Question

Vinnie’s Painting Company specializes in painting houses. Their cost schedule is as follows:

OUTPUT	TFC	TVC	TC	AFC	AVC	ATC	MC
0			1000
1		100
2							100
3		400
4						450
5		1600
6		3200
7		6400

a) Given the partial data available, finish the table and calculate all the costs.

b) What is the minimum efficient scale of Vinnie’s company?

c) What is the marginal cost of 6 houses?

d) If Vinnie charges $825 per house, how many houses he should paint to maximize profits?

Answer 1

(a)

Output	TFC	TVC	TC	AFC	AVC	ATC	MC
0	1000	0	1000	---	----	----	----
1	1000	100	1100	1000	100	1100	100
2	1000	200	1200	500	100	600	100
3	1000	400	1400	333.33	133.33	466.67	200
4	1000	800	1800	250	200	450	400
5	1000	1600	2600	200	320	520	800
6	1000	3200	4200	166.67	533.33	700	1600
7	1000	6400	7400	142.86	914.29	1057.14	3200

TC = TFC at zero output level. And TFC remains same at each level of output.

TVC_n = TVC _n-1 + MC_n.

and

TC_n = TC _n-1 + MC_n.

Where n is output level.

TC = TVC + TFC

=> TVC = TC - TFC

-----

ATC = TC / output

AVC = TVC / output

AFC = TFC / output

ATC = AFC + AVC

----

MC = change in TC / change in output.

MC = change in TVC / change in output

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(b) Minimum efficient scale is output level to acheive minimum ATC

Minimum efficient scale occurs at the minimum point of ATC,

The minimum point of ATC is 450 at output level of 4.

hence, the minimum efficient scale is 4 units of output.

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(c) Marginal cost of 6 houses is 1600

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(d) A house should be paint till price is higher than MC.

Price is $825.

Till 5 houses, Price is higher than MC (note: The MC of 6th house is 1600)

Hence, 5 houses should be paint to maximize profit