Question

(From section 6.4) How will a firm react to an increase in the price of one input relative to another?

2.             When is a production function said to have constant returns to scale, increasing returns to scale, or decreasing returns to scale?

3.             You have been asked by your manager to choose between the following three production functions based on returns to scale:

                                Q = 10K²L¹

                                Q = 10K^0.5 L^0.5 (read as 10 times K taken to the 0.5 power times L taken to the 0.5 power)

                                Q = 10K^0.25 L^0.5

  

                She would like you to choose the one that exhibits increasing returns to scale and to provide evidence to support your decision.

Answer 1

If the price of one input increase relative to other , firms reacts by lowering the amount of that input used . Two effects work here:

1) substitution effect : this cause the firm to substitute the relatively dearer input with the other input , so the use of dearer input falls

2) output effect : Since the input price has risen , the real value of budget of the firm also falls so firm reduces its output to maximise profits so it reduces its demand for the dearer product.

SO , because of these two effects , use of dearer input falls .

Q = 10K²L¹

if both K and L are increased by z then new function will be

Q' = 10(zK)²(zL¹)

Q' = z³10K²L¹

Q' = z³Q

so this function exhibits increasing returns to scale

Q = 10K^0.5L^0.5

if both K and L are increased by z then new function will be

Q' = 10(zK)^.5(zL)^0.5

Q' = zQ

so this function exhibits constant returns to scale

Q = 10K^0.25L^0.25

if both K and L are increased by z then new function will be

Q' = 10(zK)^.25(zL)^0.25

Q' = z^0.5Q

so this function exhibits decreasing returns to scale

so she would choose this function : Q = 10K²L¹