Learning by doing is often measured by progress ratios. This number represents the cost of production after cumulative production doubles. Dutton and Thomas (1984) survey various industries and find the ratio to be typically around 80%. Thus, if a good has progress ratio of 80% and costs $100 to produce after producing 100 units, when cumulative production reaches 200 units, it will cost $80 to produce. Formally, for some commodity, if Cost(t) is cost at time, t, d(t) is the number of doublings of cumulative output of the commodity in time, t, and a is the percent reduction in cost for each doubling of cumulative output (note: 1-a is the progress ratio), then we have Cost(t) = Cost(0)(1-a)^d.