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},

wherea,bare two positive constants and the subscripts 1 and 2 represent different firms, respectively. The market prices for capital and labour arerandw.

) What are the minimal total costsTC1andTC2for Firms 1 and 2 when they produceq1andq2amounts, respectively? What are the average costsAC1andAC2, respectively?

(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 levelq1is at least twice of Firm 2's output levelq2, (i.e.,q12q2).