1. **Stating the problem:** Given the demand function $P=36-4Q$ and the supply function $P=18+2Q$, we need to find: (a) Equilibrium price and quantity before subsidy. (b) New supply function after a subsidy of 6 units. (c) Market equilibrium after subsidy. (d) Shares of subsidy received by consumers and producers, and total government subsidy. (e) Plot supply and demand curves before and after subsidy. 2. **Finding equilibrium before subsidy:** Equilibrium occurs where demand equals supply: $$36-4Q=18+2Q$$ Bring terms involving $Q$ together: $$36-18=2Q+4Q$$ $$18=6Q$$ Divide both sides by 6: $$Q=3$$ Find equilibrium price by plugging $Q$ into demand or supply: $$P=36-4(3)=36-12=24$$ Equilibrium price $P=24$, quantity $Q=3$. 3. **New supply function after subsidy:** A subsidy of 6 units reduces producers' effective cost by 6, so the price suppliers require is $P+6$ equal to original supply price. Original supply: $$P=18+2Q$$ With subsidy, suppliers accept price $P$ but receive $P+6$ effectively, so: $$P+6=18+2Q$$ Solve for $P$: $$P=18+2Q-6=12+2Q$$ New supply function is: $$P=12+2Q$$ 4. **Market equilibrium after subsidy:** Find new equilibrium where demand equals new supply: $$36-4Q=12+2Q$$ Bring $Q$ terms together: $$36-12=2Q+4Q$$ $$24=6Q$$ Divide both sides: $$Q=4$$ Find price by plugging $Q$ into new supply: $$P=12+2(4)=12+8=20$$ New equilibrium price $P=20$, quantity $Q=4$. 5. **Subsidy shares and total subsidy:** Before subsidy price was 24; after subsidy price is 20. Consumers pay 20 instead of 24, so consumer gains subsidy portion of $24-20=4$ per unit. Producers receive $20+6=26$ per unit, so producers gain $26-24=2$ per unit. Total subsidy per unit is 6. Total units sold after subsidy is 4, so total government subsidy is: $$6 \times 4=24$$ 6. **Summary:** (a) Equilibrium before subsidy: $P=24$, $Q=3$. (b) New supply: $P=12+2Q$. (c) New equilibrium: $P=20$, $Q=4$. (d) Consumer subsidy per unit: 4; producer subsidy per unit: 2; total subsidy: 24. (e) See Desmos for supply and demand curves before and after subsidy.