Manegerial economics

Chapter 6

Question 1: (p212)

  1. Explain the difference between short run and long run production function, cite one example of this difference in a business situation.

Short run production function:

Themaximum quantity of a good or service that can be produced by a set of inputs assuming the amount of at least one of the inputs used remains unchanged as output varies

Q= a + bL +cL2 – dL3

In the short run production function there are three stages of production:

Stage I: start at zera and ends at the point where the firm has reached the max level of average product

Stage II; start after end of stage I until the point where the firm has reached the level of max. total production

Stage III; continues from this point on

Long run production function:

The maximum quantity of a good or service that can be produced by a set of inputs assuming the firm is free to vary the amount of all inputs being used

Q= f(L,K)

On the long run as the firm expand it may experience

economies of scale where the average production of the firm increase as capacity increase.

d.t. :

  1. procurement economies
  2. technology economies
  3. financial economies
  4. human resource economies
  5. advertising economies

after that any more expansion in scale, the firm will collect diseconomies of scale

d.t.:

1) management coordianation and control problem

2) disproportion increase in staffin relation to indirect labor

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Question 5: (p212)

Define return to scale, why is this considered a long run phenomenon.

Return to scale: is the increase in output that results from an increase in all the firm's input by some proportion.

a)Increasing Return to scale: (IRTS) The output increases by a great proportion than the increase in input.

b)Constant return to scale: (CRTS) the output increase by the same proportion as the input

c)Decrease return to scale: (DRTS) the output increase by a smaller proportion than the increase in input.

It is considered a long run phenomenon because the firm is free to vary the amount of all inputs being used.

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Problems 1: (p213)

(T) or (F), explain:

  1. When the law of diminishing return takes effect as firm's average product will start to decrease (F)

Because at law of diminishing return the unit increase in variable input causes the output to increase at lower rate (MP ) while the total average production remains constant for a while before it start to decrease

  1. Decrease in return to scale occurs when a firm has to increase all its inputs at an increasing rate to maintain a constant rate of increase in its output (T)
  1. A linear short run production function implies that the law of diminishing return does not take effect over the range of output being considered. (T)

It may be possible to identify a linear production function and this function may exhibit no diminishing return,

  1. Stage one of production processes ends at the point where the low diminishing return occur (F)

Stage one of production processes ends at the point of optimum AP whish usually start after low of diminishing return has occurred.

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Problem 8 (P215):

Q= 7V- 0.5 V2

(V: No of workers)

a), b), c)

V / Q / MPL / APL
0 / 0
1 / 6.5 / 6.5 / 6.5
2 / 12 / 5.5 / 6
3 / 16.5 / 4.5 / 5.5
4 / 20 / 3.5 / 5
5 / 22.5 / 2.5 / 4.5
6 / 24 / 1.5 / 4
7 / 24.5 / 0.5 / 3.5
8 / 24 / -0.5 / 3
9 / 22.5 / -1.5 / 2.5
10 / 20 / -2.5 / 2
11 / 16.5 / -3.5 / 1.5
12 / 12 / -4.5 / 1
13 / 6.5 / -5.5 / 0.5

d)The difference between the equation in problem 8 and problem 7 is the difference between quadratic equation and cubic form

Q = 7V+ 0.6 V2-0.1V3 (cubic equation)

Q=7V – 0.5 V2( Quadratic equation)

where firms with quadratic equation for production function implies that law of diminishing return takes effect as soon as the firm starts to produce, while for firms with cubic equation for production function the all three stages of production are present.

chapter( 7)

question 1: (p270)

define and compare following types of cost:

Sunk cost / Incremental cost
A cost incurred in the past that is not affected by current decision
It has no market value in an alternative use
e.g. fixed overhead cost / The total cost associated with a particular decision
It can be considered the change in total variable cost
e.g. cost of building an additional wing to an office building
Fixed cost / Variable cost
The cost that remains constant as the level of output varies
In the short run fixed cost is incurred even if the firm produce no output / The total cost associated with the level of output
This can also be considered the total cost to a firm of using its variable endings
Incremental cost / Marginal cost
The change in the total variable cost deltaTVC / Consider the change in the total variable cost divided by the change in the output
∆ TVC / ∆ Q
Opportunity cost تكلفة الفرصة البديلة / Out of pocket cost
The amount of subjective value forgone in choosing one activity over the next best alternative
Is implicit or indirect cost / Accounting cost by virtue of the fact that such money-denominated costs are visible, readily monitored, and hence easily included by accountants
is explicit or direct cost

Question 4 (p270)

If it were not for the law of diminishing return the firm AC and AVC would not increase in the short run. (do u agree, explain)

I agree with this because in this case( the case of linear cost functions)in contrast to cubic and quadratic cost functions, the firm is experiencing neither increasing nor diminishing returns when variable input is added to its fixed input, (each additional unit of variable input add the same amount of additional output), as the marginal cost remains constant as output increases,but in this case the average variable cost is equal to the marginal cost as shown in the figure both AVC and MC are overlapping as if they were one line,so it appers to remain constant not increasing.

Question 8- p270

Define Economies of scope Is this concept related to economies of scale? Explaine

Economies of scope: It's the reduction in cost resulting from joint production of two or more goods or services jointly rather than separately.

Economies of Scale: the reduction in the unit cost of production as the firm increase its capacity ( i.e. increase all its inputs) it is considered a long run phenomenon.

In a sense, the concept economies of scope is closely related to economies of scale,considering that a company's expansion intodifferent lines of business naturally increases its scale of operation.

However, economies of scale don't necessarily lead to economies of scope and economies of scope don't depend on the existence of economies of scale.

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Problems:

Problem 4-p272:

TC = 100 + 60 Q – 3 Q² + 0.1 Q³

(cubic equation)

Q / TC / FC / AVC / AC
TC/Q / MC
TC2-TC1
0 / 100 / 100 / 60
1 / 157.1 / 100 / 57.1 / 157.1 / 57.1
2 / 208.8 / 100 / 54.4 / 104.4 / 51.7
3 / 255.7 / 100 / 51.9 / 85.23 / 46.9
4 / 298.4 / 100 / 49.6 / 74.6 / 42.7
5 / 337.5 / 100 / 47.5 / 67.5 / 39.1
6 / 373.6 / 100 / 45.6 / 62.27 / 36.1
7 / 407.3 / 100 / 43.9 / 58.19 / 33.7
8 / 439.2 / 100 / 42.4 / 54.9 / 31.9
9 / 469.9 / 100 / 41.1 / 52.21 / 30.7
10 / 500 / 100 / 40 / 50 / 30.1
11 / 530.1 / 100 / 39.1 / 48.19 / 30.1
12 / 560.8 / 100 / 38.4 / 46.73 / 30.7
13 / 592.7 / 100 / 37.9 / 45.59 / 31.9
14 / 626.4 / 100 / 37.6 / 44.74 / 33.7
15 / 662.5 / 100 / 37.5 / 44.17 / 36.1
16 / 701.6 / 100 / 37.6 / 43.85 / 39.1
17 / 744.3 / 100 / 37.9 / 43.78 / 42.7
18 / 791.2 / 100 / 38.4 / 43.96 / 46.9
19 / 842.9 / 100 / 39.1 / 44.36 / 51.7
20 / 900 / 100 / 40 / 45 / 57.1

c- Here the firm is experiencing a cubic total cost relationship with output,

where as output increase, total cost first increase at a decreasing rate because the firm is experiencing increasing return to its variable input, when law of diminishing return takes effect, the firm begins to experience decreasing return to its variable input, thereby causing its variable cost to begin increasing at an increasing rate.

So the MC falls till reach min., then start to inc. as law of diminishing return takes effect, as it increase MC intersect with AVC at its min. point

TC = 100 + 600 Q – 3 Q²

(Quadratic equation)

Q / TC / FC / AVC / AC / MC
0 / 100 / 100 / 60
1 / 163 / 100 / 63 / 163 / 63
2 / 232 / 100 / 66 / 116 / 69
3 / 307 / 100 / 69 / 102.3333 / 75
4 / 388 / 100 / 72 / 97 / 81
5 / 475 / 100 / 75 / 95 / 87
6 / 568 / 100 / 78 / 94.66667 / 93
7 / 667 / 100 / 81 / 95.28571 / 99
8 / 772 / 100 / 84 / 96.5 / 105
9 / 883 / 100 / 87 / 98.11111 / 111
10 / 1000 / 100 / 90 / 100 / 117
11 / 1123 / 100 / 93 / 102.0909 / 123
12 / 1252 / 100 / 96 / 104.3333 / 129
13 / 1387 / 100 / 99 / 106.6923 / 135
14 / 1528 / 100 / 102 / 109.1429 / 141
15 / 1675 / 100 / 105 / 111.6667 / 147
16 / 1828 / 100 / 108 / 114.25 / 153
17 / 1987 / 100 / 111 / 116.8824 / 159
18 / 2152 / 100 / 114 / 119.5556 / 165
19 / 2323 / 100 / 117 / 122.2632 / 171
20 / 2500 / 100 / 120 / 125 / 177

c- here the firm is experiencing quadratic relationship, where the total cost function increase at increasing rate from the outset of production, this implies that the law of diminishing return take effect as soon as the firm start to produce.

That is why the MC and AVC are increase as soon as production begins

And still MC intersect with AC and AVC at their min. points.

TC = 100 + 600 Q

(linear equation)

Q / TC / FC / AVC / AC / MC
0 / 100 / 100 / 60
1 / 160 / 100 / 60 / 160 / 60
2 / 220 / 100 / 60 / 110 / 60
3 / 280 / 100 / 60 / 93.33333 / 60
4 / 340 / 100 / 60 / 85 / 60
5 / 400 / 100 / 60 / 80 / 60
6 / 460 / 100 / 60 / 76.66667 / 60
7 / 520 / 100 / 60 / 74.28571 / 60
8 / 580 / 100 / 60 / 72.5 / 60
9 / 640 / 100 / 60 / 71.11111 / 60
10 / 700 / 100 / 60 / 70 / 60
11 / 760 / 100 / 60 / 69.09091 / 60
12 / 820 / 100 / 60 / 68.33333 / 60
13 / 880 / 100 / 60 / 67.69231 / 60
14 / 940 / 100 / 60 / 67.14286 / 60
15 / 1000 / 100 / 60 / 66.66667 / 60
16 / 1060 / 100 / 60 / 66.25 / 60
17 / 1120 / 100 / 60 / 65.88235 / 60
18 / 1180 / 100 / 60 / 65.55556 / 60

c- here the firm experience linear cost function, this indicate that total cost increase at a constant rate, this means that the firm is experiencing neither decreasing nor increasing return as its variable inputs is added. Each additional unit of variable inputs adds the same amount of additional output (MP), therefore the change in the total cost relative to change in output is the same throughout the range of output considered

Now we can see that AVC=MC and extend as to equal horizontal lines denating that marginal cost remains constant as output increase.

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Problem 5-p262

T OR F, explain

a)A decision maker must always use the historical cost of raw materials in making an economic decision (F)

Because raw materials are not the only variable that should be considered, there are many other variables

b)The MC curve always intersect the AC curve at the AC lowest point (T)

Because when MC = AC average cost is at its minimum.

c)The portion of the long run cost that is horizontal indicate that the firm is experiencing neither economies nor diseconomies of scale (T)

Because at this portion of the long term function the average cost remains constant as output increase or decrease.

d)MC is relevant only in the short run analysis of the firm(F)

Because MC can also be used at long run analysis because even fixed cost varies in the long run

e)The rational firm will try to operate most efficiently by producing at the point where the average cost is minimized (F)

Because the rational firm will operate at where profit is maximized.