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Dynamic Competitive Equilibrium - Detailed Calculations

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Wal mart and other movie DVD retailers including online vendors like amazon.com employ a two steps pricing policy. During the first 6 months following a theatrical release movie DVD buyers are willing to pay a premium for new releases. Total and marginal revenue relations for a typical newly released movie DVD are given by the following relations. TR=$28Q - $0.000045Q^2 MR=change in TC/ change in Q $28-$0.009Q
T0tal cost and marginal cost for production and distributions are TC=$4,500 +$3Q+$0.0005Q^2 MC=change in TC/change in Q=$3+$0.001Q
Where Q is in thousands of units DVDS, Because units are in thousands, both total revenues and total costs are in thousand of dollars. Total costs include a normal profit.
A. Use the marginal revenue and marginal cost relations given above to calculate DVD out put price, economic profits at the profits-maximizing activity level for new releases.

B. After six months, price sensitivity DVD buyers appear willing to pay no ore than $6.00 per DVD. Calculate the equilibrium price-output activity level in this situation Is this a stable equilibrium

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Solution Preview

>A. Use the marginal revenue and marginal cost relations given above to calculate DVD output, price, economic profits at the profits-maximizing activity level for new releases.

MR = 28 - 0.009Q
MC = 3 + 0.001Q

Let MR = MC
28 - 0.009Q = 3 + 0.001Q
28 - 3 = 0.009Q + 0.001Q
25 = 0.01Q
Q = 2500 (thousand)

TR = 28Q - 0.0045Q^2
TR = 28(2500) - 0.0045(2500^2)
TR = ...

Solution Summary

This solutions gives detailed, step-by-step calculations to determine the equilibrium price, output, revenue and cost for sellers of DVDs.

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