Question

Imagine Chiquita owns a start up – Swanky Dog Inc. – a firm that sells high end winter coats for dogs. Dog coats sell for $80 each without deviation. She only has enough capacity in her facility to produce a maximum of 10 coats per week. The fixed costs of production are $100. The total variable costs are as follows:

price	quantity	FC	VC
80	0	100	0
80	1	100	55
80	2	100	84
80	3	100	114
80	4	100	184
80	5	100	270
80	6	100	389
80	7	100	513
80	8	100	651
80	9	100	809
80	10	100	977

Using the above information, start an Excel worksheet. Make categories and calculate the values for each of the following: price, quantity, fixed cost, variable cost, average variable cost, total costs, average total costs, marginal cost, total revenue, marginal revenue, and profit.

After finding all values in the worksheet, determine what the profit maximizing quantity is for Chiquita’s firm. How can you tell?

c)      Plot the data. In one plot, show ATC, AVC, MC, and MR for Q=[0, 10]. In a separate plot, show Profits as a function of quantity produced over Q=[0,10].

Answer 1

From the table, we extend the data to produce the schedules for TC (TC = FC + VC), AVC (AVC = VC/Q), ATC (ATC = TC/Q), MC = (difference in successive TC)/difference in sucessive Q). Profit is the difference of TR and TC.

Price	Q	FC	VC	TC	AVC	ATC	MC	TR	MR	Profit
80	0	100	0	100				0		-100
80	1	100	55	155	55.0	155.0	55	80	80	-75
80	2	100	84	184	42.0	92.0	29	160	80	-24
80	3	100	114	214	38.0	71.3	30	240	80	26
80	4	100	184	284	46.0	71.0	70	320	80	36
80	5	100	270	370	54.0	74.0	86	400	80	30
80	6	100	389	489	64.8	81.5	119	480	80	-9
80	7	100	513	613	73.3	87.6	124	560	80	-53
80	8	100	651	751	81.4	93.9	138	640	80	-111
80	9	100	809	909	89.9	101.0	158	720	80	-189
80	10	100	977	1077	97.7	107.7	168	800	80	-277

Note that the profit maximizing quantity for Chiquita’s firm, is Q = 4. At this level, profit is maximum at $36 and difference between MR and MC is minimum and positive.

b) Graph plots are provided below