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introduction to microeconomics

Questions and Answers of Introduction To Microeconomics

When prices are (p1, p2) = (1, 2) a consumer demands (x1, x2) = (1, 2), and when prices are (q1, q2) = (2, 1) the consumer demands (y1, y2) = (2, 1). Is this behavior consistent with the model of
If a consumer has a utility function u(x1, x2) = x1x4 2, what fraction of her income will she spend on good 2?
Suppose that you have highly nonconvex preferences for ice cream and olives, like those given in the text, and that you face prices p1, p2 and have m dollars to spend. List the choices for the
Suppose that a consumer always consumes 2 spoons of sugar with each cup of coffee. If the price of sugar is p1 per spoonful and the price of coffee is p2 per cup and the consumer has m dollars to
Suppose that indifference curves are described by straight lines with a slope of −b. Given arbitrary prices and money income p1, p2, and m, what will the consumer’s optimal choices look like?
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? (Hint: consider the case f(u) =
Could Figure 3.2 be a single indifference curve if preferences are monotonic
Can an indifference curve cross itself? For example, could Figure 3.2 depict a single indifference curve?
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?
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 of t, 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
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 equation
What do you suppose the effect of a tax would be on the number of apartments that would be built in the long run?
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
An entrepreneur has a venture that will make either $100 million or $0.The chance that this venture will make $100 million depends on the effort level expended by the entrepreneur: If she tries hard,
As an insurance underwriter, you have been asked to write a policy that insures a factory against loss by fire for a period of 1 year. If the factory has a fire, it will be a total loss of $8
This problem takes you to the precise solution of a very standard (toy)model of incentive compensation. We imagine a salesperson whom you have employed to make one sales call. If he succeeds, you
Change the FECBUS/Beantown Casualty story of Problem 20.2 as follows.All students at FECBUS are identical in their chances of getting a job, but to land a job, they must put in an effort. They choose
Three construction firms, Ace, Base, and Case, are considering whether to declare their willingness to undertake a contruction project for the Freedonian government. The cost of fulfilling this
In the U.S. real estate brokerage industry, brokers employed by large brokerage firms have traditionally worked for a portion of the commissions they generate. That is, if a house sale generates a 6%
In the 1980s and 1990s, a large number of first-tier firms offered no-layoff employment. These firms promised employees that, perhaps after a probationary period, an employee had a job for life; he
In some countries, title to an automobile includes a history of previous owners. And in those countries, the price for a particular car, holding fixed the car model and features, miles driven, and
Among the benefits offered by corporations, at least in the United States, is health insurance. One explanation for why corporations offer such insurance is that this benefit is tax favored:
In a particular economy, all homeowners own identical homes worth$80,000 apiece. These homes are subject to complete loss via fire, and the Old Reliable Insurance Company (ORIC) offers policies
At the Famous East Coast Business School (FECBUS), all MBA students want summer jobs working for investment banks in New York City. They want this sort of job so much that, if they are not offered a
The seminal paper on the topic of adverse selection (in the literature of economics) is Akerlof’s “The Market for Lemons.” He describes a used-car market in which each used car that is worth X
John, Paul, George, and Ringo are partners in a venture that has four possible outcomes: $100,000 with probability 0.4, $200,000 with probability 0.3,$300,000 with probability 0.2, and $400,000 with
Jan, Joe, and Jess MBA each own a gamble with equally likely outcomes of $50,000 and −$25,000. Each is attempting to sell 1% shares to friends and associates. But all the friends and associates of
Consider the following market in equity shares in entrepreneurial ventures:• Each share represents a 1% share in a venture.• Each venture will pay off either $50,000 or −$25, 000 (and there is
Jan MBA’s gamble does indeed pay off $50,000 with probability 0.7 (and loses $25,000 with probability 0.3). But to sell shares in her venture, Jan has to reveal some of the details of her venture.
Suppose Jan MBA is convinced that her gamble will pay $50,000 with probability 0.7 (and lose $25,000 with probability 0.3). But everyone else in the world thinks the two probabilities are 0.5 and
Suppose Jan from Problem 19.1 tries to sell an ↵ share of the gamble to a risk-averse expected-utility maximizer. No risk-averse person would pay “full EMV price,” or $12,500↵, for an ↵
Consider the plight of Jan MBA, who owns a gamble with two equally likely prizes, $50,000 and −$25,000. Jan is an expected utility maximizer with utility function u(x) = −e−0.0000211x . As we
(This problem foreshadows the topic of Chapter 19; it is well worth trying.If you have problems with the exponential utility function, please see the discussion in the Online Supplement.)Jan MBA has
Suppose we offered Professor Patel from Problem 18.1(c) his choice of the following three gambles:• Gamble A pays $50,000 with certainty.• Gamble B pays $100,000 with probability 0.8 and $0 with
A decision-maker faces the following decision under conditions of uncertainty.This decision-maker has $1 million in assets. Most of those assets,$750,000, are the individual’s equity in his house.
Jack and Jim are twins who have the same utility function, given by u(x) = px, where x is the amount of money they have in the bank after the results of any gambling they undertake in the course of
To the three individuals in Problem 18.1, we add three more:(a) Alice, whose utility function for her final bank account is u(x) = x1/2 and who starts with $50,000 in the bank.(b) Bob, whose utility
Consider the three gambles depicted in Figure 18.8 and three decisionmakers, each of whom chooses among gambles based on expected utility. For each of these three, the utility function argumentis
Among the ways to protect your car or truck from theft are “crowbar”devices that lock the steering wheel in place and the LoJackTM theft-recovery system. The LoJack system works by hiding a small
Consider a firm with the sort of shared resource–congestion problem sketched in the final section of this chapter. Imagine that the shared facility has a capacity for, say, 500 units of work per
The Freedonian people love fish caught in Lake Bella, a large lake in the middle of Freedonia. This fish is a great delicacy, and Freedonians are willing to pay quite a lot for it. In addition, the
The business district of the capital of Freedonia, Freedonia City, sits on an island. Most of the people who work in this district commute from the mainland. Specifically, 400,000 people make this
Suppose that a particular perfectly competitive industry has 10 identical firms, each with the marginal-cost function MC(y) = 4 + y . Suppose that the demand function for the item in question is D(p)
In the chapter, I asserted that, if the world supply curve of rice is nearly flat, it is clear that foregone Japanese consumer surplus from any combination of quotas and tariffs is greater than the
Onpage 367, I described three “programs” by which the government could support the price of a good above the equilibrium price that would be set in a competitive market. In the first program, the
Suppose that, in the situation of Problem 16.7, Prime Minister Firefly considers a different course of action: He would allow the importation of some sorghum, by granting to each of 10 good friends
Rufus T. Firefly, prime minister of the country of Freedonia, faces an economic crisis. The citizens of his country are demanding the free importation of sorghum, and sorghum producers are
(a) Consider a firm with market power that faces the inverse-demand function P(x) = (100 − 0.001x) and has a constant marginal cost of production equal to $20. The government decides to subsidize
Derive formulas similar to those given in the text for taxes on a competitive industry, but for a subsidy of size s per unit, paid directly to the manufacturer by the government.
Suppose, in a competitive market, the supply function is S(p) = 5000(p−2)and the demand function is D(p) = 2000(16 − p) . If a tax of $0.70 is placed on the good, by how much does the equilibrium
And derive the formulas on page 361 for a tax imposed on a firm with market power.
If you did Problem 16.1, you know that the formulas really do work. So now the question is why. Derive the formulas given on pages 357-8 for a tax placed on a competitive industry. The key is to
(a) Consider a good for which the supply function is S(p) = 2000(p−4) (for prices 4 and above) and the demand function is D(p) = 1000(10 − p) . What are the equilibrium price and quantity for
Imagine a market for a good in which demand is given by D(p) =10,000(10 - p). Twenty-five identical firms supply this good, each of which has the total-cost function TC(x) = 47 + 12/200. All these
Suppose the demand for pairs of shoes in the People's Republic of Slynavia is given by D(p) = 250.000(90 - p). (To keep the discussion simple, assume that each consumer wishes to buy at most a single
Imagine a monopoly whose marginal-cost function is MC(r) = 4+1/1000, facing a demand function given by D(p) = 3000(20 - p). What producer and consumer surpluses result if the monopoly maximizes its
Figure 15.8 depicts the average- and marginal-cost functions for a firm with a fixed cost and rising marginal cost. It also gives a demand function and marginal-revenue function for the firm,
Refer to Problem 14.7. An industry has free entry and exit for an unlim-ited number of firms, each having total-cost function TO(=) = 100+ 3x +0.0471.The industry demand is initially given by D(p) =
Problem 14.9 described a perfectly competitive industry with four firms having the total cost function TO(r) = 50 + 1 + 0.04x" and an unlimited supply of firms having the total cost function TO(x) =
Suppose the supply of a particular good is given by S(p) = 1000(p while demand is given by D(p) = 3000(20 - p). What is consumer surplus at the equilibrium of this market? What is producer surplus?
Suppose that, in the toy model with sunk costs given beginning on page 324, the sunk cost of entry is $100,000. Redo the analysis to find the “long-run equilibrium” in terms of number of active
I assert that a profit-maximizing competitive firm that turns a strictly positive profitmustproduceabove its efficient scale. Backonpage 144, I asserted that a profit-maximizing firm with market
Suppose that, in Problem 14.8, instead of eight firms with the cost function from Problem 14.7, an unlimited number of firms possess this cost function.Assume that all fixed costs can be avoided if a
Suppose, in the industry of Problem 14.7, four firms have a superior production technology, which gives each the total-cost function TC(x) = 50 +x + 0.04x2 . An additional eight firms have the cost
Suppose that, in a particular perfectly competitive industry, the technology for making the product (by any single firm) has the total-cost function TC(x) =100 + 3x + 0.04x2. An unlimited supply of
Suppose that, in a perfectly competitive industry, every firm has totalcost function TC(x) = 10 million + 2x + x2/100,000. Demand is given by D(p) =500,000(42 − p) .(a) If the industry consists of
Suppose a particular perfectly competitive industry has 10 identical firms, each with the total-cost function TC(x) = 4x + x2/2. There is no possibility of entry into or exit from this industry. If
A consumer with the money-left-over utility function u(x) + m =10 ln(x + 1) + m is endowed with 100 units of x and $1000. This consumer can buy or sell the commodity in question, depending on its
A competitive firm has the marginal-cost function MC(x) = 8 − x/10 +x2/2000 and the total-cost function TC(x) = 8x − x2/20 + x3/6000. What is this firm’s supply function? Suppose the firm has a
A competitive firm has marginal cost function MC(x) = 3 + x/20,000. The total cost function for this firm is TC(x) = F1 + F2 + 3x + x2/40,000, where F1 and F2 are fixed costs: The firm can avoid
Acompetitivefirmhas total cost function TC(x) = 5 million+5x+x2/10,000.Regarding its fixed cost of $5 million, $4 million can be avoided if the firm produces 0, but $1 million is completely
This problem concerns a market for a commodity item in which there are many sellers, all firms that produce the item, and many buyers, who are consumers. Supply of the product depends on the price
Go back to the basic story of a firm with production function f(m, l) =l1/3m1/6 , where pl = 4 and pm = 1, where the firm has additional fixed costs of 300, and where inverse demand is given by P(x)
Derive the SRTC function displayed in the middle of page 276. (This should not be that hard.)
(a) Using Excel or some similar program, plot LRTC and SRTC for Story 2 (page 275), for x in the range 10 to 20.(b) Derive the short-run total-cost function given on page 275 for Story 2. This will
Suppose a firm that uses three inputs, k, l, and m, has production function f(k, l,m) = k1/2l1/3m1/6.The prices of the three inputs are, respectively, pk = 48, pl = 16, and pm = 1.The firm faces
(If you know linear programming, you might find it helpful to try to solve this problem by formulating the cost-minimization problem as a linear programming problem.) Suppose that we complicate
A firm that makes a particular bulk chemical can use either of two processes.The first involves hydration and then distillation. The second involves a completely separate catalytic process. The
Consider a one-product firm that has access to three sources for its output.If x1 units are produced by the first source, the total cost is TC1(x1) = x21/1000 +3x1. If x2 units are produced by the
Suppose f has fixed coefficients but not constant returns to scale. Specifically, suppose f(y) = G✓min⇢y1 b1, . . . , y`b`#◆, where G is an increasing real-valued function of one variable with
On page 254, I asserted that if we define the firm’s cost-minimization problem with a weak inequality in the constraint f(y) ! x, if f is continuous, and if f(0) = 0, then at the solution to the
Recall that the general Cobb-Douglas production function, for a firm with a single output and ` inputs, takes the form f(y1, . . . , y`) = Ky↵1 1 y↵2 2 . . . y↵`` , for strictly positive
Look at the isoquant diagram in Figure 11.5. In this figure, I give you the ten-unit isoquant only.(a) Suppose I told you this firm has constant returns to scale. Where would the 20-unit isoquant
A firm makes a patented product, called xillip, out of two inputs, raw material and labor. Letting x stand for the amount of xillip produced, m be the amount of raw material, and l the amount of
Figure 11.4 shows the 100-unit isoquant of a firm that makes a single product, utemkos, out of labor and materials. This isoquant comes from the production function f(l,m) = l1/2m1/2.(The isoquant is
Use calculus to solve the following cost-minimization problem. The firm has production function f(y1, y2, y3) = 10y1/2 1 y1/3 2 y1/6 3 .The three inputs have prices r1 = 6, r2 = 1, and r3 = 0.5.(a)
In Figure 11.3 and the discussion of it on pages 259 and 260, we found, using the graph, that if f(y1, y2) = 4y1/2 1 y1/3 2 and if the price of the two inputs were $6 for input 1 and $1 for input 2,
Afirmthat manufactures widgets(and only widgets)has a fixed-coefficients and constant-returns-to-scale technology, in which each widget made requires 10 units of labor, 12 units of material 1, 16
Imagine a single consumer whose utility function takes the money-leftover form U(x1, x2, . . . , xk,m) = v1(x1) + V (x2, . . . , xk) + m, where m is money left over after purchases of goods 1 through
(This problem is primarily for readerswholove math.) Figure 10.5 depicts a demand function that hits quantity 0 at a finite price and that (seemingly) goes to infinity as the price approaches 0. This
(a) Suppose a consumer has utility function U(b,c, f,m) = ln(b) + ln(c + 3) + (2f − f2) + m, where b is loaves of bread, c is kilos of cheese, f is kilos of fudge, and m is money left over. The
Aconsumer with $10 to spend on bread, cheese, and salami has the utility function U(b,c, s) = 4 ln(b) + ln(c+1) + 0.5 ln(s) . Describe as completely as you can the demand function of this consumer
Imagine a consumer choosing bundles consisting of an amount of cotton candy and an amount of double chocolate fudge. The consumer has a certain amount she can spend on these two confections and she
In Figure 10.6, I depict four indifference curves for an individual trying to decide how much wine to buy (where we consider money left over as the second good).(a) Suppose the price of wine is $10
Suppose that a consumer has $24 to spend for bread and cheese, where bread costs $1.20 per loaf and cheese costs $3 per kilo. Ona piece of graph paper,
Go back to Figure 10.3 and number the five dots consecutively, moving from left to right. Then, for the consumer whose indifference curves are shown in panel b of Figure 10.3, what is the rank order
Imagine a consumer who wants to purchase some cotton candy. This consumer’s choice behavior (in terms of her purchase of cotton candy) is described by utility maximization for the utility function
(a) Solve the consumer’s problem for a consumer with utility function U(b,c, s) = 10 ln(b) + ln(c + 1) + 0.5 ln(s + 4), if the prices are pb = $2, pc = $5, and ps = $10, and if the consumer has $83
(a) Solve the consumer’s problem for a consumer with the utility function U(b,c, s) = 8 ln(b + 2) + 6 ln(c + 1) + 2 ln(2s + 1), if the prices are pb = $1, pc = $2, and ps = $4, and the consumer has

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