Micro-foundations for Consumption (50 marks total) Consider an economy in which a representative household lives for two periods (year t and year t + 1). The representative household derives utility from consumption and discount the future at rate . The households life time utility is given by: U = ln ct + ln ct+1 The household receives income from work in both period yt and yt+1 respectively and has no nancial wealth. The inter-temporal budget constraint for an household can be written in present discounted values as ct + ct+1 1 + R = yt + yt+1 1 + R where you can interpret yt+1 as expected income. a) (5 marks) Write down the maximization problem in detail