Question 3: 30 points Suppose that you are putting on a wine-tasting festival fo
ID: 1132490 • Letter: Q
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Question 3: 30 points Suppose that you are putting on a wine-tasting festival for the bourgeoisie done extensive research into the characteristics of each possible attendant a provide to each attendant, you come to the following conclusions about your individual's demand: of Eugene. Having nd the costs to costs and each D(p) = 100-2p C(g) 20q where C(q) is the cost to provide q samples of wine and D(p) is each consumer's demand for wine samples given the price you set p. Because your wine-tasting festival is so far superior to every other festival in the area, you essentially have monopoly over each incredibly wealthy attendant (This is just a story to motivate the ridiculously high numbers you'll get).Explanation / Answer
Demand function: D(p): Q = 100 - (p/2) = 100 - 0.5p
Supply function: MC = dC(q)/dQ = 20
(a) Price elasticity of demand (Ed) = (dQ/dp) x (p/Q)
= - 0.5 x [p / (100 - 0.5p)]
= - 0.5p / (100 - 0.5p)
= p / (p - 200) [Multiplying both sides by (-2) for simplification]
(b) A monopolist will equate marginal revenue (MR) with MC.
Demand: Q = 100 - 0.5p
0.5p = 100 - Q
p = 200 - 2Q
Total revenue (TR) = p x Q = 200Q - 2Q2
MR = dTR/dQ = 200 - 4Q
Equating with MC,
200 - 4Q = 20
4Q = 180
Q = 45
p = 200 - (2 x 45) = 200 - 90 = 110
Profit = Q x (p - MC) = 45 x (110 - 20) = 45 x 90 = 4050
(c) This is a case of perfect price discrmination where price of wine sampls is equal to MC, and entry fee is equal to entire consumer surplus (CS).
Equating price and MC,
200 - 2Q = 20
2Q = 180
Q = 90
Price = MC = 20
From demand function, when Q = 0, p = 200 (Reservation price)
CS = Area between demand curve and market price = (1/2) x (200 - 20) x 90 = 45 x 180 = 8100
Therefore, fixed entrance fee = 8100
(d) Price is maximum when Q = 0, i.e. maximum price is 200. In this case profit equals entire consumer surplus, equal to 8100 as derived in part (c).
NOTE: As per Chegg Answering Policy, first 4 parts have been answered.
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