清华大学中级微观经济学讲义(清华 李稻葵)24

http://www.sem.tsinghua.edu.cn/ Chapter Twenty-Four Monopoly
What do we do in this chapter
We studied the case of pure competition, in which case, each firm is very small; We now study the other extreme: There is a single firm.
Quantity Tax Levied on a Monopolist
A quantity tax of $t/output unit raises the marginal cost of production by $t. The quantity tax is distortionary. See the following figure.
t
The amount of the tax paid by buyers is t
p(y ) − p(y*).
Quantity Tax Levied on a Monopolist
(k + t)ε kε tε p(y ) − p(y*) = − = 1+ ε 1+ ε 1+ ε
t
Because ε < -1, ε /(1+ε) > 1 and so the monopolist passes on to consumers more than the tax!
Marginal Revenue
E.g. if p(y) = a - by then R(y) = p(y)y = ay - by2 and so MR(y) = a - 2by < a - by = p(y) for y > 0. a p(y) = a - by
a/2b
a/b y MR(y) = a - 2by
$
Marginal Cost
c(y) = F + αy + βy2
F $/output unit y MC(y) = α + 2βy β α y
Profit-Maximization; An Example
$/output unit a
p(y*) = a−b a−α 2(b + β)
p(y) = a - by MC(y) = α + 2βy β
so, for y = y*,
d dc(y) . (p(y)y) = dy dy
Profit-Maximization
$
R(y) = p(y)y
y
Profit-Maximization
$
R(y) = p(y)y c(y)
y
Profit-Maximization
$
R(y) = p(y)y c(y)
Markup Pricing
1 + 1 = k ⇒ p(y*) = k = kε p(y*) 1 1+ ε ε 1+ ε
is the monopolist’s price. The markup is
kε k p(y*) − k = . −k = − 1+ ε 1+ ε
The markup rises as the own-price elasticity of demand rises towards -1.
y*
y Π(y)
Profit-Maximization
$
R(y) = p(y)y c(y)
y*
y Π(y)
Profit-Maximization
$
R(y) = p(y)y c(y)
y*
At the profit-maximizing output level the slopes of the revenue and total cost Π(y) curves are equal; MR(y*) = MC(y*).
A Profits Tax Levied on a Monopoly
A profits tax levied at rate t reduces profit from Π(y*) to (1-t)Π(y*). Π What is the impact of t on y*? Zero impact! I.e., the profits tax is a neutral tax.
yt y* MR(y)
y
Quantity Tax Levied on a Monopolist
$/output unit p(y) p(yt) p(y*) The quantity tax causes a drop in the output level, a rise in the output’s price and a decline in demand for inputs. MC(y) + t t MC(y)
Pure Monopoly
$/output unit p(y)
Higher output y causes a lower market price, p(y).
Output Level, y
Pure Monopoly
Suppose that the monopolist seeks to maximize its economic profit,
yt y* MR(y)
y
Quantity Tax Levied on a Monopolist
Can a monopolist “pass” all of a $t quantity tax to the consumers? Suppose the marginal cost of production is constant at $k/output unit. With no tax, the monopolist’s price is
kε p(y*) = . 1+ ε
Quantity Tax Levied on a Monopolist
The tax increases marginal cost to $(k+t)/output unit, changing the profit-maximizing price to
(k + t)ε p(y ) = . 1+ ε
α源自文库
y* = a−α 2(b + β)
y MR(y) = a - 2by
Monopolistic Pricing & Own-Price Elasticity of Demand
Suppose that market demand becomes less sensitive to changes in price (i.e. the own-price elasticity of demand becomes less negative).
p(y) dy 1 + 1. ε= so MR(y) = p(y) ε y dp(y)
Monopolistic Pricing & Own-Price Elasticity of Demand
1 + 1. MR(y) = p(y) ε
Suppose the monopolist’s marginal cost of production is constant, at $k/output unit. For a profit-maximum 1 + 1 = k MR(y*) = p(y*) which is k ε p(y*) = . 1 1+ ε
Markup Pricing
Markup pricing: Output price is the marginal cost of production plus a “markup.” How big is a monopolist’s markup and how does it change with the own-price elasticity of demand?
Monopolistic Pricing & Own-Price Elasticity of Demand d dp(y) MR(y) = (p(y)y) = p(y) + y dy dy
y dp(y) = p(y)1 + . p(y) dy
Own-price elasticity of demand is
Marginal Cost
Marginal cost is the rate-of-change of total cost as the output level y increases; dc(y) MC(y) = . dy E.g. if c(y) = F + αy + βy2 then
MC(y) = α + 2βy.
Π(y) = p(y)y − c(y).
What output level y* maximizes profit?
Profit-Maximization
Π(y) = p(y)y − c(y).
At the profit-maximizing output level y*
dΠ(y) d dc(y) = =0 (p(y)y) − dy dy dy
Pure Monopoly
A monopolized market has a single seller. The monopolist’s demand curve is the (downward sloping) market demand curve. So the monopolist can alter the market price by adjusting its output level.
The Inefficiency of Monopoly
A market is Pareto efficient if it achieves the maximum possible total gains-to-trade. Otherwise a market is Pareto inefficient.
y
Marginal Revenue
Marginal revenue is the rate-of-change of revenue as the output level y increases; d dp(y) MR(y) = (p(y)y) = p(y) + y . dy dy dp(y)/dy is the slope of the market inverse demand function so dp(y)/dy < 0. Therefore dp(y) MR(y) = p(y) + y < p(y) dy for y > 0.
Monopolistic Pricing & Own-Price Elasticity of Demand
1 + 1 = k, Notice that, since MR(y*) = p(y*) ε 1 + 1 > 0 ⇒ 1 + 1 > 0 p(y*) ε ε 1 > −1 ⇒ ε < −1. That is, ε So a profit-maximizing monopolist always selects an output level for which market demand is own-price elastic.
Quantity Tax Levied on a Monopolist
$/output unit p(y) p(y*) MC(y)
y* MR(y)
y
Quantity Tax Levied on a Monopolist
$/output unit p(y) p(yt) p(y*) MC(y) + t t MC(y)
Monopolistic Pricing & Own-Price Elasticity of Demand
p(y*) = k 1 1+ ε .
So as ε rises towards -1 the monopolist alters its output level to make the market price of its product to rise.