

My answer : No. The reason is that facing the new law, firms probably will change their behavior. Because it is now difficult for them to fire workers once they have hired them, firms will be more cautious and less active in hiring workers, making the number of jobs

2

available decrease, and thus reducing the rate of job finding f.

Note: If this is the case, because both f and s fall, it is unclear what direction the ratio f/s and thus the natural rate of unemployment (U/L) will change in reponse to the law. Some empirical studies have reported the result that U/L increases rather than decreases because f fallsfaster than s so f/s↓. This means that, by implementing the policy, the government not only fails in reducing unemployment but even worsens it. This is a good example of unintended outcomes of a policy. It suggests that the behavior of people (firms and consumers) is crucial in determining the succsess of a policy, and the government must consider that when planning and implementing any policy. Note: I also accept any different answer if the logic is right.

Problem 3 (20pts) (References: topic 5 and chapter 4)

We learned that money has three functions: unit of account, store of value and medium of exchange. Very high inflation (or hyperinflation) will destroy these functions and as a result people stop using the national currency for which hyperinflation is occuring and use other forms of money such as USD and gold. Below are some more details.

 Hyperinflation means that prices of goods, the values of goods measured in the units of the national currency, are changing very quickly. This in turn means that the national currency is not appropriate to measure the values of goods, or in other words, it loses its unit-of-account function. In such a situation, people will look for other forms of money that can perform this function.

 Hyperinflation also means that the national currency is losing its value very quickly. No one wants to keep their income or wealth in the form of such an asset that is losing its own value. People are rational (they indeed are!), and they will look for other assets such as USD and gold or real estate to use as a store of value.

 Given the explanation above, when hyperinflation occurs, no one wants to hold the national currency, people refuse to accept it in their transactions. This means that the national currency loses its function as a medium of exchange as well, and people will look for other forms of money that can perform this function.

Problem 4 (5pts^×8) (References: topic 3 and chapter 3)

1. The economic meaning of each of the equations (4)~(6): (4) is the production function which shows how output are related to the two inputs labor and capital. (5) and (6) show that the amounts of labor and capital available in the economy are fixed at certain levels; this reflects the fact that we are considering the long run in this model. 2. The investment equation (3) noted above includes the interest rate with a negative

3

sign because the interest rate affect the cost of investment: the higher is the interest rate, the more costly is investment and the lesser investment that firms and consumers want to do. Note that the concept “cost” here includes the opportunity cost of investment.

3. Equilibrium levels of the interest rate, investment and consumption: (4) _ Y

_{ }

K

_{ }

L=4*100+5*80 = 800 (i)

(i) & (2) _ C_{ }C₀ a Y(  = 60+0.6*(800-300) = 360 T) ⁽ⁱⁱ⁾ (i), (ii) & (2) _ I

_{  }

Y C G=800-360-300 = 140 (iii)

(iii) & (3) _{ r =}(I_0I) /b= [200 - 140]/600 = 60/600 = 0.1 or 10%.

4. When the government raises taxes (T) by 10%, the new level of taxes is Tnew=(1+0.1)*

T

= 1.1*300 = 330. For convenience, we shall anwer (c) first.

(c) No. This is because GDP (or Y) depends solely on the amounts of labor and capital available in the economy, which are fixed in the long run as shown in (4), and are not affected by the policy. Thus Y =800. (iv)

(a) Effects of the policy on the interest rate, consumption and investment: (iv) & (2) _ C_new=C_0a Y( _T_new) = 60+0.6*(800-330) = 342 (v) (iv), (v) & (2) _ I

_{  }

Y C G=800-342-300 = 158 (vi) (vi) & (3) _ r_new(I_0I) /b= [200 - 158]/600 = 60/600 = 0.07 or 7%.

Thus, the policy reduces the interest rate by 3% (=r_new ), reduces consumpion by 18 r (=C_new ), and increases investment by 18 (=C ^Inew ). ^I

(b) An intuitive explanation for these results in (a) on the interest rate and investment: T^↑ _{ (Y – T)}^↓_{ C}^↓ national saving (S) =(Y – C – G)^↑ r^{↓& I↑.}

A graph to explain the results qualitatively

5. The consumption equation is revised to include the interest rate:

C _{ } C

₀

a Y ( _{ } T ) dr

(2')

S, I E'

E

investment saving

r' r

r

4

(a) Equation (2') includes the interest rate with a negative sign because the interest rate is the opportunity cost of consumption: if the consumer has one unit of income and he/she deposits that income in a bank then he/she yeilds an interest income of r, if he/she does not do so but instead consumes that income then he/she loses the interest income of r. We can also explain using saving (S): r^↑ _{ saving}^↑ _ C^↓ (given Y &T and note that C+ saving = Y -T)

(b) We can do the same as above to answer, but it is more convenient to first calculate algebraically (i.e. with letters) the change of each variable due to the policy of changing taxes (T) as follows.

(2’) & (3) 

^I

0

   ^{br Y [ C}

0

 ^{a Y (}   ^{T ) dr ]}  ^G

_

( b d r _ ) _{   } I

₀

C

₀

G aT _{ } (1 a Y )

or

r _ [ I

₀

_{  } C

₀

G aT _{ } (1 a Y ) ]/( b d _ )

(vii)

Noting that Y is not affected by the policy and G is unchanged, the change in the interest rate (

_

r) due to the the policy of can be calculated from (vii):

0 0

[ (1 ) ]/( ) /( )

r G a T a Y b d a T b d

 

            

^(vii’)

From (2’)&(vii’), the change in consumption (

_

C) due to the the policy is

0

( ) [ /( )]

C a Y T d r a T d r a T d a T b d

                 





[1 /( )] /( )

a T d b d ab T b d

        

^(2’’)

From (3)&(vii’), the change in investment (

_

I) due to the the policy is

/( )

I b r ab T b d

      

⁼



^{C (3’)}

Substitute the values of a,b,d and

_{ }

T

0.1*

T =30 into (vii’), (2’’) and (3’) to have

0.6 30 /(600 300) 0.02

   

r

  

^{or -2%}

0.6 600 30 /(600 300) 12

   

C

   

I C

  

⁼¹²

Thus, in this case, the policy reduces the interest rate by 2%, reduces consumption by 12, and increases investment by 12.