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Supply and demand curves are fundamental in economics, helping us understand how the market operates. These curves graphically represent the relationship between the price of a good and the quantity supplied or demanded by the market. The supply curve generally slopes upwards, reflecting the idea that higher prices incentivize producers to supply more of a product. In our original exercise, the supply curve is represented as \(q = 0.5p - 25\), indicating how the quantity supplied, \(q\), increases with price, \(p\).
A demand curve, on the other hand, typically slopes downwards, signifying that consumers tend to buy more at lower prices. For the exercise, the demand curve is \(q = 165 - 0.5p\). Here, it shows that as the price increases, the quantity demanded decreases.

• Supply Curve: Quantity supplied increases with price.
• Demand Curve: Quantity demanded decreases as price increases.
• Intersection: Equilibrium is found where these curves intersect.

Taxes directly impact the supply curve. When a tax is imposed on producers, it effectively increases the cost of production per unit. This upward shift can be illustrated by shifting the supply curve vertically. In the exercise, a tax of \(\$8\) per unit changes the supply curve from \(q = 0.5p - 25\) to \(q = 0.5p - 29\). This equation shows that for any given price, the quantity supplied decreases by the amount of the tax.

• Effect of Tax: The supply curve shifts up, decreasing the quantity supplied at every price point.
• Consumer Impact: Prices tend to increase when the supply curve shifts upwards, affecting consumers.
• Business Impact: Producers adjust supplied quantities due to added costs, balancing between pricing and quantity supplied.

Understanding this shift helps to see the broader economic implications of taxing suppliers, such as potential decreases in production or adjustments in pricing strategies.

Calculating equilibrium is crucial in analyzing market trends and setting strategic pricing. The equilibrium price and quantity occur where the supply and demand curves intersect, meaning the quantity demanded equals the quantity supplied. In the exercise without tax, the supply \( q_s = 0.5p - 25 \) and demand \( q_d = 165 - 0.5p \) were set equal to find the initial equilibrium price of \( \\(190 \) and quantity of 70 units.
After a tax is introduced, the supply curve shifts, creating a new point of intersection with the unchanged demand curve. This new equilibrium is determined by solving \( q_s = 0.5p - 29 \) against \( q_d = 165 - 0.5p \), leading to a new equilibrium price of \( \\)194 \) and a reduced equilibrium quantity of 68 units.

• Initial Conditions: Equilibrium found by setting original supply and demand equations equal.
• With Tax: New equilibrium derived from updated supply curve.
• Resulting Impact: Price covers cost of tax, quantity slightly decreases.

Equilibrium calculations show how market forces adjust to new economic conditions, such as taxes, ensuring a balance is maintained.