Question

. Consider a firm that has a production function y = f(x1, x2) = 2x ^1/4 1 x ^1/4 2 facing input prices w1 = 2 and w2 = 4. Assume that the output price p = 8.

• What will be the profit maximizing output level?
-What will be the profit? •
-If this firm is divided up into two equal-size smaller firms, what would happen to its overall profits? Why

Answer 1

maxmizing profit by equating first derivative with respect to output to 0

Part (1) Profits are maxmized at output of 3 (approximately)

Part (2)

Part (3)

we have to find how profits will be impacted when firm is divided in 2 equal smaller sized firms

for this we check whether the production function exhibhits increasing returns to scale or decreasing returns to scale

since doubling the quantity of inputs (doubled its scale of operation) does not leads to doubing of ouptut and leads to an output level less than that

We can say the above production function exhibhits decreasing returns to scale

Therefore, when firm is divided in 2 equal sized firms. the 2 smaller firms would operate at half the scale of operation of the bigger firms

Given fixed prices, total revenue will be more than half of the original revenue. Given fixed prices, cutting its scale of operation by half will cut total cost by half and hence, the overall profit will increase.

This can be shown by checking how the level of output changes when quantity of inputs (scale of operation ) is reduced by half

therefore halving the quantity of inputs does not lead to an output level half the original output level