Longrunisaplanninghorizonoverwhichproducerscanvaryallfactorsofproduction. Expansion path ofa firm is the locus of points where the firm's isoquant curves corresponding to variousoutputsaretangenttotheisocostlines,assumingthatinputpricesremainunchanged.The expansion path also shows the least costly combinations of inputs that produce various levels of output.Suppose points A, B, C, and D given below are some of those input combinations of labor (L) and capital (K) on thefirm'sexpansion path when labor costs$20 per unit and capital costs $30 per unit.

a) Calculate thefirm'slong-runtotalcost(LTC)andlong-runaveragecost(LAC)and complete the table.(16 points)(L, K) Quantity of output (q)LTCLACA (10, 5) 60_____________B (20, 10) 150_____________C (30,15) 300_____________D (60, 30) 675_____________

b)Determine the nature of the production process from one input combination to another interms of returns to scale. Discuss the implications of returns to scale for the firm's LAC curve, i.e., explain why the LAC curve has the U-shape it does.