### Question Description

Industrial Organization–Homework 1Due date: Feb. 20, Friday (class time)

1. Suppose the demand for Netflix is given by

qN =a−bNpN +bHpH (1)

where qN is the number of Netflix subscriptions, pN is the price of a Netfilx plan, and pH is theprice of a Hulu plan.

(a) What is the price elasticity of Netflix subscriptions? (Hint: Use the definition of elasticityin Theorem 1 below)

(b) Suppose a = 500, bN = 10, bH = 5, and pN = pH = 50. What are Netflix’s demand elasticityand cross-price elasticity? Are products of Hulu and Netflix substitutes or complements?

(c) How much do consumers get in surplus at these prices?

2. Music Ventures sells a very popular MP3 player, the MP34u. The firm currently sells onemillion unites for a price of $100 each. Marginal cost is estimated to be constant at $40, whereas average cost (at the output level of one million units) is $90. The firm estimates that itsdemand elasticity (at the current price level) is approximately -2.

(a) Should the firm raise price, lower price, or leave price unchanged? Explain you answer.

Theorem 1 (own-price elasticity and cross-price elasticity)Suppose the demand function for some good is

Q = β0 + β1p + β2p ̃,

where β0, β1, β2 are constant numbers, Q is the quantity demanded, p is its price, and p ̃ is the

price of another good. Then the own-price elasticity is

ε = β1p/q,1

and the cross-price elasticity is

ε ̃ = β2p ̃/q

3. Las-O-Vision is the sole producer of holographic TVs, 3DTVs. The weekly demand for3DTVs is

q = D(p) = 10200 − 100p (2)

The cost of producing q 3DTVs per week is q2/2 (note this implies that MC = q).

(a) What is Las-O-Vision’s total revenue schedule?

(b) What is Las-O-Vision’s marginal revenue schedule?

(c) What is the profit-maximizing number of 3DTVs for Las-O-Vision to produce each week?What price does Las-O-Vision charge per 3DTV?

Theorem 2 (Relationship between total revenue and marginal revenue)Suppose the total revenue function TR(q) is

TR(q) = a + bq + cq2,

where a,b,c are constant numbers. Then the marginal revenue function MR(q) is

MR(q) = b + 2cq.Theorem 3 (Relationship between total cost and marginal cost)

Suppose the total cost function TC(q) is

TC(q) = a + bq + cq2,

where a,b,c are constant numbers. Then the marginal cost function MC(q) isMC(q) = b + 2cq.