Two firms 1 and 2 are using both capital (K) and labour (L) to produce identical products. They have different technologies in their productions, which are described as the following production functions:

f1(K1,L1) = aK1 +bL1; f2(K2,L2) = min{aK2,bL2},

where a,b are two positive constants and the subscripts 1 and 2 represent different firms, respectively. The market prices for capital and labour are r and w.

previous question : (c) What are the minimal total costs TC1 and TC2 for Firms 1 and 2 when they produce q1 and q2 amounts, respectively? What are the average costs AC1 and AC2, respectively?

My question : (d) Use suitable analytical tools (either algebraic or graphic) to show that, if the minimal total costs are the same for both firms (i.e., TC1 = TC2), then Firm 1's output level q1 is at least twice of Firm 2's output level q2, (i.e., q1 2q2).