ECO101 Tutorial 11

ECO101 - Week 11 Competition.pdf

• Stuff to study
  • Abatement #tk
• 1
  • $D=680-20p$
  • Chart
    • AC: $8,4.5,4,4.25,4.8,5.5$
  • Perfect competition
  • When $MC=AC$
    • When $AC=4=MC$
  • $p=MC$
  • $4=p$
  • $D=680-20(4)=600$
  • $n=\frac{Q}{q}=\frac{600}{3}=200$ firms
• 2
  • $C=20q^2+80$
  • $MC=40q$
  • $Q=2400-20p$
  • $s=20$
  • Bundle A: before subsidy
    • Average Cost
      • $AC=20q+80q^{-1}$
    • Perfect Competition
      • $MC=AC$
      • $40=20q+\frac{80}{q}$
      • $q=2$
    • $MC=p$
      • $40q=p$
      • $40(2)=p$
      • $80=p$
    • Quantity Demanded
      • $2400-20p$
      • $2400-20(80)=800$
    • Firms
      • $n=\frac{Q}{q}=\frac{800}{2}=400$
    • $MC=p$
      • $40q=p$
      • $q=\frac{1}{40}p$
    • Supply curve
      • $S=nq$
      • $S=n\left(\frac{1}{40}p\right)$
      • $S=400(\frac{1}{40}p)$
      • $S=10p$
  • Bundle C: after subsidy
    • Cost curve
      • $C_c=C_a-s$
      • $C_c=20q^2+80-20q$
        • $20$ times every quantity of something sold as subsidy
    • Avg Cost Curve
      • $AC=20q+80q^{-1}-20$
    • $MC$
      • $MC=40q-20$
    • Perfect Competition
      • $AC=MC$
      • $20q+80q^{-1}-20=40q-20$
      • $q=2$
    • $MC=p$
      • $MC=p$
      • $40(q)-20=p$
      • $40(2)-20=p$
      • $p=60$
    • Demand
      • $2400-20p$
      • $2400-20(60)=1200$
    • firms
      • $n=\frac{Q}{q}$
      • $n=\frac{1200}{2}=600$
      • $400\to 600$
      • Allows more firms to enter the industry
    • $MC=p$
      • $40q-20=p$
      • $q=\frac{p}{40}+\frac{1}{2}$
    • Supply Curve
      • $S_c=nq$
      • $S_c=600(\frac{p}{40}+\frac{1}{2})$
      • $S_c=15p+300$
      • p-int : -20
      • q-int : 300
  • Bundle B
    • Cost Curve from C
      • $C_c=20q^2-80-20$
    • MC from C
      • $M{C}_c=40q-20$
    • Avg from C
      • $A{C}_c=20q+80q^{-1}-20$
    • Number of firms from A
      • $n_A=400$
    • $p=MC$ perfect comp
      • $p=40q-20$
      • $q=\frac{p}{40}+\frac{1}{2}$
    • Supply Curve
      • $S_B=nq$
      • $S_b=400(\frac{p}{40}+\frac{1}{2})$
      • $S_b=10p+200$
      • p-int: -20
      • q-int: 200
    • Equate supply and demand
      • $10p+200=2400-20p=2400-20p$
      • $p=\frac{220}{3}$
    • Quantity
      • $q=2400-20\left(\frac{220}{3}\right)=\frac{2800}{3}=933.33$
    • Output for B
      • $q=\frac{p}{40}+\frac{1}{2}$
      • $q=\frac{\frac{220}{3}}{40}+\frac{1}{2}=\frac{7}{3}=2.33$
  • Graph:
  • In the tax thing, we add tax to bundle c for cost.
• 4
  • Firm A
  • Firm B
  • $SMC$
  • $SMC=2q_a$
    • $SMC=2q_a$
    • $q_a=\frac{1}{2}{p}_a$
  • $SMC=4q_b$
    • $SMC=p_b$
    • $4q_b=p_b$
    • $q_b=\frac{1}{4}{p}_b$
  • $SM{C}_t=q_a+q_b$
    • $SM{C}_t=\frac{1}{2}p+\frac{1}{4}p=\frac{3}{4}p$
    • $S=nq$
    • $S_a=\frac{1}{2}{p}_a$
    • $S_b=\frac{1}{4}{p}_b$
    • Because $n=1$ firm
    • $S_t=\frac{3}{4}p$
  • $S_a=D$
    • $\frac{1}{2}p=60-0.75p$
    • $p=48$
    • $q=24$
  • $S_b=D$
    • $\frac{1}{4}p=60-0.75p$
    • $p=60.0$
    • $q=60-0.75(60)$
    • $q=15$
  • $S_t=D$
    • $\frac{3}{4}p=60-0.75p$
    • $p=40.0$
    • $q=60-0.75(40)$
    • $q=30$
  • Graph: