Final answer:
The demand functions for coffee and theorems show that as the price increases, the quantity demanded decreases. These functions follow the law of demand and indicate the professors' sensitivity to price changes in their consumption choices. Graphing these demand curves would illustrate their relationship with supply to determine equilibrium price and quantity.
Step-by-step explanation:
When analyzing the consumption choices of professors in the Economics department for coffee and theorems, we look at their demand functions: daily demand for coffee is represented as QCd = 9 - PC and daily demand for theorems is QTd = 12 - 2PT. These equations imply that as the price of coffee (PC) increases, the quantity demanded for coffee (QCd) decreases, and similarly for theorems, as price (PT) increases, the quantity demanded for theorems (QTd) decreases at twice the rate. This characteristic shows a negative relationship between price and quantity demanded that is typical in demand functions, following the law of demand.
The implications for consumption choices are such that if the price of either good increases, professors will demand less of it. This also establishes an inversely proportional relationship between the price of a good and its demanded quantity, which is a fundamental concept in economics. If we plot these functions on a graph with price on the vertical axis and quantity on the horizontal, we would get a downward sloping line representing the demand curve for each good. Where this demand curve intersects with the supply curve (not given in the question), it would determine the equilibrium price and quantity, reflecting the point at which the quantity demanded equals the quantity supplied.a