Answer to Question #196159 in Microeconomics for Dhage Lee

Question

The productive capability of an economy is such that to produce 5 units of military 

good it takes 2 workers to be employed while 10 units of consumer goods require 3 

workers. Resources are limited in such a way that only 75 units of military good can 

be produced when all resources are employed.

a) How much workers are in the economy?

b) What is the maximum amount of consumer goods that can be produced?

c) Construct the production possibility schedule and curve for this economy.

d) Graphically represent what would happen if 12 additional workers were added 

to the economy.

e) Graphically represent what would happen if the productivity of the workers 

were reduced to 2 units of military good and 5 units of consumer goods.

f) Graphically represent what would happen if productivity for military goods 

remained the same but it now required 2 workers to produce 10 units of 

consumer goods?

Answer 1

(a)Number of military goods produced per worker could produce

$=\frac{Number\space of\space military\space goods\space produced}{Number\space of\space workers\space taken \space to \space produce\space it }$

$=\frac{5\space units\space of \space military\space \space goods}{2\space workers}$

=2.5 units of military goods per worker

Number of workers used for production

$=\frac{Number\space of\space military \space goods\space produced}{Number\space of\space military\space goods \space produced\space per\space worker}$

$=\frac{75\space units\space of \space goods}{2.5\space military\space goods\space per\space worker}$

= 30 workers

Number of consumer goods produced per worker could produce

$=\frac{Number\space of\space consumer\space goods\space produced}{Number\space of\space workers\space taken\space to \space produce \space it}$

$=\frac{10\space units\space of\space consumer\space goods}{3\space workers}$

= 3.33 units of consumer goods per worker.

(b)

Number of consumer goods produced

$=Number\space of\space workers\space used\space for \space production \times Number\space of\space consumer\space goods\space produced\space per\space worker$

$=30\space workers\times 3.33\space consumer\space goods\space per\space worker$

$=99.99\space units\space of\space consumer\space goods\space produced.$

$\approx100\space units\space of\space consumer\space goods\space produced$

 (c)There are total of 30 workers in the economy which results in producing 75 units of military good or 100 units of the consumer goods.

(d)

 The increase in the 12 workers of the labor force would result in total of 42 workers which would increase the production of both the military goods and consumer goods. Thus, the ppf would shift from AB to AB'.

(e)The fall in the productivity would result in the quantity of military goods to fall to 2 per worker and consumer goods change to 5 units per worker which would result in the unequal shift in the production possibility frontier. Thus, the ppf changes from AB to AB" producing 60 units of military goods and 150 units of consumer goods.

(f)

with the change in productivity;

2 workers = 10 units of consumer goods

1 worker = 5 units

30 workers = 150 units

Hence, the production possibility frontier will shift outward on the y-axis, where we have consumer goods.