Final answer:
To derive the demand curves for Roger's utility function, we assess the optimal choice of consumption for goods B and Z given his income and the prices of the goods. The demand curve is plotted by mapping the changes in quantity demanded as a result of varying prices (ceteris paribus) and income changes for different goods.
Step-by-step explanation:
The student's question involves deriving demand curves from Roger's utility function, which is given in a Cobb-Douglas form. To derive the demand curves for goods B and Z, we need to use Roger's income, the prices of the goods, and his utility function.
By doing so, we are looking for the combination of goods B and Z that maximizes Roger's utility subject to his budget constraint, which can be mathematically represented as Y = pB * B + pZ * Z. Varying the prices of B and Z and recalculating the optimal quantities gives us different points on the demand curve for each good.
As the price of a good increase, ceteris paribus, the budget constraint rotates clockwise, leading to a change in the utility-maximizing choice and a shift in the quantity demanded of that good. This relationship between price and quantity demanded is plotted to create the demand curve. Similarly, when income changes, the budget constraint will shift, which in turn modifies the demand for normal and inferior goods. All of these principles help to shape the demand curve by tracing how Roger's optimal choices change in response to price and income variations.