Hello i am stuck on this question regarding consumer consumption.

Hello i am stuck on this question regarding consumer consumption. Can i please get some help and caculations

QUESTION 2. A consumer starts with an income of $120 which she can spend on either food (measured on the x-axis), or on booze (measured on the y axis). If the price of food is $5 and the price of booze is $2, the consumer’s budget constraint is 5x + 2y = 120. We are going to compare three different policies for two different consumers. The policy options are:

A) The government subsidizes the price of food by1 dollar for the consumer

B) Gives the consumer $15

C) Gives the consumer 3 units of food which cannot be traded for booze.

a) For the first part, assume the consumer has an MRS = y/x. Show the following:

i) Given the consumer’s choice under policy (A), policy (A) and (B) cost the same

ii) Draw the two budgets under policy (A) and (B) together on the same graph. Specifically find where they intersect. Draw the indifference curve through the optimal in (A), then explain why the optimal point with (B) must make the consumer better off.

iii) Policy (B) and (C) are exactly the same for the consumer

b) Now assume the consumer has an MRS = y/17x. Now show that the policy in (B) and the policy in (C) are not the same for this consumer. Find the optimal food and booze under budget (B) but explain that is not possible under policy (C).

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