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    General expressions for average productivity of labor and capita

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    Please see the attached file for full problem description.

    Solutions:1

    a) If Twinkies cost $0.10 each and Slice costs $0.25 per cup, what is his budget constraint? Write down the budget equation and draw the budget line:

    Budget constraint $0.10T + $0.25S = $1

    to draw the budget line: for example consider this two points A( T=0; S=4) and B(T=10; S=0) AND c(T=5, s=2)

    B) Where does the budget line intersect (touch) the indifference curve for U =10^1/2. To answer a question like this first, one should determine the TMS between T and S which is the point in which budget line is tangeant to the utility fonction. U't/U's=Price of T / price of S. (1/2*S^1/2*T^-1/2)/(1/2*T^1/2*S^-1/2) = $0.1/$0.25 After doing all the claculation we get S/T=0.1/0.25 which is S=0.4*T . we will now replace S in the budget equation to find T then S. T*=5 and S*=2. Thus, the intersection point is T=5 and S=2.

    C) Show different combinations of T and S that satisfy the budget constraint, give the corresponding utility value, and verify that the combination of T and S obtained in part b, in fact, maximizes Paul's utility.

    S T U

    0 10.00 0

    0.50 8.75 2.09

    1.00 7.50 2.74

    1.50 6.25 3.06

    2.00 5.00 3.16

    2.50 3.75 3.06

    3.00 2.50 2.74

    3.50 1.25 2.09

    4.00 0 0

    d. Suppose the school tries to discourage Twinkie consumption by raising the price to $0.40. But Paul's mother also increases his lunch allowance by $1. Can Paul achieve the same level of utility he received in part b with this extra allowance? What is the new combination of T and S that gives U= 10^1/2.

    With this new situation: U't/U's = Price T / price S, thus S/T= 0.4/0.25 which gives S= 1.6 T replace this in the budget. 0.4 T + 0.25(1.6T)= 2 Then T= 2.5 and S=4

    Solution 2. Show calculations for a, b, and include demand curves for c

    a) she should purchase: Wf=1 and Wc=10

    b) she will buy : Wf=2 and Wc=10

    c) To draw the demand curve for Wf use the TMS

    2Wc/wf= Pf/Pc thus Wf=Pc/pf*2Wc yes they are related goods. substitutes goods.

    solution 3.

    a)

    i) Elasticity revenue: relative variationof quantities per relative variation of revenu.

    ii) Elasticity price: relative variation of quantities per relative variation of price.
    iii) If Emily's tastes change and she decides to spend only one-fourth of her income on clothing, how does her demand curve change? Draw a diagram to show the change in demand. What are her income elasticity and price elasticity now?

    iii) By reducing the income allocated to clothing it will reduce the level of quantities bought.

    b. Two drivers - Tom and Jerry - each drive up to a gas station. Before looking at the price, each places an order. Tom says, "I'd like 10 gallons of gas." Jerry says, "I'd like $10 worth of gas." What is each driver's price elasticity of demand? Draw diagrams of their respective demand curves.

    b) Tom : elasticity to price will be very high. On the other hand jerry does not have any elasticity price because he knows the amount he will spend.

    c) Qb=500-100Pb+2I-200Ps I=$1000, Pb=$2, Ps=$1 Qb= 2100 .eQ,P;eQI; eq,ps? to determine this is to do the variation relative of each variable P, I and Ps to see the changes in Qb. for examples : Pb increase from 2 to 2.5 then Qb = 2050. eQpb= (2050-2100)/2100)/(2.5-2)/2 = -0.092 . The elasticity demand Qb due to Pb: When the price Pb increase per 50% the demand will decrease by 9.2%. Please clarify what eQ,I and eQ,ps are equal to.

    The production of barstools (q) is characterized by a production function of the form

    a. Derive general expressions for average productivity of labor and capital for barstool production as functions of K and L. (Hint: By definition, = q/L and = q/K)

    b. Graph and curve for K=100

    c. Graph the q= 10 isoquant. Show all K-L combinations in a table.
    For q = 10, we get K =
    L K=100/L
    1 100
    2 50
    3 33.33333
    4 25
    5 20
    6 16.66667
    7 14.28571
    8 12.5
    9 11.11111
    10 10
    11 9.090909
    12 8.333333
    13 7.692308
    14 7.142857
    15 6.666667
    16 6.25
    17 5.882353
    18 5.555556
    19 5.263158
    20 5
    21 4.761905
    22 4.545455
    23 4.347826
    24 4.166667
    25 4
    26 3.846154
    27 3.703704
    28 3.571429
    29 3.448276
    30 3.333333
    31 3.225806
    32 3.125
    33 3.030303
    34 2.941176
    35 2.857143
    36 2.777778
    37 2.702703
    38 2.631579
    39 2.564103
    40 2.5
    41 2.439024
    42 2.380952
    43 2.325581
    44 2.272727
    45 2.222222
    46 2.173913
    47 2.12766
    48 2.083333
    49 2.040816
    50 2
    51 1.960784
    52 1.923077
    53 1.886792
    54 1.851852
    55 1.818182
    56 1.785714
    57 1.754386
    58 1.724138
    59 1.694915
    60 1.666667
    61 1.639344
    62 1.612903
    63 1.587302
    64 1.5625
    65 1.538462

    d. The point K=10, L=10 is one point on the q =10 isoquant. What value of K corresponds to L= 11 on that isoquant? What is the approximate value for the RTS at K = 10, L=10?
    From the table above, corresponding to K = 10, L = 9.090909. What is the approximate value for the RTS at K = 10, L=10?

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    Solution Summary

    Write down the budget equation and draw the budget line.

    $2.19