Question

The table below shows the weekly marginal cost (MC) and average total cost (ATC) for Buddies, a perfectly competitive firm that produces novelty ear buds in a competitive market. The market price of ear buds is $6.00 per pair. Buddies Production Costs Quantity MC ATC of Ear Buds ($) ($) 10 3.5 15 2 2.44 2.86 3.56 4.02 3.17 5.48 3.5 40 5.98 3.81 45 8.49 4.33 20 25 35 Instructions: In part a, enter your answer as the closest given whole number. a. If Buddies wants to maximize its profits, how many pairs of ear buds should it produce? pairs Instructions: In parts b-d, round your answers to 2 decimal places. b. At the profit-maximizing quantity, what is the total cost of producing ear buds? c. If the market price for ear buds is $6 per pair, and Buddies produces the profit-maximizing quantity of ear buds, what is Buddies weekly profit? d. If the market price is $5.50 per pair, and Buddies produces the profit-maximizing quantity of ear buds, what is Buddies weekly profit?

Answer 1

As per the information provided in the question, a firm producing novelty ear buds operates in a competitive market

Though firm operates in competitive market structure or perfect competition market structure, it Price=Average Revenue(AR) = marginal revenue(MR)

The buddies production cost is given in the below table

Quantity of ear buds or Q	Marginal cost (MC) in $ =	Average total cost (ATC) in $	Average Revenue(AR)= Marginal revenue(MR)=Price=$6	Profit =(AR-ATC)xQ
10		3.5	6	25
15	2	3	6	45
20	2.44	2.86	6	62.8
25	3.56	3	6	75
30	4.02	3.17	6	84.9
35	5.48	3.5	6	87.5
40	5.98	3.81	6	87.6 (Maximum profit)
45	8.49	4.33	6	75.15

(A)if buddies want to maximise profit, it should produce 40 pairs of ear buds

Explanation:- to maximise profit firm should operate at the quantity where Marginal cost (MC) should equal with Marginal revenue(MR) and MC should cuts MR from its below. In this problem at 40 units of quantity of ear buds the MR=$6 and MC=$5.98, which is close MR=$6.

(B) At profit maximising quantity the value of total cost in producing ear buds is =$152.4

Explanation:-

Profit maximising quantity = 40

ATC at profit maximising quantity = $3.81

Total cost = ATC x Profit maximising quantity = $3.81 x 40 =$152.4

(C) if the market price per buds is $6 per pair and Buddies operates at profit maximising quantity of ear buds its weekly profit is =$87.6

Explanation

Price=Average Revenue(AR) = marginal revenue(MR) =$6

To maximise profit firm should operate at the quantity where Marginal cost (MC) should equal with Marginal revenue(MR) and MC should cuts MR from its below. In this problem at 40 units of quantity of ear buds the MR=$6 and MC=$5.98, which is close to MR=$6.

Profit maximising quantity = 40

ATC at profit maximising quantity = $3.81

Profit =(AR-ATC)xQ = (6-3.81)x40 =$87.6

(D) if the market price per buds is $5.50 per pair and Buddies operates at profit maximising quantity of ear buds its weekly profit is =$70

Explanation

Price=Average Revenue(AR) = marginal revenue(MR) =$5.50

To maximise profit firm should operate at the quantity where Marginal cost (MC) should equal with Marginal revenue(MR) and MC should cuts MR from its below. In this problem at 35 units of quantity of ear buds the MR=$5.50 and MC=$5.48, which is close to MR=$5.50.

Profit maximising quantity = 35

ATC at profit maximising quantity = $3.5

Profit =(AR-ATC)xQ = (5.50-3.5)x35 =$70

Quantity of ear buds or Q	Marginal cost (MC) in $ =	Average total cost (ATC) in $	Average Revenue(AR)= Marginal revenue(MR)=Price=$5.5	Profit =(AR-ATC)xQ
10		3.5	5.5	20
15	2	3	5.5	37.5
20	2.44	2.86	5.5	52.8
25	3.56	3	5.5	62.5
30	4.02	3.17	5.5	69.9
35	5.48	3.5	5.5	70 (Maximum profit)
40	5.98	3.81	5.5	67.6
45	8.49	4.33	5.5	52.65