ECO101 Test Prep 1

ECO101 TT1.pdf

• 1
  • The eloss from an import tariff will be largest when
  • When demand and supply are elastic
• 2
  • Declining Equilibrium price and rising Equilibrium quantity could be caused by increase in price of
  • Complement in production
  • Because the other good to be produced got higher
  • So they want to produce these two goods more, which makes it cheaper.
• 3
  • $D_X=11-P_X-P_Y$
  • $D_{X_1}=6-P_X$
  • $D_{X_2}=10-P_X$
  • $S_X=P_X$
  • $P_Y=5\to 1$
  • At original equilibrium
    • $D_{X_1}=S_X$
    • $6-P_X=P_X$
    • $6=2P_X$
    • $3=P_X$
    • $(3,3)$
  • New
    • $D_{X_2}=S_X$
    • $10-P_X=P_X$
    • $5=P_X$
    • $(5,5)$
  • Cross price elasticity
  • ${\eta }_{xy}=\frac{\frac{\mathrm{\Delta }Q}{\overline{Q}}}{\frac{\mathrm{\Delta }p}{\overline{p}}}$
  • ${\eta }_{xy}=\frac{\frac{2}{4}}{\frac{4}{3}}=0.375$
• 4
  • Three roommates plan to purchase a public good at a price of $8$ dollars per unit.
  • $MC=8$
  • $P_A=2-q$
  • $P_B=10-q$
  • $P_C=12-q$
  • How many units of the public good should be purchased?
  • How many should be bought
    • $MB=P_A+P_B+P_C$
    • $MB=(2-q)+(10-q)+(12-q)$
    • $MB=24-3q$
    • $M{B}_{ABC}=MC$
      • $24-3q=8$
      • $16=3q$
      • $\frac{16}{3}=q$
      • $\frac{16}{3}>2$
      • This doesn't work
    • $M{B}_{BC}=MC$
      • $22-2q=8$
      • $2q=14$
      • $q=7$
      • $2\le 7\le 10$
      • This works
    • $M{B}_C=MC$
      • $12-q=8$
      • $4=q$
      • $10\nleqq 4$
      • So this isn't valid
    • Quantity that works is at $M{B}_{BC}=MC$ because roommate $A$ doesn't want to buy much
    • They should buy $7$ units.
• 5
  • $D=180-10p$
  • $S=20p-60$
  • $t=3$
  • $D=S$
  • $180-10p=20p-60$
  • $240=30p$
  • $8=p$
  • $D(8)=180-10(8)=100$
  • $(100,8)$
  • Intercepts
    • $0$ supply
      • $60=20p$
      • $p=3$
      • $(0,3)$
    • $0$ demand
      • $180=10p$
      • $18=p$
      • $(0,18)$
    • $0$ price
      • $180$
      • $(180,0)$
  • 3 dollar tax
  • Suppliers receive less or demanders pay more
  • So I can - tax on supply or + tax on demand
  • $S-t=D$
  • $20(p-t)-60=180-10p$
  • $20(p-3)-60=180-10p$
  • $S^{\prime }=20p-120$
    • $0$ supply
    • $120=20p$
    • $6=p$
  • $20p-120=180-10p$
  • $300=30p$
  • $10=p$
  • $S^{\prime }(10)=20(10)-120=80$
  • $(80,10)$
    • $20p-60=80$
    • $140=20p$
    • $7=p$
  • Consumer Surplus
    • Before:
      • $\frac{bh}{2}=\frac{(100-0)(18-8)}{2}=0.5(1000)=500$
    • After:
      • $\frac{bh}{2}=0.5(80-0)(18-10)=320$
  • Producer Surplus:
    • Before:
      • $\frac{bh}{2}=0.5(100-0)(8-3)=250$
    • After:
      • $\frac{bh}{2}=0.5(80-0)(10-6)=160$
  • Government Surplus:
    • Before:
      • $0$
    • After:
      • $bh=(80-0)(10-7)=240$
  • Total Surplus:
    • Before:
      • $500+250=750$
    • After:
      • $320+160+240=720$
• 6
  • Negative Externality
  • Social Cost is higher than Private Cost
  • $MB=60-10q$
  • $M{C}_P=10q$
  • $M{C}_S=20q$
  • Private Solution
    • $MB=M{C}_P$
    • $60=20q$
    • $3=q$
    • $MB(3)=60-10(3)=30$
    • $(3,30)$
  • Social
    • $MB=M{C}_S$
    • $60-10q=20q$
    • $60=30q$
    • $2=q$
    • $MB(2)=60-10(2)=40$
    • $(2,40)$
  • Ints
    • $0$ supply
      • $(0,0)$
    • $0$ demand
      • $60$
      • $(0,60)$
    • $0$ price
      • $60=10q$
      • $6=q$
      • $(6,0)$
  • Tax:
    • $MEC=MSC-MC$
    • $MEC=20q-10q$
    • $MEC=10q$
    • $(10)(2)=20$ Tax
  • New $MC$
  • $MC+T=MB$
  • $10q+20=MB$
  • $10q+20=60-10q$
  • $10q-40=-10q$
  • $-40=-20q$
  • $2=q$
  • $MB(2)=60-10(2)=40$
  • $(2,40)$
  • Done
  • Efficiency loss is:
    • $M{C}_S(3)=20(3)=60$
    • $\frac{bh}{2}=0.5(60-30)(3-2)=15$