NotesAtHKU

Simple monopoly

Ability to raise price > marginal cost without losing all customers

Marginal revenue = marginal cost

There are multiple sources that can lead to this: !!! tip "Derivation of Marginal Revenue"

Quantity: n

Discrete: MR = TR (n)- TR (n-1)

Continous: MR curve has twice the slope of D curve. (Coefficienct of $Q\times2$ )

Simple monopoly pricing

Find D curve
Obtian MR curve ^^ (discrete vs continous)
Find Profit-maximizing Q* quantity @ MR=MC
Price is intersection of D curve and Q=Q*

More elastic demand -> Lower price, smaller markup Less elastic demand -> Higher price, higehr markup

Markup

\text{Markup} = \frac{P - MC}{MC} = \frac{-1}{1+\eta_d} \implies \propto \frac{1}{\eta_d}

Where $\eta_d$ is the price elasticity of demand.

Inefficiency

Q* < Qe -> DWL is the efficiency loss

CS top part, PS bottom part including rectangle

Price $P*$ Intersect(q=q*, D) is the price that monopoly charges. (Monopoly pricing)

Revenue is $P*\times Q*$

Total marginal cost (TVC) is the trapesium under left triangle and Q=Q*.

Producer surplus = Profit if no fixed cost (Profit=TR-TVC-FC=PS-FC) (PS=TR-TVC)

Price control on monopoly

Price ceiling: New MR will be line from intersection of D and ceiling to yaxis and xaxis. Marginal revenue is constant for q < x(intersection).

x(intersection) is maximum quantity that the market sells.

Price ceiling @ D=MC -> Socially efficient quantity, profit maximizing, no dwl Price ceiling @ D=AC -> Zero profit, DWL triangle under x(intersection) and above MC. (Zero profit)