Econ 3070Returns to scale and M arginal CostMarch 13, 2007Example 1 F (L, K)=min{L, K} . Optimal input combination to produce Qunits of output: ..L = K = Q. Cost function: wL + rK = Q (w + r)=C (Q) .Marginal cost is constant, MC (Q)=w + r>0.Example 2 F (L, K)=L1/3K1/3,w=14,r=7Optimal input combination toproduce Q units of output: L∗=pQ3/2; K∗=p2Q3, so C (Q)=wpQ3/2+rp2Q3|w=14,r=7=14√2pQ3.C(Q)QFigure 1: C(Q)=14√2pQ3Mar ginal c ost: MC(Q)=∂∂QC(Q)=∂∂Q14√2pQ3=21√2√Q3Q21MCQMC(Q)=21√2√Q3Q2Example 3 F (L, K)=LK = Q. Increasing returns. Optimal input combina-tion satisfies: L∗/K∗= r/w, L∗K∗= Q. L∗= rK∗/w, and (rK∗/w) K∗= Q,Solution is: K∗=1r√rQw,then L∗= r¡1r√rQw¢/w =√rQww. Cost function:C (Q)=w√rQww+ r1r√rQw =2√rQw|w=14,r=7=2√14√7√QTC(Q)QFigure 2: TC(Q)=C (Q)=2√14√7√QMC (Q)=∂∂QC(Q)=∂∂Q2√14√7√Q =7√2√Q2MC(Q)QMC (Q)=7√2/√QCONCLUSIONS:Returns to scale MC,ACconstant constan tincreasing decreasingdecreasing increasingExplain why (in
View Full Document
Unlocking...