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Perfectly Competitive Equilibrium

Calculating optimal output and profits and comparing monopoly to perfectly competitive markets.

1. Perfectly Competitive Equilibrium. Bada Bing, Ltd., supplies standard 128 MB-RAM chips to the U.S. computer and electronics industry. Like the output of its compet6itors, 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 = δTC/δQ = $20 + $0.0002Q

where Q is the number of chips produced.
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 equilibrium output, price, and profit levels.

2. Monopoly Versus Perfectly Competitive Equilibrium. Big Apple Music, Inc., enjoys an exclusive copyright on music written and produced by the Fab Four, a legendary British rock group. Total and marginal revenues for the group's CDs are given by the following relations:

TR = $150Q - $0.000005Q2
MR = δTR/δQ = $15 - $0.00001Q

Marginal costs for production and distribution are stable at $5 per unit. All other costs have been fully amortized.
A. Calculate Big Apple's output, price, and profits at the profit-maximizing activity level.
B. What record price and profit levels would prevail following expiration of copyright protection based on the assumption that perfectly competitive pricing would result?

See attached file for full problem description.

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1. Perfectly Competitive Equilibrium. Bada Bing, Ltd., supplies standard 128 MB-RAM chips to the U.S. computer and electronics industry. Like the output of its compet6itors, 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 = δTC/δQ = $20 + $0.0002Q

where Q is the number of chips produced.
A. Calculate Bada Bing's optimal output and profits if chip prices are stable at $60 each.
For profit maximization MC=MR=P
Hence we have 20+0.0002Q=60
Solving we get Q=2000000
Profits = TC - ...

Solution Summary

Perfectly Competitive Equilibrium is assessed.

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