ECO101 Lecture 03

• ECO101 - Week 03 Regulation.pdf

Market Efficiency

• Consumer Surplus and Producer Surplus
• 1
  • $D=12-2p$
  • $S=2p$
  • P-int
    • $D=12$
    • $S=0$
  • Q-int
    • Demand
      • $12=2p$
      • $6=p$
  • Eq
    • $D=S$
    • $12-2p=2p$
    • $12=4p$
    • $p=3$
    • $12-2(3)=6$
  • a
    • Consumer Surplus
  • b
    • Producer Surplus

Tax

• 2
  • Consumer Surplus is area abf
  • a
    • $D=S$
    • $(6,3)$
  • b
    • Consumer Surplus:
      • Calculate the area between Equilibrium price and below demand
      • Inverse the function, to make it in terms of quantity
        • $q=12-2p$
        • $q-12=-2p$
        • $\frac{q-12}{-2}=p$
        • $-\frac{q}{2}+6$
        • $6-\frac{q}{2}=p$
      • Between the equilibrium price and below demand, means the bottom function is just the price, $p=3$
      • So we evaluate ${\int }_0^6(6-\frac{q}{2})-3dq$
      • ${\int }_0^6(6-\frac{q}{2})-3dq$
      • Antiderive
        • $6q-\frac{1}{4}{q}^2-3q$
        • $(3q-\frac{1}{4}{q}^2){}_0^6$
        • $(3(6)-\frac{1}{4}(6{)}^2)-(3(0)-\frac{1}{4}(0{)}^2)$
        • $9$
    • Producer Surplus:
      • Calculate the area between the supply line and equilibrium quantity
      • Inverse supply:
        • $S=2p$
        • $q=2p$
        • $\frac{q}{2}=p$
      • Bottom function is the supply
      • Top function is the equillibrium price line
      • ${\int }_0^{6}3-\frac{q}{2}dq$
      • Antiderive
        • $(3q-\frac{1}{4}{q}^2){}_0^6$
        • $(3(6)-\frac{1}{4}(6{)}^2)-0$
        • $(18-\frac{1}{4}(6{)}^2)-0$
        • $(18-\frac{1}{4}36)-0$
        • $(18-9)-0$
        • $9$
    • Total Surplus is Consumer Surplus and Producer Surplus
      • So $9+9=18$
  • c
    • With tax, suppliers receive less
    • $D=12-2p$
    • $S=2(p-2)$
    • $S=2p-4$
    • Eq:
      • $D=S$
      • $12-2p=2p-4$
      • $16=4p$
      • $4=p$
      • $12-2(4)$
      • $4$
      • $(4,4)$
    • Q-int:
      • $D=12$
      • $S=-4$
    • P-int:
      • $(12,0)$
    • Cs
      • Inverse demand
      • $12-2p⟹6-\frac{q}{2}$
      • ${\int }_0^4(6-\frac{q}{2})-4dq$
      • Antiderive
        • $(6q-\frac{1}{4}{q}^2-4q)$
        • $(2q-\frac{1}{4}{q}^2){}_0^4$
        • $(2(4)-\frac{1}{4}{4}^2)$
        • $(8-\frac{1}{4}16)$
        • $(8-4)$
        • $(4)$
    • Ps
      • Inverse supply
      • $q=2p-4$
      • $q+4=2p$
      • $\frac{q}{2}+2=p$
      • ${\int }_0^{4}4-(\frac{q}{2}+2)dq$
      • Antiderive
        • $4q-\frac{1}{4}{q}^2-2q$
        • $(2q-\frac{1}{4}{q}^2){}_0^4$
        • $(2(4)-\frac{1}{4}(4{)}^2)$
        • $(8-\frac{1}{4}16)$
        • $4$
    • Ts
      • $8$

    ---

    • $\begin{array}{cccc}x& p\ast & t=2& \text{change}\\ cs& 9& 4& 5\\ ps& 9& 4& 5\\ gs& 0& 8& 8\\ ts& 18& 16& 2\end{array}$

    ---

    • Producers summary
      • lose area c and e.
      • Means they're selling less units and prices are less
    • Consumers summary
      • lose area e
      • Pay a higher price, and reduced quantity
    • Government Surplus
      • gains the areas lost
      • deadweight loss
  • Does elasticity matter?
    • If sellers are inelastic, the sellers pay most of the tax
    • Incidence on Tax
  • This results in a smaller government revenue box.
  • So the Efficiency loss is larger

Subsidy

• Subsidy
• 4 Variations
  • 1
    • $s=2$ onto a market
    • If ${\eta }^s$ and ${\eta }^d$ are both elastic
  • 2
    • $s=2\to 0$
    • Now we gain efficiency and Total Surplus
    • Subsidy off
  • 3
    • $s=2\to 3$
  • 4
    • $s=2\to 1$

Price Controls

• Price Ceiling
• Should we put a Price Ceiling on gas?:
• Rent Controls
• Interest Rates
• Price Floor

Production Quota

• Output Quota