Question

8. Show your workings clearly!

Suppose Px = 60 w + 40 r and Py = 75w + 25r (where the numbers indicate how much per unit labor and per unit capital are needed in producing each good). If Px = Py = 120, solve the simultaneous equations to get w (wages) and r (rental) values! Next if Px = 120 and Py = 200, assuming everything else unchanged, solve the simultaneous equations to get w and r values! By what percentage have wages changed? By what percentage have rental rates changed? Is product Y labor or capital intensive? Why or why not?

Answer 1

Px = 60w + 40r

Py = 75w + 25r

1) Px = Py = 120

Px = 60w+40r

120 = 60w + 40r

Divide by 20 on both sides

6 = 3w + 2r ------------eq1

Py = 75w + 25r

120 = 75w + 25r

Divide by 5 on both sides

24 = 15w + 5r -------eq2

5*eq1 - eq2 gives

6 = 5r

r = 1.2

From eq2

w = (24-5*1.2)/15

w = 1.2

So w = r = 1.2

2) Px = 120 = 60w + 40r

Divide by 20 on both sides

6 = 3w + 2r ------- eq1

Py = 200 = 75w + 25r

Divide by 25 on both sides

8 = 3w + r -------- eq2

Eq1 - Eq2

r = -2

Using r value in eq2

w = (8-(-2))/3 = 10/3 = 3.33

% Change in wage = ((3.33/1.2)-1)*100 = 177.78%

%change in rent = ((-2/1.2)-1)*100 = -266.67%

There is fall in rent value by 266.67%

Product Y is labour extensive as it is heavily dependent on labour that is the reason the wages of the product went up where price of good Increase.