Order Producers in the Short Run

Order Producers in the Short Run

Question 2

a) law of (eventually) diminishing returns (to the variable factor)

b) marginal product (of the variable factor)

c) above; below

Question 4

The table is completed below. Note that for marginal product (MP), the computation is

done for the change in output and labour input between rows. Thus, the first value in the

table for MP reflects the change in output from 0 to 2 and the change in labour from 0 to

1; the marginal product is therefore equal to ∆TP/∆L = 2/1 = 2.

Inputs of Labour Number of Snowboards AP MP

(per week) (per week)

0 0 —

1 2 2 2

2 5 2.5 3

3 9 3 4

4 14 3.5 5

5 18 3.6 4

6 21 3.5 3

7 23 3.3 2

8 24 3 1

Question 6

Order Producers in the Short Run(Q = KL – .1L2

), the values for Q are easily found. The answers are:

K L Q = KL – .1L2

10 5 50 – .1(25) = 47.5

10 10 100 – .1(100) = 90

10 15 150 – .1(225) = 127.5

10 20 200 – .1(400) = 160

10 25 250 – .1(625) = 187.5

10 30 300 – .1(900) = 210

10 40 400 – .1(1600) = 240

10 50 500 – .1(2500) = 250

© 2005 Pearson Education Canada Inc.

b) The following diagram shows the relationship between L and Q, for K fixed and equal

to 10. Note that the curve goes through the origin because when L equals 0, Q also equals

0 (independent of the value of K).

c) If K increases to K = 20, then the values of Q will also increase (for any given value of

L). The re-computed values for Q are in the table below. The new curve is shown in the

diagram above, indicated by K = 20.

K L Q = KL – .1L2

20 5 100 – .1(25) = 97.5

20 10 200 – .1(100) = 190

20 15 300 – .1(225) = 277.5

20 20 400 – .1(400) = 360

20 25 500 – .1(625) = 437.5

20 30 600 – .1(900) = 510

20 40 800 – .1(1600) = 640

20 50 1000 – .1(2500) = 750

d) A larger capital stock means that any given amount of labour now has more capital to

work with, and thus can produce more output. This increase in the average product of

labour is reflected simply by the upward shift in the curve shown above. Note also,

however, that in this case (and in many others), the increase in K also increases the

marginal product of labour for any given level of labour input. This is shown by the

increase in the slope of the curve for any level of L. For example, for L = 25, the slope of

© 2005 Pearson Education Canada Inc.

the K = 20 curve is greater than the slope of the K = 10 curve. This shows that the increase

in K has made labour more productive at the margin.

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