ECO101 Tutorial 09

ECO101 - Week 09 Short Run Firms.pdf

• 1
  • $SVC=q^3-40q^2+1400q$
  • $SFC=4000$
  • $SMC=3q^2-80q+1400$
  • Shutdown price
  • Find shortrun average variable cost
    • $SAVC=\frac{SVC}{Q}$
    • $SAVC=\frac{Q^3-40q^2+1400q}{Q}$
    • $SAVC=q^2-40q+1400$
  • Find shortrun average fixed cost
    • $SAFC=\frac{SFC}{Q}$
    • $SAFC=\frac{1}{q}4000$
  • Find shortrun average cost
    • $SAC=SAVC+SAFC$
    • $SAC=(q^2-40q+1400)+\left(\frac{1}{q}4000\right)$
    • $SAC=q^2-40q+1400q^0+4000q^{-1}$
  • Shutdown price
    • When $SMC=SAVC$
    • $3q^2-80q+1400=q^2-40q+1400$
    • $2q^2=40q$
    • $2q=40$
    • $q=20$
    • Sub quantity in
    • $p=SMC$
    • $p=3q^2-80q+1400$
    • $p=3(20{)}^2-80(20)+1400$
    • $p=1000$
• 2
  • $q=2\sqrt{k}\sqrt{l}$
  • $w=2\to 1$
  • $k=16$
  • $r=1$
  • $p=4$
  • How many units of labour will increase
  • Bundle A
    • $w=2$
    • Marginal Propensity of Labour
      • $q=2\sqrt{k}\sqrt{l}$
      • $q=2\sqrt{16}\sqrt{l}$
      • $q=8\sqrt{l}=MPL$
      • How much each additional hire will add to production
      • $q^2=64l$
      • $\frac{q^2}{64}=l$
    • Short run total costs
      • $STC=SVC+SFC$
      • $STC=(wl)+(kr)$
      • $STC=2l+16$
      • $STC=\frac{1}{32}{q}^2+16$
    • Short run marginal costs
      • $SMC=\frac{d}{dq}STC$
      • $\frac{1}{16}q$
    • Maximum profits
      • When $p=SMC$
      • $p=4$
      • $4=\frac{1}{16}q$
      • $64=q$
      • $l=\frac{1}{64}{q}^2$
      • $l=\frac{1}{64}{64}^2$
      • $l=64$ employees at point $A$
  • Bundle B
    • $w=1$
    • Short run total costs
      • $STC=SVC+SFC$
      • $STC=(wl)+(kr)$
      • $STC=l+16$
      • $STC=\frac{1}{64}{q}^2+16$
    • Short run marginal costs
      • $SMC=\frac{d}{dq}STC$
      • $\frac{1}{32}q$
    • Maximum profits
      • When $p=SMC$
      • $p=4$
      • $\frac{1}{32}q=4$
      • $q=128$
      • $l=\frac{1}{64}{128}^2$
      • $l=256$
  • So then labour increases from $l=64\to 256$
  • $192$ workers will be hired.
  • Profit function
    • Revenue, costs, labour
    • $\pi =pq-rk-wl$
    • $q=\frac{rk+\pi }{p}+\frac{wl}{p}$
    • Bundle A
      • ${\pi }_a:4(64)-(1)(16)-2(64)=112$
      • $q=\frac{16+112}{4}+\frac{2(l)}{4}$
      • $q=\frac{1}{2}L+32$
    • Bundle C
      • ${\pi }_b:(4)(128)-1(16)-1(256)=240$
      • $q=\frac{16+240}{4}+\frac{1(L)}{4}$
      • $q=\frac{1}{4}L+64$
• 4
  • $q=\sqrt{k}\sqrt{l}$
  • $k=16$
  • $w=4$
  • $r=4$
  • $p=2\to 8$
  • How much output do they supply at $2$
  • MPL
    • $q=\sqrt{k}\sqrt{l}$
    • $q=\sqrt{16}\sqrt{l}$
    • $q=4\sqrt{l}$
    • $q^2=4^{2}l$
    • $q^2=16l$
    • $\frac{1}{16}{q}^2=l$
  • Short run total costs
    • $STC=SVC+SFC$
    • $STC=wl+rk$
    • $STC=\frac{1}{4}{q}^2+64$
  • Short run marginal costs
    • $SMC=\frac{d}{dq}STC$
    • $\frac{1}{2}q$
  • Max profit
    • Bundle A
      • $p=smc$
      • $2=\frac{1}{2}q$
      • $q=4$