19.9 A competitive, profit-maximizing firm uses two inputs a and 6. Its producti

Question

19.9 A competitive, profit-maximizing firm uses two inputs a and 6. Its production function is F(a, b) = a1/2 + 61/2. Its output sells for $5 per unit. The price of input a is $1 per unit. If the price o output rises to S6 per unit but factor prices do not change, este presidente (a) it will increase its purchases of factor a by 11/4 units. (b) it will increase its purchases of factor a by 9/4 units. (c) it will increase its purchases of factor a by 3/4 units. (d) we would need to know the price of factor b to be able to determine the change in demand for a. (e) none of the above is true.

Explanation / Answer

Option a is correct

Profit (P) = P x F(a,b) - 1 x a - wb x b

Profit would be maximized when dP/da = 0 (b remains constant)

When P = 5:

dP/da = 2.5/a0.5 -1 = 0  

a = 6.25

When P = 6:

3/a - 1 = 0

a = 9

Therefore, a increases by 2.75 or 11/4 (= 9 - 6.25)

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