Final answer:
To find the rate of change in demand for a given price using the demand function, solve the function for Qd in terms of P and the rate of change is the coefficient of P. In the example, the demand function P = 8 - 0.5Qd can be rearranged to Qd = 16 - 2P, hence the rate of change is -2.
Step-by-step explanation:
To find the rate of change in the demand x (Qd) for the given price p, we can use the demand function provided. In this context, the rate of change is essentially the derivative of the demand function with respect to the price, which measures how demand changes as price changes. According to the information provided, the demand function is represented by the equation P = 8 - 0.5Qd. Here, P represents the price, and Qd represents the quantity demanded. We can rearrange this equation to make Qd the subject, obtaining Qd = 16 - 2P. The rate of change is then the coefficient of P when the demand function is written in this form, which is -2. That means for every unit increase in price, the quantity demanded will decrease by 2 units.
The given scenario shows that for a price of $2, the quantity demanded and supplied is 12, indicating the point of equilibrium as per the supply and demand model. This calculation also complies with the economic principle where quantity demanded equals quantity supplied (Qd = Qs) at equilibrium.
Cross-price elasticity has also been mentioned. It is measured as the percentage change in the demand for one good divided by the percentage change in the price of another good. For example, an increase of the price of oranges by 3% leads to a decrease in the demand for apples by 1.2%, assuming a cross-price elasticity of 0.4.