Lucy’s utility function is 2XL + GL and Melvin’s utility function is XMGM, where G is their aggregate consumption units of a public goods (i.e., G = GL + GM) and where XL and XM are their respective private consumption of good X. The total amount they have between them to spend on private goods and public goods is £28,000. They agree on a Pareto optimal allocation in which the amount that is spent on Lucy’s private consumption is £10,000. Assuming that the unit price of X and G is £1. How much do they spend on public goods? Explain your steps in reaching your answer and any relevant concepts.