1'Explain why training might be unduprovided in a free market explain and illustrate the effect of subsidy equal to the marginal external benefit being given to the training providers.

2,

A level assurance is payable immediately on the death of a man aged 40 provided (1) he dies after his 50th birthday, and (2) his death occurs after, but within 15 years of, the death of another life now aged exactly 45. Derive an expression in terms of assurance functions payable on first death for valuing this benefit, assuming that both lives are subject to the same mortality table. [7]