The Lager curve 3; = R\") proposes a simple theoretical relationship between a government's tax revenue R(t} and tax rate t: RU] = 1W). where Mt) is the tax base for tax rate 1 that is, the total dollar amount of economic activity taxable at tax rate t. The dependence of b(t) on t comes from things like changes in people's spending habits or companies' investment plans based on the tax rate. Because t represents a tax rate, it is restricted to be in the interval [0, 1]. (For example, if you have a tax base of $20billion and a. tax rate of %, $5 billion goes to the government through taxes, and $15 billion remains with the economic actors.) In this assignment, you may use without proof the assumption that b(t) is continuous on the interval [1}. 1] and cliHerentiable on the interval {0.1). You may also look up terms and arguments online, though it is certainly possible to get full marks on the assignment without doing so. 2. (a) In a paragraph, explain why it is plausible that H\") (I on the interval (0, I}? Justify your answer in one or two paragraphs. You may assume that b'(t)