Problem 1 Explain your answers!
In Spring 2020 Gary consumed two goods: packs of toilet paper (with quantity denoted by t) and `dollars spent on everything else' (quantity denoted by e).
a) Suppose a pack of toilet paper costs $6 and Gary's income is m = $60. Write down Gary's budget constraint and plot his budget set and budget line (put t on the horizontal axis, as good 1). Label the axes, intercepts and everything else carefully. Find the slope of the budget line.
The following applies for parts (b)-(d). Now suppose that there are only two stores Gary could go to Costco and Save on Foods. Save on Foods allows each customer to purchase maximum 2 packs of toilet paper, at $6 each. Costco sells packs of toilet paper for $5 each but only if a customer spends at least $30 on everything else (no toiled paper can be bought otherwise). Gary's income is still $60.
(b) Plot Gary's budget line if he goes to Costco. On the same graph, plot his budget line if he goes to Save on Foods instead.
(c) Can Gary buy the bundle (5 , 30) (5 toilet paper packs and $30 spent on everything else) from Save on Foods? How about from Costco? Explain why or why not.
(d) Are there valid preferences for Gary (plot an example indifference curve) so that he would rather go to Save on Foods instead of Costco? Explain why or why not.
Problem 2 Explain your answers!
Andy consumes only coffee and sandwiches and has a utility function u(x1, x2) = 3ln(x1) + 6ln(x2) where x1 is the quantity of coffee and x2 is the number of sandwiches consumed. ln(x) denotes the natural logarithm of x. Suppose a coffee costs $2 and a sandwich costs $p. Andy's income is $m.
(a) Write down Andy's consumer's problem of choosing his optimal consumption bundle.
(b) Find Andy's demand function for sandwiches. How does it depend on p and m (increasing, decreasing, constant)? Are sandwiches an ordinary good for Andy? Explain why or why not.
(c) Find the equation of Andy's Engel curve for sandwiches (i.e., express m in terms of x2). Are sandwiches a normal good for Andy?
(d) How many coffees and sandwiches would Andy consume if his income is m=$120 and a sandwich costs p=$5? Starting from that, how would Andy's optimal consumption bundle change if a $1 quantity tax is imposed on coffee and Andy is given $15 lump-sum subsidy to his income? Is he better off or worse off after the tax and subsidy compared to before?
(e) Jenny also consumes only coffee (at price $2) and sandwiches (at price $p) but has the utility function 2x1 + 25 ln(x2). If her income is $55 and p = $5 find her optimal consumption bundle. What quantities of coffee and sandwiches would Jenny consume if her income was $10 instead?