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Addis Music Company : Demand and Cost Analysis

Addis Music Company of D.C. enjoys an exclusive copyright for music written by KuKu, a legendary African Reggie group. Total revenue and cost for the group is as given below:

C=f(Q)=880+0.25Q+0.0025Q^2
P=20.25-0.01Q

P (the second equation) is the inverse demand curve. it is also the price (thus = P(Q)
C is total cost
Q is CDs produced and sold in units (demand)

A. Calculate the unit price if the ventor sold 200 CDs.
B. Calculate the demand curve for CD.
C. Calculate the fixed and variable costs.
D. Calculate the break even quantities (number of CDS).
E. Calculate the profit maximizing level of operation, the number of CDs the company will produce to maximize profit.

Solution Preview

A. Calculate the unit price if the vendor sold 200 CDs.
P=20.25-0.01*Q
Put Q=200
P=20.25-0.01*200=$18.25

B. Calculate the demand curve for CD.
P = 20.25 - .01Q
On rearranging we get
0.01Q=20.25-P
Q=2025-100P

C. Calculate the fixed and variable costs.
C = 880 + 0.25Q + 0.0025Q^2
Fixed cost can be found by putting Q=0
Fixed Cost=C at zero ...

Solution Summary

Solution depicts the steps to calculate the unit price, demand equation, fixed cost, BEP and optimal output level in the given case.

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