Question

Suppose Melody owns a business giving piano lessons. Assume that the market for piano lessons is perfectly competitive and that the equilibrium price of a piano lesson is $20. Melody’s total costs vary depending on the number of piano lessons she offers each day, as shown in the table below.

Number of lessons per day	Total cost per day ($)
0	30
1	50
2	68
3	78
4	96
5	115
6	138
7	168
8	208

a. When Melody gives 3 lessons per day, what is her average variable cost?

b. What is the profit-maximizing number of lessons for Melody to give each day?

c. What is Melody's daily economic profit at her profit-maximizing number of lessons?

Answer 1

Number of lessons per day	Total cost per day ($)	TR	FC	VC	AVC	MC	PROFIT
0	30	0	30	0			-30
1	50	20	30	20	20	20	-30
2	68	40	30	38	19	18	-28
3	78	60	30	48	16	10	-18
4	96	80	30	66	16.5	18	-16
5	115	100	30	85	17	19	-15
6	138	120	30	108	18	23	-18
7	168	140	30	138	19.71429	30	-28
8	208	160	30	178	22.25	40	-48

TR=P*Q, VC=TC-FC, MC=change in TC/change in Q, Profit = TR-TC, AVC=VC/Q

a) When Melody gives 3 lessons per day, her average variable cost is 16

b) Profit maximizing number of lessons for Melody is where P=MC = 5

c) Daily economic profit = TR-TC = 100-115 = -15