Final answer:
After the government introduces a $5 subsidy, the new supply equation becomes P = 30 + 2Q, and setting it equal to the demand yields a new equilibrium price of $76 and an equilibrium quantity of 23 units of gasoline.
Step-by-step explanation:
The student's question pertains to finding the new equilibrium price and quantity after the government introduces a gasoline subsidy. Initially, the demand is given by P = 145 – 3Q, and the supply is P = 35 + 2Q. A subsidy shifts the supply curve downwards, which means the new supply equation will be P = 30 + 2Q, since the producers will receive an additional $5 from the government for each unit sold.
To find the new equilibrium, we set the demand equal to the new supply:
- 145 – 3Q = 30 + 2Q
- 5Q = 115
- Q = 23
Substituting Q = 23 into either the demand or new supply equation, we find:
- P = 145 – 3(23)
- P = 145 – 69
- P = $76
Therefore, the new equilibrium price is $76, and the equilibrium quantity is 23 units of gasoline. This analysis is similar to understanding how varying price levels such as $1.40 per gallon versus $1.80 per gallon affect the quantity demanded and supplied as described in Figure 3.4.