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I need some explanation too! Show how each is calculated.?
ABC Pest Control Company specializes in pest control services for single-family homes. Entry is easy in the local market and a large number of local firms offer similar services. The contract provides whole house service, including one interior spraying per month and a yearly foundation spray. The cost to the company can be regarded as a constant amount per unit at:
AVC = R5 (five rands) per month per home
Management now estimates the firm’s demand curve for household service to be:
Q = 25 000 – 2 000P (what is the 25 000 and the 2000 and I assume P is price or service charge)
Where Q is the quantity of homes under service contract and P is the monthly service charge.
Based on management’s estimate of demand, calculate each of the following:
1.1 Marginal revenue (5)
1.2 Profit maximizing price (5)
1.3 Profit maximizing quantity (5)
1.4 The monthly profit if the monthly fixed costs are R12 000.
2 Answers
- Anonymous9 years agoFavorite Answer
Given the demand function, Q = 25000 - 2000P, Total Revenue can be found by TR = P x Q.
For that rewrite the demand function in terms of P.
i.e., P = (25000 - Q)/2000
P = 12.5 - 0.5Q
TR = P x Q
TR = (12.5 - 0.5Q)Q
TR = 12.5Q - 0.5QxQ............................................ Q square
MR = d(TR)/dQ
MR = 12.5 - Q
AVC = TC/Q
Hence total cost, TC = 5Q
A firm will be in equilibrium at the profit maximization point. MR = MC is the profit maximization condition.
MC = d(TC)/dQ
MC = d(5Q)/dQ = 5
MR = MC at equilibrium point
12.5 - Q = 5
Q = 12.5/5 = 2.5 ....................................profit maximizing quantity
Substituting Q = 2.5 in demand function P = 12.5 - 0.5Q
P = 12.5 - 0.5 x 2.5 = 12.5 - 1.25 = 11.25..............................profit maximizing price
When FC = 12000, TC = FC + VC = 12000 + 5Q
Profit = TR - TC
Profit = (12.5Q - 0.5QxQ) - (12000 + 5Q)
= 7.5Q - 0.5QxQ - 12000
= 17.5 -3.125 -12000
= 14.375 - 12000
= -11985.625
