8 Let the total cost of producing x units, c(x), be given by c(x) = kx^1-b (0 < b < 1). This cost curve is called the learning or experience cost curve.

a Show that the cost of producing a unit is a decreasing function of the number of units that have been produced.

b Suppose that each time the number of units produced is doubled, the per-unit product cost drops to r%

of its previous value (because workers learn how to perform their jobs better). Show that r = 100(2^-b).