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### Sample Exercise

Q1: Essential goods are goods that have to be present in positive quantities in a consumption bundle in order for the individual to get utility above what he/she would get by not consuming anything at all.

1. Draw an indifference curve where x1 is essential, but x2 is non-essential.
2. Is it possible for tastes to be non-monotonic but still homothetic?
3. Is it possible for tastes to be monotonic, homothetic but strictly non-convex? Illustrate this, if it is
4. Construct an indifference map for a consumer who consumes goods andwhere there is a satiation point such that there is an overall best bundle. What can we say about the slope of the indifference curves at different points?
5. Say you are stranded on a deserted island, with no hope of rescue. Construct an indifference map where the two ‘goods’ are ‘Amount of cash’ and ‘units of food per week’. (Think about ‘cash’ as a useless good – after all, it’s useless on a deserted island). What would indifference curves look like and why?

Q2 Consider two goods X and Y. Draw the budget constraint for these two goods, with X on the horizontal axis and write out the equation for it, assuming income is denoted by M and the prices of X and Y are denoted Clearly mark the intercepts and identify the slope of the budget constraint.

Assume that is Pasta and Y is coffee. What will happen to the budget constraint if:

1. The government imposes a quantity tax (t) on coffee?
2. a lump sum tax?
3. rations pasta to ?
4. The government imposes a tax, t, on past consumed beyond ?
5. The consumer receives an in-kind transfer of 40g of pasta?
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