Consider a two-commodity (one private good and one public good) economy. The price of the private good is constant and PG is the price of each unit of the public good.

(a) In what condition is the fraction of the budget spent on the public good increases as the (relative) price of public good increases. Show calculation and explain your work.

(b) The demand for the public good at time t, is given by the function Gt = log(Yt) + (1/2)(Yt)^beta-1, where Yt is national income at time t. What is the income elasticity of demand? What is the effect of an increase in income on demand for the public good when beta > 1.

(c) Now consider the same demand function as the previous part while the price for each unit of the public good is p. Assume there are n consumers in the economy who have been equally divided into two groups. Group L who have low income and group H with high income. Government redistributes income by taking an amount (alpha) from each consumer of group H and giving that to consumers in group L. Also assume members in L receive unequal shares. Calculate the new Gt.