Can someone please help with question 2 and 3?

The Laffer curve y = R(t) proposes a simple theoretical relationship between a governments tax revenue R(t) and tax rate t:

R(t) = tb(t), where b(t) is the tax base for tax rate t 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 peoples 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 $20 billion and a tax rate of 1/4 , $5 billion goes to the government through taxes, and $15 billion remains with the economic actors.)

1. (a) In a paragraph, explain why it is plausible that b(t) < 0 on the interval (0, 1).

(b) Which scenario do you think is more plausible: that b(t) < 0 on the interval (0, 1), or that b(t) > 0 on the interval (0, 1)? Justify your answer in one or two paragraphs. You may assume that b(t) < 0 on the interval.

In the remainder of this assignment, you may assume that b(t) < 0 and b(t) < 0 on the interval (0, 1).

2. (a) Find R(0).

(b) In a paragraph, explain why it is plausible that R(1) = 0.

(c) Determine the concavity of R(t).

3. Draw a sketch of y = R(t).