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1
1.What is the equivalent future value of student emergency funds of $5000 from now to year 5 at annual compound interest 5%? To have $5000 in 2025, what is the required deposit in 2020 to a savings account that earns annual compound interest 10%?
2.what is A to make two cash flow diagrams equivalent, at i = 10%? A $100 0 1 2 3 4 5 6 7 8 0 1 2 3 4 5 6 7 8
3. Adam’s Recycle-Bicycle Shop builds bicycles out of recycled materials; its production function is shown in the accompanying table. Adam owns a small shop with four machines for taking recyclable materials and turning them into steel for bicycle frames and rubber for tires. He also uses up to ten workers, paint, seats, and wires in the production process. # of Workers 0 I 2 3 Total product per month 0 200 500 700 800 850 875 890 4 5 6 7 8 900 a. What are Adam's fixed inputs? What are his variable inputs? b. Using table and figures, calculate Adam's marginal product and plot his total product and marginal product curves. c. What principle explains why the marginal product per worker decline as the number of workers employed increases? a. 4. Using the production function for Adam's Recyle-Bicycle Shop above and knowing that he has fixed cost of production equal to $2,000 and his variable cost are $400 per worker, calculate the relevant cost data for Adam. Plot the total cost, total variable cost, and total fixed cost in one figure and the average total cost, average fixed cost, average variable cost, and marginal cost in another figure b. Why does average fixed cost fall continuously? c. Why may average variable cost fall and then definitely rise? d. Why does average total cost fall and then rise? How does marginal cost of production relate to the marginal product of each worker? e.
Expert Solution
1.formula for compound interest:- A=P(1+r/n)^nt = 5000 (1+0.05/1)^1x5
=5000x1.276= 6381.4
$6381.4 is the future value of $5000
2. formula for compound interest :- A=P(1+r/n)^nt
5000=P(1+0.1/1)^1x5
5000=P(1.1)^5
5000=P(1.61)
5000/1.61=P
P=3105.59
so to receive $5000 by 2025 the person would have to deposit $3105.59 in the year 2020.
2.Diagram 1
Annual Cash Flows in the first 4 years = $100
Interest Rate = 10%
Calculate the Present Worth.
PW = $100 (P/A, 10%, 4)
PW = $100 (3.16987)
PW = $316.98 or $317 (rounded off)
Diagram 2
There will be 4 annual equal cash flows from EOY 5 to EOY 8
Calculate the value of "A", so that both the diagrams will be equivalent.
PW of Diagram 1 = PW of Diagram 2
$317 = A (P/A, 10%, 4) (P/F, 10%, 4)
$317 = A (3.16987) (0.68301)
$317 = A (2.165052909)
A = $146.42
The Value of A will be $146.42 so that both the cash flow diagrams will be equivalent.
The problem can solved by using the Future Worth Method also.
Diagram 1
FW = 100 (F/A, 10%, 4) (F/P, 10%, 4)
FW = 100 (4.64100) (1.46410) = 679.49
Diagram 2
679.49 = A (F/A, 10%, 4)
679.49 = A (4.64100)
A = 146.41
The "A" will be 146.41
3.
Adam's fixed inputs are---- four machines
Variable inputs are--- 10 workers and raw material like paint,seats,wires in the production process
b) TP and MP-----
| Workers | TP | MP |
|---|---|---|
| 0 | 0 | -- |
| 1 | 200 | 200 |
| 2 | 500 | 300 |
| 3 | 700 | 200 |
| 4 | 800 | 100 |
| 5 | 850 | 50 |
| 6 | 875 | 25 |
| 7 | 890 | 15 |
| 8 | 900 | 10 |
TP and MP curves-----
C) The law of diminishing Marginal returns ( DMR) explains that the marginal Product per worker declines as the number of workers employed increases.
4) Calculating relevant cost data-----
| Workers | Fixed cost ( FC) | Variable cost( VC)($400 per worker) |
Total cost(TC= FC+VC) |
| 0 | 2000 | 0 | 2000 |
| 1 | 2000 | 400 | 2400 |
| 2 | 2000 | 800 | 2800 |
| 3 | 2000 | 1200 | 3200 |
| 4 | 2000 | 1600 | 3600 |
| 5 | 2000 | 2000 | 4000 |
| 6 | 2000 | 2400 | 4400 |
| 7 | 2000 | 2800 | 4800 |
| 8 | 2000 | 3200 | 5200 |
(a) Graph of TC,TvC,TFc-----------------
Ac,Avc,Afc and MC----
| Output(TP) | AC=TC/q | AvC=TvC/Q | AfC=TFC/q | MC=?TC/?q | |
| 0 | - | - | -- | -- | |
| 200 | 12 | 2 | 10 | 2 | |
| 500 | 5•6 | 1•6 | 4 | 3•33 | |
| 700 | 4•57 | 1•7 | 2•85 | 2 | |
| 800 | 4•5 | 2 | 2•5 | 4 | |
| 850 | 4•71 | 2•35 | 2•35 | 8 | |
| 875 | 5•03 | 2•74 | 2•29 | 16 | |
| 890 | 5•39 | 3•14 | 2•24 | 26•67 | |
| 900 | 5•78 | 3•55 | 2•22 | 40 |
Curve------
b) AFC falls continuesly because it remains fixed irrespective of increase of output.
c) AVC initially falls because initially the TP rises at increasing rate and then it falls as TP starts increasing at diminishing rate
d) AC initially falls and then rises due to implications of law of variable proportion
e) MC is related to the MP of each worker because Mp is the addition to total product and MC is the addition to total cost of employing each additional worker.
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