8.11: Exercises for Chapter 8

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EXERCISE 8.1

The relationship between output Q and the single variable input L is given by the form . Capital is fixed. This relationship is given in the table below for a range of L values.

L	1	2	3	4	5	6	7	8	9	10	11	12
Q	5	7.07	8.66	10	11.18	12.25	13.23	14.14	15	15.81	16.58	17.32

Add a row to this table and compute the MP.
Draw the total product (TP) curve to scale, either on graph paper or in a spreadsheet.
Inspect your graph to see if it displays diminishing MP.

EXERCISE 8.2

The TP for different output levels for Primitive Products is given in the table below.

Q	1	6	12	20	30	42	53	60	66	70
L	1	2	3	4	5	6	7	8	9	10

Graph the TP curve to scale.
Add a row to the table and enter the values of the MP of labour. Graph this in a separate diagram.
Add a further row and compute the AP of labour. Add it to the graph containing the MP of labour.
By inspecting the AP and MP graph, can you tell if you have drawn the curves correctly? How?

EXERCISE 8.3

A short-run relationship between output and total cost is given in the table below.

Output	0	1	2	3	4	5	6	7	8	9
Total Cost	12	27	40	51	61	70	80	91	104	120

What is the total fixed cost of production in this example?
Add four rows to the table and compute the TVC, AFC, AVC and ATC values for each level of output.
Add one more row and compute the MC of producing additional output levels.
Graph the MC and AC curves using the information you have developed.

EXERCISE 8.4

Consider the long-run total cost structure for the two firms A and B below.

Output	1	2	3	4	5	6	7
Total cost A	40	52	65	80	97	119	144
Total cost B	30	40	50	60	70	80	90

Compute the long-run ATC curve for each firm.
Plot these curves and examine the type of scale economies each firm experiences at different output levels.

EXERCISE 8.5

Use the data in Exercise 8.4,

Calculate the long-run MC at each level of output for the two firms.
Verify in a graph that these LMC values are consistent with the LAC values.

EXERCISE 8.6

Optional: Suppose you are told that a firm of interest has a long-run average total cost that is defined by the relationship LATC=4+48/q.

In a table, compute the LATC for output values ranging from . Plot the resulting LATC curve.
What kind of returns to scale does this firm never experience?
By examining your graph, what will be the numerical value of the LATC as output becomes very large?
Can you guess what the form of the long-run MC curve is?

1. Note that the long-run average total cost is not the collection of minimum points from each short-run average cost curve. The envelope of the short-run curves will pick up mainly points that are not at the minimum, as you will see if you try to draw the outcome. The intuition behind the definition is this: With increasing returns to scale, it may be better to build a plant size that operates with some spare capacity than to build one that is geared to producing a smaller output level. In building the larger plant, we can take greater advantage of the scale economies, and it may prove less costly to produce in such a plant than to produce with a smaller plant that has less unused capacity and does not exploit the underlying scale economies. Conversely, in the presence of decreasing returns to scale, it may be less costly to produce output in a plant that is used "overtime" than to use a larger plant that suffers from scale diseconomies.

2. Two English farmers changed the lives of millions in the 18^th century through their technological genius. The first was Charles Townsend, who introduced the concept of crop rotation. He realized that continual use of soil for a single purpose drained the land of key nutrients. This led him ultimately to propose a five-year rotation that included tillage, vegetables, and sheep. This rotation reduced the time during which land would lie fallow, and therefore increased the productivity of land. A second game-changing technological innovation saw the introduction of the seed plough, a tool that facilitated seed sowing in rows, rather than scattering it randomly. This line sowing meant that weeds could be controlled more easily—weeds that would otherwise smother much of the crop. The genius here was a gentleman by the name of Jethro Tull.