Econ 300 Final

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6.1 An economy has two people, Charlie and Doris. There are two goods, apples and bananas. Charlie has an initial endowment of 3 apples and 4 bananas. Doris has an initial endowment of 6 apples and 2 bananas. Charlie's utility function is U(AC, BC) = ACBC, where AC is his apple consumption and BC is his banana consumption. Doris's utility function is U(AD, BD) = ADBD, where AD and BD are her apple and banana consumptions. At every
Pareto optimal allocation

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Charlie consumes 9 apples for every 6 bananas that he consumes

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6.1 An economy has two people, Charlie and Doris. There are two goods, apples and bananas. Charlie has an initial endowment of 3 apples and 8 bananas. Doris has an initial endowment of 6 apples and 4 bananas. Charlie's utility function is U(AC, BC) = ACBC, where AC is his apple consumption and BC is his banana consumption. Doris's utility function is U(AD, BD) = ADBD, where AD and BD are her apple and banana consumptions. At every
Pareto optimal allocation

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Charlie consumes 9 apples for every 12 bananas that he consumes

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6.3 An economy has two people, Charlie and Doris. There are two goods, apples and bananas. Charlie has an initial endowment of 5 apples and 10 bananas. Doris has an initial endowment of 10 apples and 5 bananas. Charlie's
utility function is U(AC, BC) ACBC, where AC is his apple consumption and BC is his banana consumption.
Doris's utility function is U(AD, BD) ADBD, where AD and BD are her apple and banana consumptions. At every Pareto optimal allocation

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Charlie consumes 15 apples for every 15 bananas that he consumes

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6.4 Ken's utility function is U(QK, WK) = QKWK and Barbie's utility function is U(QB, WB) = QBWB. If Ken's initial endowment were 8 units of quiche and 11 units of wine and Barbie's endowment were 16 units of quiche and 11 units of wine, then at any Pareto optimal allocation where both persons consume some of each good,

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Ken would consume 24 units of quiche for every 22 units of wine that he consumes

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6.5 Suppose that Morris has the utility function U(b, w) = 6b + 6w and Philip has the utility function U(b, w) =bw.
If we draw an Edgeworth box with books on the horizontal axis and wine on the vertical axis and if we measure Morris's consumptions from the lower left corner of the box, then the contract curve contains

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a straight line with slope 1/1 passing through the upper right corner of the box

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6.6 Astrid's utility function is U(HA, CA) = HACA. Birger's utility function is min{HB, CB}. If Astrid's initial
endowment is no cheese and 20 units of herring and if Birger's initial endowments are 4 units of cheese and no herring, then where p is a competitive equilibrium price of herring and cheese is the numeraire, demand equals
supply in the herring market. This implies that

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4/(p + 1) + 10 = 20

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6.7 Suppose that Mutt's utility function is U(m, j) = max{4m, j} and Jeff's utility function is U(m, j) = 3m + j. Mutt is initially endowed with 6 units of milk and 2 units of juice, and Jeff is initially endowed with 2 units of milk and 6 units of juice. If we draw an Edgeworth box with milk on the horizontal axis and juice on the vertical axis and if we measure goods for Mutt by the distance from the lower left corner of the box, then the set of Pareto optimal allocations includes the

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bottom edge of the Edgeworth box but no other edges

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6.8 Professor Nightsoil's utility function is UN(BN, PN) = BN + 4Pn^1/2 and Dean Interface's utility function is UI(BI,PI) = BI + 2Pi^1/2. If Nightsoil's initial endowment is 4 bromides and 15 platitudes and if Interface's initial endowment is 7 bromides and 15 platitudes, then at any Pareto efficient allocation where both persons consume positive amounts of both goods

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Interface consumes 6 platitudes

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6.9 In a pure exchange economy with two persons and two goods, one person always prefers more to less of both goods and one person likes one of the goods and hates the other so much that she would have to be paid to consume it. Both are initially endowed with positive amounts of both goods. The competitive equilibrium price of the good that one person hates

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must be postive

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6.10 If an allocation is Pareto optimal and if indifference curves between the two goods have no kinks, then

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two consumers who consume both goods must have the same MRS between them, but consumers may consume the goods in different ratios

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6.11 Colette and Hans both consume the same goods in a pure exchange economy. Colette is originally endowed
with 15 units of good 1 and 12 units of good 2. Hans is originally endowed with 97 units of good 1 and 4 units
of good 2. They both have the utility function U(x1, x2)= x1^1/3 x2^2/3. If we let good 1 be the numeraire, so that p1=$1, then what will be the equilibrium price of good 2?

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$14

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6.12 A situation is Pareto efficient if

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there is no way to make someone better off without making someone else worse off.

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6.13 Xavier and Yvette are the only two persons on a desert island. There are only two goods, nuts and berries.
Xavier's utility function is U(Nx,Bx)= NxBx. Yvette's utility function is U(Ny,By)= 2Ny + By. Xavier is endowed
with 5 units of berries and 13 units of nuts. Yvette is endowed with 6 units of berries and 8 units of nuts. In a competitive equilibrium for this economy, how many units of berries does Xavier consume?

answer

15.50

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6.14 Adelino and Benito consume only two goods, X and Y. They trade only with each other and there is no
production. Adelino's utility function is given by U(xA, yA) 2xA 5yA and Benito's utility function is given by
U(xB, yB) 2(6xB 15yB)
1/2. In the Edgeworth box constructed for Adelino and Benito, the set of Pareto optimal allocations is

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the entire contents of the Edgeworth box

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6.15 Tamara and Julio consume only bread and wine. They trade only with each other and there is no production. They both have strictly convex preferences. Tamara's initial endowment of bread and wine is the same as Julio's.

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If they have identical utility functions, then the initial allocation is Pareto optimal

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6.16 Abduls utility is U(X A, Y A) = min{X A, Y A}, where X A, and Y A are his consumptions of goods X and Y respectively. Babettes utility function is U(X B, Y B) = X B Y B, where X B and Y B are her consumptions of goods X and Y. Abduls initial endowment is no units of Y and 6 units of X. Babettes initial endowment is no
units of X and 10 units of Y. If X is the numeraire good and p is the price of good Y, then supply will equal demand in the market for Y if

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6/(p+1) +5 = 10

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6.17 Abduls utility is U(X A, Y A) = min{X A, Y A}, where X A and Y A are his consumptions of goods X and Y respectively. Babettes utility function is U(X B, Y B) = X B Y B, where X B and Y B are her consumptions of goods X and Y. Abduls initial endowment is no units of Y and 7 units of X. Babettes initial endowment is no units of X and 6 units of Y. If X is the numeraire good and p is the price of good Y, then supply will equal demand in the market for Y if

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7/(p+1) +3 = 6

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6.18 Professor Nightsoils utility function is U N (BN, PN) =Bn + 4Pn^1/2 and Dean Interfaces utility function is Ui(BI, PI) = Bi + 2Pi^1/2 where Bn and Bi are the number of bromides and P N and P I are the number of platitudes consumed by Nightsoil and Interface respectively. If Nightsoils initial endowment is 4 bromides and 25 platitudes and if Interfaces initial endowment is 2 bromides and 20 platitudes, then at any Pareto efficient
allocation in which both consume positive amounts of both goods,

answer

Interface consumes 9 platitudes

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6.19 Astrids utility function is U(H A, C A) = HaCa. Birgers utility function is min{Hb, Cb}. If Astrids initial endowment is no cheese and 11 units of herring and if Birgers initial endowments are 4 units of cheese and no herring, then where p is a competitive equilibrium price of herring and cheese is the numeraire, it must be that demand equals supply in the herring market. This implies that

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4/(p+1) + 6= 12

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6.20 Astrid's utility function is U(HA, CA)= HACA. Birger's utility function is min{HB, CB}. If Astrid's initial endowment is no cheese and 13 units of herring and if Birger's initial endowments are 8 units of cheese and no herring, then where p is a competitive equilibrium price of herring and cheese is the numeraire, it must be that
demand equals supply in the herring market. This implies that

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8/(p+1) + 6.5 =13

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7.1 A firm has the production function $f(x1, x2)= x1^0.90 x2^0.30. The isoquant on which output is 80^3/10 has the equation

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x2= 80x1^-3

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7.2 A firm has the production function f(x, y)= x^1.20y^2
This firm has

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none of the above:
a. constant returns to scale.
b. decreasing returns to scale and increasing marginal product for factor x.
c. increasing returns to scale and decreasing marginal product for factor x.
d. decreasing returns to scale and diminishing marginal product for factor x

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7.4 A firm uses 3 factors of production. Its production function is f(x, y, z) = min{x^3/y, y^2, (z^4- x^4)/y2}. If the amount
of each input is multiplied by 6, its output will be multiplied by

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7.5 If the exponents in a Cobb-Douglas production function were 0.80 for x1 and 0.20 for x2, this production function would exhibit (constant, increasing, decreasing) returns to scale and (would, would not) have
diminishing technical rate of substitution

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constant, would

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7.6 In any production process, the marginal product of labor equals

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the change in output per unit change in labor input for "small" changes in the amount of
input

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7.7 Which of the following production functions exhibit constant returns to scale? In each case y is output and K
and L are inputs. (1) y=K^1/2L^1/3. (2) y=3K1/2L^1/2. (3) y=K^1/2 + L^1/2. (4) y=2K + 3L.

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2 & 4

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7.8 A firm has the production function f(x, y) =60x^4/5y^1/5. The slope of the firm's isoquant at the point (x, y)= (40, 80) is (pick the closest one)

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-8

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7.9 A firm has the production function f(x, y)= 20x^3/5y^2/5. The slope of the firm's isoquant at the point (x, y)= (20,40) is (pick the closest one)

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-3

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7.10 A firm has the production function f(x1, x2)= x1^0.60x2^0.30. The isoquant on which output is 803/10 has the equation

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x2= 80x1^-0.30

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7.11 The UJava espresso stand needs two inputs, labor and coffee beans, to produce its only output, espresso. Producing an espresso always requires the same amount of coffee beans and the same amount of time. Which of the following production functions would appropriately describe the production process at UJava, where B represents ounces of coffee beans, and L represents hours of labor?

answer

Q= min(2B, 60L)

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7.12 The production function is f(x1, x2)=x1^1/2 x2^1/2. If the price of factor 1 is $4 and the price of factor 2 is $6, in what proportions should the firm use factors 1 and 2 if it wants to maximize profits?

answer

x1= 1.5x2

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7.13 A competitive firm produces output using three fixed factors and one variable factor. The firm's short-run production function is q= 305x - 2x^2, where x is the amount of variable factor used. The price of the output is $2 per unit and the price of the variable factor is $10 per unit. In the short run, how many units of x should the firm
use?

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7.14 A competitive firm produces a single output using several inputs. The price of output rises by $3 per unit. The
price of one of the inputs increases by $6 and the quantity of this input that the firm uses increases by 12 units. The prices of all other inputs stay unchanged. From the weak axiom of profit maximization we can tell that

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the output of the good must have increased by at least 24 units

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7.15 A profit-maximizing competitive firm uses just one input, x. Its production function is q= 8x^1/2. The price of output is $24 and the factor price is $8. The amount of the factor that the firm demands is

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144

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7.16 Jiffy-Pol Consultants is paid $1,000,000 for each percentage of the vote that Senator Sleaze receives in the upcoming election. Sleaze's share of the vote is determined by the number of slanderous campaign ads run by Jiffy-Pol according to the function S= 100N/(N + 1), where N is the number of ads. If each ad costs $3,600
approximately how many ads should Jiffy-pol buy in order to maximize its profits?

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1666

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7.17 The production function is given by F(L)= 6L^2/3. Suppose that the cost per unit of labor is $16 and the price of output is $8. How many units of labor will the firm hire?

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7.18 The production function is given by F(L)=6L^2/3. Suppose that the cost per unit of labor is $16 and the price of output is $12. How many units of labor will the firm hire?

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7.19 The production function is f(x1, x2)=x1^1/2 x2^1/2. If the price of factor 1 is $12 and the price of factor 2 is $24, in what proportions should the firm use factors 1 and 2 if it wants to maximize profits?

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x1=2x2

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7.20 If the short-run marginal costs of producing a good are $20 for the first 400 units and $30 for each additional unit beyond 400, then in the short run, if the market price of output is $24, a profit-maximizing firm will

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produce exactly 400 units

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8.1 If the demand schedule for Bong's book is Q=3,000-100p, the cost of having the book typeset is $10,000, and
the marginal cost of printing an extra book is $4, then he would maximize his profits by

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having it typeset and selling 1,300 copies

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8.2 If the demand for pigeon pies is given by p(y)= 140-y/3, then the level of output that will maximize Peter's
profit is

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none of the above:
a. 630.
b. 214.
c. 420.
d. 42.

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8.3 A profit-maximizing monopoly faces an inverse demand function described by the equation p(y)= 60 - y and its total costs are c(y)= 10y, where prices and costs are measured in dollars. In the past it was not taxed, but now it must pay a tax of 4 dollars per unit of output. After the tax, the monopoly will

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increase its price by 2 dollars

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8.4 A firm has invented a new beverage called Slops. It doesn't taste very good, but it gives people a craving for
Lawrence Welk's music and Professor Johnson's jokes. Some people are willing to pay money for this effect, so
the demand for Slops is given by the equation q= 10-p. Slops can be made at zero marginal cost from
old-fashioned macroeconomics books dissolved in bathwater. But before any Slops can be produced, the firm
must undertake a fixed cost of $30. Since the inventor has a patent on Slops, it can be a monopolist in this new
industry.

answer

A Pareto improvement could be achieved by having the government pay the firm a subsidy of $35 and insisting that the firm offer Slops at zero price.

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8.5 A firm has invented a new beverage called Slops. It doesn't taste very good, but it gives people a craving for
Lawrence Welk's music and Professor Johnson's jokes. Some people are willing to pay money for this effect, so
the demand for Slops is given by the equation q= 18-p. Slops can be made at zero marginal cost from
old-fashioned macroeconomics books dissolved in bathwater. But before any Slops can be produced, the firm must undertake a fixed cost of $86. Since the inventor has a patent on Slops, it can be a monopolist in this new
industry

answer

A Pareto improvement could be achieved by having the government pay the firm a subsidy of $91 and insisting that the firm offer Slops at zero price.

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8.7 A profit-maximizing monopolist faces the demand curve q=100-3p. It produces at a constant marginal cost of $20 per unit. A quantity tax of $10 per unit is imposed on the monopolist's product. The price of the monopolist's product

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rises by $5

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8.8 The demand for a monopolist's output is 6,000/(p + 7)^2, where p is its price. It has constant marginal costs equal
to $5 per unit. What price will it charge to maximize its profits?

answer

$17

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8.9 A natural monopolist has the total cost function c(q)= 350 + 20q, where q is its output. The inverse demand
function for the monopolist's product is p= 100 - 2q. Government regulations require this firm to produce a positive amount and to set price equal to average costs. To comply with these requirements

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the firm could produce either 5 units or 35 units

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8.10 A profit-maximizing monopolist has the cost schedule c(y)= 40y. The demand for her product is given by y=600/p^4, where p is her price. Suppose that the government tries to get her to increase her output by giving her a subsidy of $21 for every unit that she sells. Giving her the subsidy would make her

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decrease her price by $28

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8.11 A profit-maximizing monopoly faces an inverse demand function described by the equation p(y)= 40- y and its total costs are c(y)=7y, where prices and costs are measured in dollars. In the past it was not taxed, but now it must pay a tax of 6 dollars per unit of output. After the tax, the monopoly will

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increase its price by 3 dollars

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8.12 A profit-maximizing monopoly faces an inverse demand function described by the equation p(y)=30 - y and its total costs are c(y)=5y, where prices and costs are measured in dollars. In the past it was not taxed, but now it must pay a tax of 2 dollars per unit of output. After the tax, the monopoly will

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increase its price by 1 dollars

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8.13 A monopolist faces the demand function Q=7,000/ (p + 3)^-2. If she charges a price of p, her marginal revenue will be

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p/2 - 3/2

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8.14 A monopolist faces the demand function Q= 4,000/(p + 6)^-2. If she charges a price of p, her marginal revenue will be

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p/2 - 6/2

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8.15 The Fabulous 50s Decor Company is the only producer of pink flamingo lawn statues. While business is not as good as it used to be, in recent times the annual demand has been Q= 400 - 6P. Flamingo lawn statues are handcrafted by artisans using the process Q= min{L, P/2} where L is hours of labor and P is pounds of pink plastic. PL=15 and PP=3. What would be the profit-maximizing output and price?

answer

Q=101 P=49.83

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8.16 An obscure inventor in Strasburg, North Dakota, has a monopoly on a new beverage called Bubbles, which produces an unexplained craving for Lawrence Welk music. Bubbles is produced by the following process: Q=
min{R/3, W}, where R is pulverized Lawrence Welk records and W is gallons of North Dakota well water. PR=PW= $1. Demand for Bubbles is Q= 1,024P^-2A^0.5. If the advertising budget for Bubbles is $100, the
profit-maximizing quantity of Bubbles is

answer

160

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8.17 If demand in the United States is given by Q1= 14,000- 1,000p1, where p1 is the price in the United States, and if the demand in England is given by 1,600- 200p2, where p2 is the price in England, then the difference between the price charged in England and the price charged in the United States will be

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8.19 If a monopolist faces an inverse demand curve, p(y)= 100- 2y and has constant marginal costs of $32 and zero fixed costs and if this monopolist is able to practice perfect price discrimination, its total profits will be

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$1156

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8.20 A price-discriminating monopolist sells in two separate markets such that goods sold in one market are never resold in the other. It charges $6 in one market and $11 in the other market. At these prices, the price elasticity in the first market is -1.40 and the price elasticity in the second market is -0.90. Which of the following actions is sure to raise the monopolist's profits?

answer

Raise p2

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8.21 A monopolist sells in two markets. The demand curve for her product is given by p1=141 - 3x1 in the first market and p2=115 -2x2 in the second market, where xi is the quantity sold in market i and pi is the price charged in market i. She has a constant marginal cost of production, c = 3, and no fixed costs. She can charge different prices in the two markets. What is the profit-maximizing combination of quantities for this monopolist?

answer

x1= 23 x2= 28

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8.22 A monopolist sells in two markets. The demand curve for her product is given by p1= 165 - 3x1 in the first market and p2= 233 - 4x2 in the second market, where xi is the quantity sold in market i and pi is the price charged in market i. She has a constant marginal cost of production, c = 9, and no fixed costs. She can charge different prices in the two markets. What is the profit-maximizing combination of quantities for this monopolist?

answer

x1= 26 x2=28

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8.23 A price-discriminating monopolist sells in two separate markets such that goods sold in one market are never resold in the other. It charges p1= $5 in one market and p2= $10 in the other market. At these prices, the price elasticity in the first market is -1.40 and the price elasticity in the second market is -0.10. Which of the following actions is sure to raise the monopolist's profits?

answer

raise p2

1 of 60

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answer

Charlie consumes 9 apples for every 6 bananas that he consumes

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Charlie consumes 9 apples for every 12 bananas that he consumes

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Charlie consumes 15 apples for every 15 bananas that he consumes

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Ken would consume 24 units of quiche for every 22 units of wine that he consumes

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a straight line with slope 1/1 passing through the upper right corner of the box

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answer

4/(p + 1) + 10 = 20

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answer

bottom edge of the Edgeworth box but no other edges

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answer

Interface consumes 6 platitudes

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must be postive

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6.10 If an allocation is Pareto optimal and if indifference curves between the two goods have no kinks, then

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two consumers who consume both goods must have the same MRS between them, but consumers may consume the goods in different ratios

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answer

$14

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6.12 A situation is Pareto efficient if

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there is no way to make someone better off without making someone else worse off.

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answer

15.50

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the entire contents of the Edgeworth box

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If they have identical utility functions, then the initial allocation is Pareto optimal

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answer

6/(p+1) +5 = 10

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answer

7/(p+1) +3 = 6

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answer

Interface consumes 9 platitudes

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answer

4/(p+1) + 6= 12

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answer

8/(p+1) + 6.5 =13

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7.1 A firm has the production function $f(x1, x2)= x1^0.90 x2^0.30. The isoquant on which output is 80^3/10 has the equation

answer

x2= 80x1^-3

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7.2 A firm has the production function f(x, y)= x^1.20y^2
This firm has

answer

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7.4 A firm uses 3 factors of production. Its production function is f(x, y, z) = min{x^3/y, y^2, (z^4- x^4)/y2}. If the amount
of each input is multiplied by 6, its output will be multiplied by

answer

question

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constant, would

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7.6 In any production process, the marginal product of labor equals

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the change in output per unit change in labor input for "small" changes in the amount of
input

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answer

2 & 4

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7.8 A firm has the production function f(x, y) =60x^4/5y^1/5. The slope of the firm's isoquant at the point (x, y)= (40, 80) is (pick the closest one)

answer

-8

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7.9 A firm has the production function f(x, y)= 20x^3/5y^2/5. The slope of the firm's isoquant at the point (x, y)= (20,40) is (pick the closest one)

answer

-3

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7.10 A firm has the production function f(x1, x2)= x1^0.60x2^0.30. The isoquant on which output is 803/10 has the equation

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x2= 80x1^-0.30

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answer

Q= min(2B, 60L)

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answer

x1= 1.5x2

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answer

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the output of the good must have increased by at least 24 units

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answer

144

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answer

1666

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7.17 The production function is given by F(L)= 6L^2/3. Suppose that the cost per unit of labor is $16 and the price of output is $8. How many units of labor will the firm hire?

answer

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7.18 The production function is given by F(L)=6L^2/3. Suppose that the cost per unit of labor is $16 and the price of output is $12. How many units of labor will the firm hire?

answer

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answer

x1=2x2

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answer

produce exactly 400 units

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answer

having it typeset and selling 1,300 copies

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8.2 If the demand for pigeon pies is given by p(y)= 140-y/3, then the level of output that will maximize Peter's
profit is

answer

none of the above:
a. 630.
b. 214.
c. 420.
d. 42.

question

answer

increase its price by 2 dollars

question

answer

A Pareto improvement could be achieved by having the government pay the firm a subsidy of $35 and insisting that the firm offer Slops at zero price.

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answer

A Pareto improvement could be achieved by having the government pay the firm a subsidy of $91 and insisting that the firm offer Slops at zero price.

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answer

rises by $5

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8.8 The demand for a monopolist's output is 6,000/(p + 7)^2, where p is its price. It has constant marginal costs equal
to $5 per unit. What price will it charge to maximize its profits?

answer

$17

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answer

the firm could produce either 5 units or 35 units

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answer

decrease her price by $28

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answer

increase its price by 3 dollars

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answer

increase its price by 1 dollars

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8.13 A monopolist faces the demand function Q=7,000/ (p + 3)^-2. If she charges a price of p, her marginal revenue will be

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p/2 - 3/2

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8.14 A monopolist faces the demand function Q= 4,000/(p + 6)^-2. If she charges a price of p, her marginal revenue will be

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p/2 - 6/2

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answer

Q=101 P=49.83

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answer

160

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answer

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$1156

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answer

Raise p2

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answer

x1= 23 x2= 28

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answer

x1= 26 x2=28

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answer

raise p2

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