On page 227 we saw an example of a Leontief input-output problem in economics, based on 1947 data from the USA. The answer we got in that example wasn’t all that interesting, but it becomes more interesting when we consider how the economy responds to changes in demand.

a. Suppose that the demand for agricultural goods increases by 10%? Show that the production of agricultural goods has to increase by less than 10%, but that there also has to be an increase in the other segments of the economy.

b. What about if the demand for services increases by 10%?
How much does production in the three segments have to change?

c. If the demand for all three segments increases by 10% then how do the production levels have to change? Can you find the answer without using a computer?
First find the answer using a computer, and then see if you can show analytically (i.e., using pen and paper) why this is the answer.

d. As we saw from page 227 this question is based around solutions of the equation 





A M S 





= C 





A M S 





+






40 60 42 





, The input-output matrix is also called where C is the input-output matrix and is given by the consumption matrix.
C = 




0.41 0.03 0.03 0.07 0.38 0.10.4 0.16 0.19













.

How would you change the input-output matrix so that a 10% increase in demand for agricultural goods requires exactly a 10% increase in agricultural production? Once You can’t easily work this out in your head, but approach this by trial and error. Try a few things, see what works and what doesn’t.

you’ve found the answer think of why it works (i.e., give a scientific justification for your answer).