Question

7. A bicycle company has the following long run total cost function: LTC(Q) = 40,000Q – 400Q2 + 203 where Q is the number of bikes produced. a. Compute the company's LMC and LAC as a function of Q b. Assume that that there is perfect competition. How many bikes would the bicycle company produce in the long run? c. Over what range of output does the company experience economies of scale? Over what range of output does it experience diseconomies of scale?

Answer 1

question (7) LTC (O) = 40,000 & - 4008² +283 (a) LMC = dTc (QI LmC = 40,000 - 800 g + 692 LAC- LTC ca LAC 40,000 - 400 a + 2a 2 (b) PeoJectery competitive from sell their product at P= mincac LAC = 40,000-400 9+292 dLAC do - 400 tuo 48 = 400 Loo - 100 4 2 For Q=100 LAC = LAC = 40,000 - 400 (100)+2 (100)

=) LAC = 40,000 - 40000 + 2 (10000) LAC = 2oooo So Company will produce g=100 units at Price of 200,00 LAG LAC = 40,000 40,000 - 400g + 29² for decreasing CAC, firme ex leviences economies of scare for increcusing dis economies of scale LAC = 40,000 - 400 9+2 9² dLAC = - 400 tu dQ For economies of scale Lo diac do .400tucs co -40ot 400 t40 L 400 40 C 400 Q < 100

For 8< 100 it exponence economies of scale for dis economies of scale dLAC so do =) -400+ ua> 0 ☺ ☺ 40 400 CS > 406 =100 4 for Q>100 it ex fericence diseconomies of