1- For each growth rate below, use the rule of 70 to calculate (i) how long it w

Question

1- For each growth rate below, use the rule of 70 to calculate (i) how long it will take incomes to double, and (ii) if each country starts with an income of $1,000 per capita, what the income will be in 30 years.     

a. 4 percent.  

b. 7 percent.  

c. 2.5 percent.    

d. 10 percent.  

e.   3 percent.

2- For each part below, determine whether the following actions will increase or decrease productivity, and name the component of productivity that each affects.  

a. The local government builds a new school.    

b. Teachers in the new school hold classes for young students.    

c. A manufacturer installs robots on its assembly line.    

d. A research team designs a more efficient sys-tem of irrigation.

e. A soda company discovers a new source of underground water that can be used to make its products.    

f.    A professor writes a new and improved economics textbook.    

g. A large number of people have less access to health care.    

h. A worker receives on-the-job training to be a mechanic.

Explanation / Answer

i> The rule of 70 estimates how long it will take for incomes to double :

a) at 4%= (70/4) it will take 17.5 years for incomes to double

b) at 7%= (70/7) it will take 10 years for incomes to double

c)at 2.5%= (70/2.5) it will take 28 years for incomes to double

d)at 10%= (70/10) it will take 7 years for incomes to double

e)at 3%= (70/4) it will take 23.333 years for incomes to double

ii> If the country starts with a $1000

We can use the formula to compute income after 30 years:

Future Income = Present Income * (1+r)^t

a) FI = 1000* (1.04)^30 =

$ 3243.4

b)  FI = 1000(1.07)^30=

$ 7612.255

c) FI =

1000(1.025)^30

$ 2097.57

d) FI = 1000(1.1)^30=

e) 1000(1.03)^30=

$

2-

a)A local government building a school will reduce capital productivity.

b. Teachers in the new school hold classes for young students will increase productivity of labor.    

c. A manufacturer installs robots on its assembly line will reduce productivity of labor.    

d. A research team designs a more efficient sys-tem of irrigation will increase productivity of capital.

e. A soda company discovers a new source of underground water that can be used to make its products will increase productivity of materials.    

f.    A professor writes a new and improved economics textbook will increase productivity.    

g. A large number of people have less access to health care will reduce productivity.    

h. A worker receives on-the-job training to be a mechanic will increase productivity of labor.

$ 3243.4

b)  FI = 1000(1.07)^30=

$ 7612.255

c) FI =

1000(1.025)^30

$ 2097.57

d) FI = 1000(1.1)^30=

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