3. Bada Bing, Ltd., supplies standard 256 MB- RAM chips to the U.S. computer and
ID: 1106582 • Letter: 3
Question
3. Bada Bing, Ltd., supplies standard 256 MB- RAM chips to the U.S. computer and electronics industry. Like the output of its competitors, Bada Bing’s chips must meet strict size, shape, and speed specifications. As a result, the chip-supply industry can be regarded as perfectly competitive. The total cost and marginal cost functions for Bada Bing are
TC = $1,000,000 + $20Q + $0.0001Q2
MC= $20+$0.0002Q
where Q is the number of chips produced.
Total costs include a normal profit.
a. Calculate Bada Bing’s optimal output and profits if chip prices are stable at $60 each.
b. Calculate Bada Bing’s optimal output and profits if chip prices fall to $30 each.
c. If Bada Bing is typical of firms in the industry, calculate the firm’s long-run equilibrium output, price, and economic profit levels.
Explanation / Answer
a) Given the industry supplies the chips in a perfect competative market, the marginal cost is equal to the price. From the given marginal cost equation we can have the following equation
$20+$0.0002Q = $60
Q = 40/0.0002 = 200000, This will be the Optimal output of the firm if the prices are $60.
The optimal profit can be given by total revenue minus total cost
Total revenue is given by the product of price and output, i.e., 60x200000 = 12000000
Total cost ifunction is given in the question itself, i.e., $1000000 + $20Q + $0.0001Q^2.
Putting the value of Q= 200000, we have total costs = 9000000,
so the total profit will be 12000000-9000000 = 3000000.
b) If the prices fall to $30, then from the marginal cost condition $20+$0.0002Q = $30, gives us Q = 50000.
Profits can be culculated from the difference of total revenue and total cost.
Total revenue is given by $30x50000 = 1500000
Total costs will be estimated from $1000000 + $20Q + $0.0001Q^2 with Q= 50000,
From this we have total costs 2250000,
Thus the total profits of the industry when the prices fall to $30 is -75000. Actually the industry is making a loss of 75000 when the prices fall to $30.
c) As the firm is in a perfect competition, there will be no fixed costs in the long run
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