Advanced Placement Microeconomics

Question

Assume that a firm uses capital as a fixed factor of production and uses labor as a variable factor. The marginal product of labor at first increases and then decreases with the amount of labor.

(a) Using a correctly labeled graph, draw and identify the form’s average total cost curve (ATC), average variable cost curve (AVC), and marginal cost curve (MC).

(b) Given your graph in part (a), answer each of the following.

(i) Why is the MC shaped as it is?

(ii) What does the difference between the AVC and the ATC represent?

(c) Define economies of scale.

(d) Draw a long-run average total cost curve that has a region of economies of scale followed by a region of diseconomies of scale, as output increases.

Answer 1

We have MP Rising, Peaking and Then Falling. At its Peak AP=MP.

AVC= W/AP  Why? Explain. If I hire 10 worker and get 100 units of output I am getting (on Average) 10q per worker. If I have to pay each worker 10 dollars, My total labor or variable cost is $100 or $1 per Unit

MC=W/MP Why? Explain If I hire one more worker and he produces an ADDITIONAL 10 units (MP=10) and he cost me $10 to hire it costs me (incrementally) $1 to expand. IF MP is initially rising then falling then w/MP is  doing just the opposite. Convince yourself of this.

AFC = rK/Q Which is always Falling Why? Explain If it Costs $100 to rent a Machine and I hire no worker, I produce nothing. The more worker I here, the more I produce. If I hire 10 workers and get a total of 100 units of output. My fixed cost is still $100 but it is $1 per Unit of output

Consider this table

Labor	MP	TP	AP
0		0
1	5	5
2	10	15	7.5
3	15	30	10
4	10	40	10
5	5	45	9
6	2	47	47/6
7	0	47	47/7

Let K= 1 machine which costs $100 to Rent.  Let w=10.

You should be able to create this table

Q	Fixed Cost	Variable (labor) Cost	Total cost
5	100	10	110
15	100	20	120
30	100	30	130
40	100	40	140
45	100	50	150
47	100	60	160
47	100	70	170

You should then be able to create this table

Q	AFC	Average Variable (labor) Cost	ATC
5	100/5	10/5	110/5
15	100/15	20/15	120/15
30	100/30	30/30	130/30
40	100/40	40/40	140/40
45	100/45	50/45	150/45
47	100/47	60/47	160/47
47	100/47	70/47	170/47

If You Sketch out these Tables You can also sketch in MC and show that is Intersect AVC and ATC at there minimums.

Economies of Scale exist when changing all factors by the same factor of proportion increases output by a greater factor of proportion. For example, Doubling all inputs triples all outputs. If we double all inputs. TC will double but output more than doubles so Cost per unit declines

A Long Run average cost Curve (all inputs expanding optimally) will be decreasing with economies of scale, Flat with Constant returns to scale and increasing with diseconomies of scale. I have been trying to do a video answer for you here But I can’t get the whiteboards Up.

If you need help, reach out and we cam book something where I can show you exactly how to do the graphs and Why they make sense.

Best, Lenny