Final answer:
To derive the demand for good X, the budget constraint PX + 5Y = 60 is used along with the utility function U = XY + 2Y to find the utility-maximizing quantities. By solving this system, one can express the demand for X as a function of its price P.
Step-by-step explanation:
You are tasked with determining the demand for good X as a function of its price P, given the utility function U = XY + 2Y, a price of £5 for good Y, and an income of £60. First, form the budget constraint by equating expenditure on goods X and Y to the income: PX + 5Y = 60. Next, find the utility-maximizing quantities by taking partial derivatives of the utility function with respect to X and Y and setting them to zero (considering the budget constraint through a Lagrange multiplier or the substitution method).
To find the demand function for X, solve the system of equations derived from the first-order conditions and budget constraint. Isolate variable X in terms of P to express the demand function for good X. Note that this problem assumes no change in the price of good Y or the income level when deriving the demand function.