Questions and Answers of Intermediate Microeconomics

In a congressional district somewhere in the U.S. West a new representative is being elected. The voters all have one-dimensional political views that can be neatly arrayed on a left-right spectrum.
Disneyland also offers a discount on admissions to residents of Southern California. (You show them your zip code at the gate.) What kind of price discrimination is this? What does this imply about
Suppose that the amusement park owner can practice perfect first-degree price discrimination by charging a different price for each ride. Assume that all rides have zero marginal cost and all
Suppose that a monopolist sells to two groups that have constant elasticity demand curves, with elasticity ε1 and ε2. The marginal cost of production is constant at c. What price is charged to each
A good can be produced in a competitive industry at a cost of $10 per unit. There are 100 consumers are each willing to pay $12 each to consume a single unit of the good (additional units have no
Suppose that the demand curve is given byD(p) = 10 − p. What is the gross benefit from consuming 6 units of the good?
Will a monopoly ever provide a Pareto efficient level of output on its own?
Suppose that a consumer is consuming 10 units of a discrete good and the price increases from $5 per unit to $6. However, after the price change the consumer continues to consume 10 units of the
Here are some drills on price elasticities. For each demand function, find an expression for the price elasticity of demand. The answer will typically be a function of the price,p. As an example,
In Gomorrah, New Jersey, there is only one newspaper, the Daily Calumny. The demand for the paper depends on the price and the amount of scandal reported. The demand function is Q = 15S1/2P−3,
What kinds of economic and technological conditions are conducive to the formation of monopolies?
If the market demand curve is D(p) = 100 − .5p, what is the inverse demand curve?
What problems face a regulatory agency attempting to force a monopolist to charge the perfectly competitive price?
An addict’s demand function for a drug may be very inelastic, but the market demand function might be quite elastic. How can this be?
True or false? Imposing a quantity tax on a monopolist will always cause the market price to increase by the amount of the tax.
If D(p) = 12 − 2p, what price will maximize revenue?
Show mathematically that a monopolist always sets its price above marginal cost.
Suppose that the demand curve for a good is given byD(p) = 100/p. What price will maximize revenue?
True or false? In a two good model if one good is an inferior good the other good must be a luxury good.
The government is considering subsidizing the marginal costs of the monopolist described in the question above. What level of subsidy should the government choose if it wants the monopolist to
What is the effect of a subsidy in a market with a horizontal supply curve? With a vertical supply curve?
Suppose that the demand curve is vertical while the supply curve slopes upward. If a tax is imposed in this market who ends up paying it?
If the demand curve facing the monopolist has a constant elasticity of 2, then what will be the monopolist’s markup on marginal cost?
What is the answer to the above question if the demand curve facing the monopolist has constant elasticity?
A monopolist is operating at an output level where|ε| = 3. The government imposes a quantity tax of $6 per unit of output. If the demand curve facing the monopolist is linear, how much does the
IfD(p) = 100/p and c(y) = y2, what is the optimal level of output of the monopolist? (Be careful.)
Suppose that all consumers view red pencils and blue pencils as perfect substitutes. Suppose that the supply curve for red pencils is upward sloping. Let the price of red pencils and blue pencils be
The United States imports about half of its petroleum needs. Suppose that the rest of the oil producers are willing to supply as much oil as the United States wants at a constant price of $25 a
Suppose that the supply curve is vertical. What is the deadweight loss of a tax in this market?
The monopolist faces a demand curve given byD(p) = 10p−3. Its cost function is c(y) = 2y. What is its optimal level of output and price?
Consider the tax treatment of borrowing and lending described in the text. How much revenue does this tax system raise if borrowers and lenders are in the same tax bracket?
The monopolist faces a demand curve given by D(p) = 100 - 2p. Its cost function is c(y) = 2y. What is its optimal level of output and price?
Does such a tax system raise a positive or negative amount of revenue when tl < tb?
Consider an auction of antique quilts to collectors. Is this a private-value or a common-value auction?
The market demand curve for heroin is said to be highly inelastic. Heroin supply is also said to be monopolized by the Mafia, which we assume to be interested in maximizing profits. Are these two
Suppose that there are only two bidders with values of $8 and $10 for an item with a bid increment of $1. What should the reservation price be in a profit-maximizing English auction?
Suppose that we have two copies of Intermediate Microeconomics to sell to three (enthusiastic) students. How can we use a sealed-bid auction that will guarantee that the bidders with the two highest
Consider the Ucom example in the text. Was the auction design efficient? Did it maximize profits?
A game theorist fills a jar with pennies and auctions it off on the first day of class using an English auction. Is this a private-value or a common-value auction? Do you think the winning bidder
Consider the production function f(x1, x2) = x21x22. Does this exhibit constant, increasing, or decreasing returns to scale?
Calculate marginal products and technical rates of substitution for several frequently encountered production functions. Consider the production function f(x1, x2) = 2x1 + √x2. The marginal
Consider the production function f(x1, x2) = 4x11/2x21/3. Does this exhibit constant, increasing, or decreasing returns to scale?
The Cobb-Douglas production function is given by f(x1, x2) = Axa1xb2. It turns out that the type of returns to scale of this function will depend on the magnitude of a+b. Which values of a + b will
The technical rate of substitution between factors x2 and x1 is −4. If you desire to produce the same amount of output but cut your use of x1 by 3 units, how many more units of x2 will you need?
True or false? If the law of diminishing marginal product did not hold, the world’s food supply could be grown in a flowerpot.
In a production process is it possible to have decreasing marginal product in an input and yet increasing returns to scale?
In the short run, if the price of the fixed factor is increased, what will happen to profits?
If a firm had everywhere increasing returns to scale, what would happen to its profits if prices remained fixed and if it doubled its scale of operation?
A Los Angeles firm uses a single input to produce a recreational commodity according to a production function f(x) = 4√x, where x is the number of units of input. The commodity sells for$100 per
If a firm had decreasing returns to scale at all levels of output and it divided up into two equal-size smaller firms, what would happen to its overall profits?
Brother Jed takes heathens and reforms them into righteous individuals. There are two inputs needed in this process: heathens (who are widely available) and preaching. The production function has the
A gardener exclaims: “For only $1 in seeds I’ve grown over $20 in produce!” Besides the fact that most of the produce is in the form of zucchini, what other observations would a cynical
Is maximizing a firm’s profits always identical to maximizing the firm’s stock market value?
If pMP1 > w1, then should the firm increase or decrease the amount of factor 1 in order to increase profits?
Suppose a firm is maximizing profits in the short run with variable factor x1 and fixed factor x2. If the price of x2 goes down, what happens to the firm’s use of x1? What happens to the firm’s
A profit-maximizing competitive firm that is making positive profits in long-run equilibrium (may/may not) have a technology with constant returns to scale.
A firm has two variable factors and a production function, f(x1, x2) = x11/2x21/4 . The price of its output is 4. Factor 1 receives a wage of w1 and factor 2 receives a wage of w2.(a) Write an
A New York City cab operator appears to be making positive profits in the long run after carefully accounting for the operating and labor costs. Does this violate the competitive model? Why or why
The model of entry presented in this chapter implies that the more firms in a given industry, the (steeper, flatter) is the long-run industry supply curve.
According to the model presented in this chapter, what determines the amount of entry or exit a given industry experiences?
True or false? In long-run industry equilibrium no firm will be losing money.
True or false? Convenience stores near the campus have high prices because they have to pay high rents.
In the short run the demand for cigarettes is totally inelastic. In the long run, suppose that it is perfectly elastic. What is the impact of a cigarette tax on the price that consumers pay in the
If S1(p) = p − 10 and S2(p) = p − 15, then at what price does the industry supply curve have a kink in it?
In a perfectly competitive market what is the relationship between the market price and the cost of production for all firms in the industry?
Is it ever better for a perfectly competitive firm to produce output even though it is losing money? If so, when?
If average variable costs exceed the market price, what level of output should the firm produce? What if there are no fixed costs?
In a purely competitive market a firm’s marginal revenue is always equal to what? A profit-maximizing firm in such a market will operate at what level of output?
What is the major assumption that characterizes a purely competitive market?
Classify each of the following as either technological or market constraints: the price of inputs, the number of other firms in the market, the quantity of output produced, and the ability to produce
If the long-run cost function is c(y) = y2 + 1, what is the long-run supply curve of the firm?
A firm has a supply function given by S(p) = 4p. Its fixed costs are 100. If the price changes from 10 to 20, what is the change in its profits?
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
In the preceding exercise, which bundle is preferred by the consumer, the x-bundle or the y-bundle?
If the supply curve is given by S(p) = 100 + 20p, what is the formula for the inverse supply curve?
A firm has a cost function given by c(y) = 10y2 + 1000. At what output is average cost minimized?
When prices are (p1, p2) = (2, 1) a consumer demands (x1, x2) = (1, 2), and when prices are (q1, q2) = (1, 2) the consumer demands (y1, y2) = (2,1). Is this behavior consistent with the model of
A firm has a cost function given by c(y) = 10y2 + 1000. What is its supply curve?
A competitive firm has a production function of the form Y = 2L + 5K. If w = $2 and r = $3, what will be the minimum cost of producing 10 units of output?
True or false? In the long run a firm always operates at the mini-mum level of average costs for the optimally sized plant to produce a given amount of output.
Casper consumes cocoa and cheese. He has an income of $16. Cocoa is sold in an unusual way. There is only one supplier and the more cocoa one buys from him, the higher the price one has to pay per
A firm produces identical outputs at two different plants. If the marginal cost at the first plant exceeds the marginal cost at the second plant, how can the firm reduce costs and maintain the same
True or false? If the demand function is x1 = −p1, then the inverse demand function is x = −1/p1.
What is the form of the inverse demand function for good 1 in the case of perfect complements?
Which of the following are true? (1) Average fixed costs never increase with output.(2) Average total costs are always greater than or equal to average variable costs. (3) Average cost can
Miss Muffet always likes to have things “just so.” In fact the only way she will consume her curds and whey is in the ratio of 2 units of whey per unit of curds. She has an income of $20. Whey
The income offer curve is to the Engel curve as the price offer curve is to. . .?
If a firm uses n inputs (n > 2), what inequality does the theory of revealed cost minimization imply about changes in factor prices (Δwi) and the changes in factor demands (Δxi) for a given
For what kind of preferences will the consumer be just as well-off facing a quantity tax as an income tax?
If a consumer has a utility function u(x1, x2) = x1x24, what fraction of her income will she spend on good 2?
Suppose that you have highly no nconvex 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 price of paper used by a cost-minimizing firm increases. The firm responds to this price change by changing its demand for certain inputs, but it keeps its output constant. What happens to the
We begin again with Charlie of the apples and bananas. Recall that Charlie’s utility function is U(xA, xB) = xAxB. Suppose that the price of apples is 1, the price of bananas is 2, and Charlie’s
Suppose that a cost-minimizing firm uses two inputs that are perfect substitutes. If the two inputs are priced the same, what do the conditional factor demands look like for the inputs?
If a firm is producing where MP1/w1 > MP2/w2, what can it do to reduce costs but maintain the same output?
Consider the utility function u(x1, x2) = √x1x2. What kind of preferences does it represent? Is the function v(x1, x2) = x21x2 a monotonic transformation of u(x1, x2)? Is the function w(x1,
What kind of preferences are represented by a utility function of the form u(x1, x2) = x1 + √x2? Is the utility function v(x1, x2) = x21 + 2x1√x2 + x2 a monotonic transformation of u(x1, x2)?
Prove that a profit-maximizing firm will always minimize costs.

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