Hi, its mainly the part a), where did the formula come from? and the final explanation of a) why did it say the mpl is less than apl , good explanation please

Q20. Unemployment & output. A country has 10 percent unemployment. The production function is Cobb-Douglas with a = 0.3. (a) By how much will production increase if unemployment is reduced to 5 percent while the capital stock, the labour force, and technology are unchanged? Explain your result. Initial production is Y1 = K\"(E(1 u)L)l'\" Y1 = K03 (E (1 0.1)L)D'? Y1 = K03 (EL)D'7(0.9)D'7 Final production is Y2 = HD-3(EL)-7(o.95)D-? The relative increase is found from 0.3 0.7 0.7 0.? Y_2 = K (EL) (0.95) _ (E) x 1.039 Y1 K-3(5L)-7(o.so)-7 0.90 Production increases by 3.9 percent, which is less than the percentage increase in labour input. With a fixed capital stock, the marginal product oflahour is lower than the average product oflabour. (b) If unemployment remains permanently on the lower level, is it likely that the capital stock will remain unchanged? With higher employment, the marginal product of capital increases, so the incentives to invest increase. In the long run, the capital stock should increase. [This adjustment is analysed in Chapter 5.]