Please answer all parts of questions 3 and 4 and please be neat and show all your work. I would greatly appreciate it.

Problem Set #2 Due: Friday, January 13, at the end of class. Econ 21, Winter 2023 Dr. Petre Instructions: ANSWER THE FOLLOWING QUESTIONS m YOUR OWN WORDS. Question 1 3) Suppose that the price of cheese is $4, the price of ham is $2, and that you have $12 to spend (income). Write an equation for the budget constraint and plot the budget constraint with cheese on the vertical axis. b) Now, suppose that the price of cheese decreases to $2 and the price of ham and income remain the same. Write an equation for your new budget constraint and plot the budget constraint with cheese on the vertical axis. What happened to the slope of the budget constraint relative to part (a)? c) Suppose that income increases to $16,and that prices are the same as in part (b). Write an equation for the budget constraint and plot the budget constraint with cheese on the vertical axis. What happened to the slope of the budget constraint relative to part (a)? Relative to part (b)? Question 2 Waldfogel argues that girgiving holidays create economic inefciency. This argument is all about the budget constraint. In this problem you will represent Waldfogel's argument in a different graphical way than he does in his paper. a) Imagine that you, a college student, have a budget of $1,000. You can spend this money on sweaters ($50 each) or \"all other goods\" (think of this as money, with a price of $1). Write your budget equation using 5 for sweaters and 1' for all other goods. Draw your budget constraint (with sweaters on the vertical axis). b) Imagine your aunts give you a gift of $500 (total). Write your budget equation. Draw your new budget constraint Shade the set of bundles you can afford now that you could not afford before. Are you probably happier than part a? Why? c) Imagine that instead your aunts give you a total of 10 sweaters (value: $50 each) and you can trade them in for their market mlue to buy other goods. Write your new budget equation. Hint: start by putting your endowment on the right-hand side of the equation (but now your endowment is not just money...) Draw your new budget constraint. Are you probably happier than part a? Than part b? Why? I d) Finally, imagine instead that your aunts gave you a total of 10 sweaters ($50 value each) but you CANNOT trade them in because your aunts will be angry. Write your new budget. Hint: this will involve the budget equation plus a second constraint. Draw your new budget constraint, Are you probably happier than part a? Than part c? Why? Question 3 For each part that follows, do the following. (Note: do not use the table from the textbook to copy down MUS and MRSs; work through it on your own.) (Note: part a will have \"well-behaved preferences,\" parts b and c will not.) i. Write an equation that could represent the utility function (in each case, there are many possible answers; just write one that meets the criteria) ii. Graph two or more indifference curves iii. For that utility function, what is the marginal utility for each good? iv. What is the MRS'.7 Do these preferences represent diminishing MRS? a) I eat chocolate (C) and \"All Other Goods" (AOG, or A). My marginal rate of substi- tution between chocolate and AOG is diminishing in chocolate (and my MRS between AOG and chocolate is diminishing in AOG). b) I snack on milk (M) and cookies (K). I insist on having one cup of milk for every three cookies. I get no pleasure from either more milk (I do not like the avor) or more cookies (too dry) beyond that ratio. (MRS will be tricky here, so describe it as clearly as you can but your notation need not be perfect.) c) I only eat strawberries. I can buy strawberries in a pint (P) or quart (Q); the straw- berries are identical in either case, but a quart is the size of two pints. Question 4 For each part that follows, assume I buy only newts (n) and frogs (f) and have income y. My budget constraint is pun + pff S y. i) Identify the type of preferences: perfect substitutes, perfect complements, or plain old diminishing marginal rate of substitution preferences. ii) For each case, solve the consumer's choice problem: nd my demand for newts and frogs as functions of market prices and income. 21) um, f) = 21m) + ln( f) b) u(n,f):3n+7f c) u(n,f) :minn, f} Question 5 For each part that follows, assume I buy only bananas (b) and mangos (m) and have income y. My budget constraint is pbb+ pmm S 1,1. For each case, solve the consumer's choice problem: nd my demand for bananas and mangos as functions of market prices and income. i) Identify the type of preferences: perfect substitutes) perfect complements, or plain old diminishing marginal rate of substitution preferences. ii) For each case, solve the consumer's choice problem: nd my demand for bananas and mangos as functions of market prices and income. a) u(b, m) : 2l7'/Zm'/2 b) u(b, m) : 2b + 2721 c) u(b, m) = min{3b, 5m} Question 6 Describe a situation in which a person's preferences violate: a) Completeness b) Monotonicity (choose something that violates even weak monotonicity; it should also be neither always good nor always bad) c) Convexity (choose something that violates even weak convexity) Question 7 What is the tradeoff represented in the slope of the indifference curve? What is the tradeoff represented in the slope of the budget constraint? How are these different from each other? Question 8 How do you know when you can use the Lagrangian method to solve a consumer choice problem? Question 9 How do these concepts relate to each other: a) Utility, preference, and indifference curves