Elina spends all her monthly income () on dahlia bulbs (for planting in her garden) and cat toys for her cat (Dino). Let good 1 be dahlia bulbs and good 2 be cat toys. Prices are given by 1 and 2 respectively. If graphs are needed, let good 1 be the x-axis good. For every budget constraint that you graph be sure to label all relevant features of the budget constraint, including any intercepts, slopes, kinks, etc. Be specific.

Please use the notation for an ad valorem tax, for a quantity tax, for a quantity subsidy or lump sum subsidy, and for an ad valorem subsidy, if needed, to be as specific as possible when you wrote equations, slopes, and intercepts, etc. (You can safely assume that any prices, taxes, and subsidies are positive and non-zero).

a. Write down the equation of Elinas monthly budget constraint. Please write this budget constraint in the form weve

practiced in class, 2 as a function of 1 ("slope-intercept form"). In fact, to help us out shortly, lets write x2 in this

budget constraint as (), the amount of cat toys affordable before any interesting policies (see below) are put into 2

place.

b. Graph Elinas budget constraint.

c. Consider the following policy: As a part of pandemic relief efforts, Elina receives a lump sum subsidy of . At the

same time, there is an ad valorem subsidy () provided for dahlia bulbs. Write down the equation of Elinas monthly budget constraint with this new policy in place. Please write this budget constraint in the form weve practiced in class, x2 as a function of x1 (slope-intercept form). In fact, to help us out shortly, lets write x2 in this new budget constraint as (xc), the amount of cat toys affordable under this policy in part (c).

d. Graph Elinas new budget constraint (you can do this in the same graph as in part b). Can you see that for any amount of dahlia bulbs, with the policies in part c, she can now afford more cat toys than before? We will formalize this below.

e. Here I want you to prove that under the policies described in part c, Elina can now afford more cat toys (given any

amount of dahlia bulbs) than she could before the policy was put in place. That is, suppose she buys the same

amount of dahlia bulbs (x1) originally and under the new policy. Prove that (at this quantity of dahlia bulbs

purchased, x1) Elina can now consume more cat toys than she originally could, due to the new policy changes in part

c. Hint, use your budget constraints in part a and c and show > h > 0. Simplify 22 22

your answer and make it as clear as possible. Remember that a proof is a mathematical explanation to your reader. Show your reader everything- dont assume they know it already!