Question

Lizzie consumes cherries and apples. Her demand function for cherries is q_c=m-20p_c-40p_a, where m is her income, p_c is price of a pound of cherries, and p_a is price of a pound apples. At what price will the revenue from the sale of cherries to Lizzie be maximized, if her income is $1,000 and the price of a pound of apples is $10?

Group of answer choices

25

0

neither one is correct

15

10

Answer 1

Demand function for cherries is as follows -

q_c = m - 20p_c -40p_a

m = 1000

p_a = 10

q_c = m - 20p_c -40p_a

q_c = 1000 - 20p_c - (40 * 10) = 1,000 - 20p_c - 400 = 600 - 20p_c

q_c = 600 - 20p_c

20p_c = 600 - q_c

p_c = 30 - 0.05q_c

Calculate the total revenue function -

TR = p_c * q_c

TR = (30 - 0.05q_c) * q_c

TR = 30q_c - 0.05q_c²

Calculate the marginal revenue function -

MR = dTR/dq_c

MR = d(30q_c - 0.05q_c²)/dq_c

MR = 30 - 0.10q_c

The total revenue is maximized when marginal revenue is equal to zero.

MR = 0

30 - 0.10q_c = 0

0.10q_c = 30

q_c = 30/0.10 = 300

p_c = 30 - 0.05q_c = 30 - (0.05 * 300) = 30 - 15 = 15

Thus,

The price at which revenune will be maximized is $15.