Profit-Maximization At the profit-maximizing output level q diig d (p(q)) d(q)=0 F.o.c d d (p(q)·q) dc(g MR(g=MC(
11 Profit-Maximization At the profit-maximizing output level q* ( ) ( ) ( ) ( ) 0 d q d dc q p q q dq dq dq Π = − = F.O.C ( ) ( ) ( ) . d d c q p q q d q d q • = MR q( ) = MC( ) q
Marginal Revenue and Marginal Cost MR(q)=2((9)y)=p(q)+q dplg dp()ldg is the slope of the market inverse demand function, so dp()ldy <0. Therefore MR(g=p(a+q dp(a dg Plg for a> 0
12 Marginal Revenue and Marginal Cost ( ) ( ) ( ) ( ) ( ) . d dp q MR q p q q p q q dq dq = = + dp(q)/d q is the slope of the market inverse demand function, so dp(q)/d y < 0. Therefore ( ) ( ) ( ) ( ) dp q MR q p q q p q dq = + < for q > 0
Marginal revenue a D=AR: pg= a-bq if p(g=a-bq then TR(g)=p(q= ag-bq2 and so a/2b a/b g AR=a-bq MR(g)=a-2bq< a-bg= MR(g=a- 2bq p(a), for g> 0
13 Marginal Revenue E.g. if p(q) = a - b q then TR(q) = p(q)q = aq - b q 2 and so AR=a-bq MR(q) = a - 2bq < a - b q = p(q), for q> 0. D=AR: p(q) = a - b q a a/b q MR(q) = a - 2bq a/2b P
Summary: Profit Max in Monopoly The monopolist is the supply-side of the market and has complete control over the amount offered for sale Profits will be maximized at the level of output where marginal revenue equals marginal cost 14
14 Summary: Profit Max. in Monopoly The monopolist is the supply-side of the market and has complete control over the amount offered for sale. Profits will be maximized at the level of output where marginal revenue equals marginal cost
Short-run Equilibrium Under monopoly
15 Short-run Equilibrium Under Monopoly