Question

Dynamic Competitive Equilibrium. Wal-Mart and other movie DVD retailers, including online vendors like Amazon.com, employ a two-step pricing policy, During the first 6 months following a theatrical release, movie DVD buyers are wiling 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 $0.0045 Q2 aTCaQ = $28 _ $0.009 Q MR Total cost (TC) and marginal costs (MC) for production and distribution are TC $4,500 $3Q+ S0.0005 Q2 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 output, B. After 6 months, price-sensitive DVD buyers appear willing to pay no more than $6 per DVD. Calculate the equilibrium price-output activity level in this situation. Is this a stable equilibrium?

Answer 1

(A)

Profit is maximized when MR = MC.

28 - 0.009Q = 3 + 0.001Q

0.01Q = 25

Q = 2,500 (thousand)

P = 28 - (0.0045 x 2,500) = 28 - 11.25 = $16.75

TR = P x Q = 16.75 x 2,500 = $41,875 (Thousand)

TC = 4,500 + (3 x 2,500) + (0.005 x 2,500 x 2,500) = 4,500 + 7,500 + 31,250 = $43,250 (Thousand)

Profit ($Thousand) = TR - TC = 41,875 - 43,250 = - 1,375 (Loss)

(B)

When P = $6, from demand function,

P = 28 - 0.0045Q

6 = 28 - 0.0045Q

0.0045Q = 22

Q = 4,889 (Thousand)

However, since $6 is lower than equilibrium price of $16.75, at this lower price, the firms will lower their quantity supplied, causing a shortage which will eventually push up the price towards equilibrium, rendering this output as an unstable outcome.