9.2 Suppose the production function for product x is given by q = kl − 0.8k 2 − 0.2l 2,

● All cost curves are drawn on the assumption that the input prices are held constant. When input prices change, cost curves will shift to new positions. The extent of the shifts will be determined by the overall importance of the input whose price has changed and by the ease with which the irm may substitute one input for another. Technical pro gress will also shift cost curves.

● Input demand functions can be derived from the irm’s total cost function through partial differentiation. These input demand functions will depend on the quantity of output that the irm chooses to produce and are there fore called ‘contingent’ demand functions.

● In the short run, the irm may not be able to vary some inputs. It can then alter its level of production only by changing its employment of variable inputs. In so doing, it may have to use non-optimal, higher-cost input combinations than it would choose if it were possible to vary all inputs.

where q represents the annual quantity of product x pro duced, k represents annual capital input and l represents annual labour input.

a.

If k = 10, graph the total and average productivity of labour curves. At what level of labour input does this average productivity reach a maximum?

How many units of product x are produced at that point?

b.

c.

d.