Questions and Answers of Intermediate Microeconomics

We claimed in the text that if preferences were monotonic, then a diagonal line through the origin would intersect each indifference curve exactly once. Can you prove this rigorously? (what would
Which of the following are monotonic transformations? (1) u = 2v − 13; (2) u = −1/v2; (3) u = 1/v2; (4) u = lnv; (5) u = −e−v; (6) u = v2; (7) u = v2 for
The text said that raising a number to an odd power was a monotonic transformation. What about raising a number to an even power? Is this a monotonic transformation? Consider the case f(u) = u2.
If the consumer is consuming exactly two goods, and she is always spending all of her money, can both of them be inferior goods?
Show that perfect substitutes are an example of homothetic preferences.
Show that Cobb-Douglas preferences are homothetic preferences.
Our thoughts return to Ambrose and his nuts and berries. Ambrose’s utility function is U(x1, x2) = 4√x1 + x2, where x1 is his consumption of nuts and x2 is his consumption of berries.(a) Let us
Are hamburgers and buns complements or substitutes?
If the preferences are concave will the consumer ever consume both of the goods together?
Donald Fribble is a stamp collector. The only things other than stamps that Fribble consumes are Hostess Twinkies. It turns out that Fribble’s preferences are represented by the utility function
What kind of preferences are represented by a utility function of the form u(x1, x2) = √(x1 + x2)? What about the utility function v(x1, x2) = 13x1 + 13x2?
Think of some other goods for which your preferences might be concave.
Joan likes chocolate cake and ice cream, but after 10 slices of cake, she gets tired of cake, and eating more cake makes her less happy. Joan always prefers more ice cream to less. Joan’s parents
Murphy was consuming 100 units of X and 50 units of Y. The price of X rose from 2 to 3. The price of Y remained at 4. How much would Murphy’s income have to rise so that he can still exactly
If good 1 is a “neutral,” what is its marginal rate of substitution for good 2?
What is your marginal rate of substitution of $1 bills for $5 bills?
Explain why convex preferences means that “averages are preferred to extremes.”
If both pepperoni and anchovies are bads, will the indifference curve have a positive or a negative slope?
Could Figure 3.2 be a single indifference curve if preferences are mono-tonic?Figure 3.2 : X2 Alleged indifference curves X1 Indifference curves cannot cross. If they did, X, Y, Z would all have to
Can an indifference curve cross itself? For example, could Figure 3.2 depict a single indifference curve?Figure 3.2: X2 Alleged indifference curves X1 Indifference curves cannot cross. If they did,
A college football coach says that given any two linemen A and B, he always prefers the one who is bigger and faster. Is this preference relation transitive? Is it complete?
Take the same group of people and consider the relation “strictly taller than.” Is this relation transitive? Is it reflexive? Is it complete?
Consider a group of people A, B, C and the relation “at least as tall as,” as in “A is at least as tall as B.” Is this relation transitive? Is it complete?
If we observe a consumer choosing (x1, x2)when(y1, y2) is available one time, are we justified in concluding that (x1, x2) ≻ (y1,y2)?
On the planet Mungo, they have two kinds of money, blue money and red money. Every commodity has two prices—a red-money price and a blue-money price. Every Mungoan has two incomes—a red income
Harry Hype has $5,000 to spend on advertising a new kind of dehydrated sushi. Market research shows that the people most likely to buy this new product are recent recipients of M.B.A. degrees and
If the income of the consumer increases and one of the prices decreases at the same time, will the consumer necessarily be at least as well-off?
Suppose that a budget equation is given by p1x1 + p2x2 = m.The government decides to impose a lump-sum tax of u, a quantity tax on good 1 oft, and a quantity subsidy on good 2 of s. What is the
Suppose that the government puts a tax of 15 cents a gallon on gasoline and then later decides to put a subsidy on gasoline at a rate of 7 cents a gallon. What net tax is this combination equivalent
Suppose that there were 25 people who had a reservation price of $500, and the 26th person had a reservation price of $200. What would the demand curve look like?
In the above example, what would the equilibrium price be if there were 24 apartments to rent? What if there were 26 apartments to rent? What if there were 25 apartments to rent?
If people have different reservation prices, why does the market demand curve slope down?
In the text we assumed that the condominium purchasers came from the inner-ring people—people who were already renting apartments. What would happen to the price of inner-ring apartments if all of
Suppose now that the condominium purchasers were all inner-ring people, but that each condominium was constructed from two apartments. What would happen to the price of apartments?
What do you suppose the effect of a tax would be on the number of apartments that would be built in the long run?
Suppose the demand curve isD(p) = 100 − 2p. What price would the monopolist set if he had 60 apartments? How many would he rent? What price would he set if he had 40 apartments? How many would he
If our model of rent control allowed for unrestricted subletting, who would end up getting apartments in the inner circle? Would the outcome be Pareto efficient?
Originally the consumer faces the budget line p1x1 + p2x2 = m.Then the price of good 1 doubles, the price of good 2 becomes 8 times larger, and income becomes 4 times larger. Write down an
What happens to the budget line if the price of good 2 increases, but the price of good 1 and income remain constant?
If the price of good 1 doubles and the price of good 2 triples, does the budget line become flatter or steeper?
What is the definition of a numeraire good?

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