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# Finding the optimal price and output combination

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A television station is considering the sale of promotional DVDs. It can have the DVDs produced by one of two suppliers. Supplier A will charge the station a set-up fee of \$1,200 plus \$2 for each DVD; supplier B has the no set-up fee and will charge \$4 per DVD. The station estimates its demand for the DVDs to be given by Q = 1,600 - 200P, where P is the price in dollars and Q is the number of DVDs. (The price equation is P = 8 - Q / 200).

a. Suppose the station plans to give away the videos. How many DVDs should it order? From which supplier?
b. Suppose instead that the stations seek to maximize its profits from sales of the DVDs. What price should it charge? How many DVDs should it order from which supplier?

#### Solution Preview

a. Suppose the station plans to give away the videos. How many DVDs should it order? From which supplier?

Q=1600-200P
Let us calculate the number of DVDs needed at nil price i.e. P=0
Q=1600-200*0=1600
He should order 1600 DVDs.

Suppose he orders from Supplier A,
Total cost=1200+2*1600=\$4400

Suppose he orders from Supplier B,
Total cost=4*1600=\$6400

Cost of ordering ...

#### Solution Summary

It is very important to choose an optimal price and output combination in the day to day business. Solution to given problem depict the steps to determine the optimal price and output combination with the help of given equation.

\$2.19

## Finding the Optimal Output Price Combination

Consider an industry dominated by one firm that acts as a price leader. The industry also has a large number of smaller price followers that can sell as much as they want at the price set by the dominant firm. The demand curve for the output of all firms in the industry is:

QT = - 42,500 + 70P

The total cost curve for the dominant firm and the aggregate cost curve for the price followers are:

TCD = 50,000 + 150Q + 0.005Q2

ΣMCf = 250 + 0.05Q

Determine the price and output combination that the dominant firm would need to maximize profit for itself.

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