y = x11/2 x22/3
Now Increasing extraction with fixed quarrying, x2 would give diminishing marginal returns.
Because d2y/dx12 = (-1/4)x1-3/2 x22/3 < which is less than 0
Realistically the marginal return gets diminished because the as one extracts up a given mine the ore amout left in it is lesser and lesser and hence the effort as well as cost of mining any additional ore increses hence the utility or marginal return generated keeps on depleting .
d2y/dx22 = -(2/9) x11/2 x2-4/3 which is always < 0 given any fixd value of x1
Thus the realistic explanation that any increased exploration exhausts more and more options of where can one find the presence of ore. So even though exploration is successful or not in finding new places for quarrying, any increased level of exploration than earlier shall reveal more and more about where the ore can be found and not and hence , it becomes rarer to carry out successful explorations.
= 2* 4 = 8
The second set of values yield :- y ‘’ = 81/2 * 162/3
= 2*4*21/2*22/3 =8*27/6 = 16 *21/6 > 16 Hence output increases more than double since production function has is increasing return to scale typr.
At input levels x1 =4; x2 = 8, output : y= 8
Therefore Revenue = 3* 8 = 24
Cost = w*x1 + r*x2 = 2*4+ 1*8 = 16
Hence Profit = revenue – cost = 24 – 16 = 8
Exercise 4. Cobb-Douglas and Increasing Returns to Scale (Mining) Exercise 4. Cobb-Douglas and increasing Returns to...
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