In the Cobb-Douglas economic growth model, the quantity of output Q depends on the quantities of raw labor L, human capital per worker H, and physical capital K used in production. Specifically, if L units of raw labor, H units of human capital per worker and K units of physical capital are used, the total output produced is Q = K a (H L) 1a with a being a production function parameter.

Assume that the rate of growth of the labor force is rL = 0.02. From all output that is produced, the proportion that is saved and invested in new physical capital is sK = 0.2. From all output produced, the proportion saved and invested in human capital is sH = 0.1. (The total proportion of output saved is therefore sK + sH = 0.3.) The production parameter a = 1/4. Show all the steps involved in deriving the rate of growth of output per worker Q/L. Provide a full explanation in words for each key step. Please note: You will not have enough information to find a complete numerical solution.