1. **Problem statement:** We have demand and supply functions for corporate bonds: $$Q_d = 460 - 10r$$ $$Q_s = 200 + 5r$$ where $r$ is the interest rate (%) and $Q$ is quantity in millions. (a) **Find equilibrium interest rate and quantity:** At equilibrium, quantity demanded equals quantity supplied: $$Q_d = Q_s$$ $$460 - 10r = 200 + 5r$$ Bring terms involving $r$ to one side: $$460 - 200 = 5r + 10r$$ $$260 = 15r$$ Divide both sides by 15: $$\frac{260}{\cancel{15}} = \frac{15r}{\cancel{15}}$$ $$r = \frac{260}{15} = 17.33$$ Substitute $r=17.33$ into either $Q_d$ or $Q_s$: $$Q = 460 - 10(17.33) = 460 - 173.3 = 286.7$$ (b) **Graphical representation:** Plot $Q_d = 460 - 10r$ and $Q_s = 200 + 5r$ with $r$ vertical and $Q$ horizontal. (c) **Calculate investor surplus (IS) and issuer surplus (FS):** Investor surplus is the area between demand curve and equilibrium price: Maximum willingness to pay at $Q=0$ is $r=46$ (from $460 - 10r=0 \Rightarrow r=46$). IS is area of triangle: $$IS = \frac{1}{2} \times (46 - 17.33) \times 286.7 = \frac{1}{2} \times 28.67 \times 286.7 = 4109.67$$ Issuer surplus is area between supply curve and equilibrium price: Minimum acceptable rate at $Q=0$ is $r= -40$ (from $200 + 5r=0 \Rightarrow r=-40$), but negative interest is not realistic, so use $r=0$ as intercept. At $r=0$, $Q_s=200$. FS is area of trapezoid: $$FS = (17.33 - 0) \times 200 + \frac{1}{2} \times (17.33 - 0) \times (286.7 - 200) = 3466 + 765.5 = 4231.5$$ (d) **New equilibrium with 3% tax on interest income:** Tax shifts supply curve upward by 3% in interest rate terms. New supply function: $$Q_s = 200 + 5(r - 3) = 200 + 5r - 15 = 185 + 5r$$ Set new equilibrium: $$460 - 10r = 185 + 5r$$ $$460 - 185 = 15r$$ $$275 = 15r$$ $$r = \frac{275}{15} = 18.33$$ New quantity: $$Q = 460 - 10(18.33) = 460 - 183.3 = 276.7$$ (e) **Tax burden sharing:** Price increase from 17.33 to 18.33 means investors pay 1% more. Suppliers receive $r - 3 = 18.33 - 3 = 15.33$, less than before (17.33), so suppliers bear 2% burden. (f) **Government tax revenue:** Tax revenue = tax rate × quantity × interest rate $$= 3 \times 276.7 = 830.1$$ Final answers: - Equilibrium interest rate: $17.33$% - Equilibrium quantity: $286.7$ million - Investor surplus: $4109.67$ - Issuer surplus: $4231.5$ - New equilibrium interest rate with tax: $18.33$% - New equilibrium quantity: $276.7$ million - Tax burden: investors pay 1%, issuers pay 2% - Government tax revenue: $830.1$ million