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# General expressions for average productivity of labor and capita

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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.

\$2.49