The weekly individual demand (i.e. each of your answers below will be in terms o
ID: 2494688 • Letter: T
Question
The weekly individual demand (i.e. each of your answers below will be in terms of person per week) for straw'berries in Elon is Q = 22 - 20*P and the total cost of producing straw'berries is C(Q) = 0. IQ. Suppose there is only one producer of straw'berries in Elon and that a city ordinance does not allow consumers to buy straw'berries from any other seller outside of Elon (not realistic, but assume it for this problem). 5* If the strawberry monopolist maximizes profits acording to standard economic theory, what condition will they use to determine how many strawberries to produce and what price to sell them for? What is the equilibrium price, quantity, monopoly profit and consumer surplus? 5* Next, suppose the monopolist knows each individual's willingness to pay and is allowed to charge them the most they are willing to pay. What is the name for this pricing strategy and how much profit will the monopolist make? (ungraded) The monopolist proposes a new system where they charge a strawberry membership fee that once paid allows consumers to buy as many strawberries as they want at a rock bottom price. If the town allows this, what will be the price per strawberry, the membership fee, the quantity of strawberries purchased and how much profits will the monopolist make?Explanation / Answer
Q = 22 - 20P
P = (22 - Q) / 20
Total revenue, TR = P x Q = (22Q - Q2) / 20
Marginal revenue, MR = dTR / dQ = (22 - 2Q) / 20 = (11 - Q) / 10
Total cost, TC = 0.1Q
Marginal cost, MC = dTC / dQ = 0.1
(a) A monopolist will maximize profits by equating MR with MC.
(11 - Q) / 10 = 0.1
11 - Q = 1
Q = 11 - 1 = 10
P = (22 - Q) / 20 = (22 - 10) / 20 = 12 / 20 = 0.6
Profit = (P x Q) - TC = P x Q - 0.1Q = Q x (P - 0.1) = 10 x (0.6 - 0.1) = 10 x 0.5 = 5
From demand function, when Q = 0, P = 22/20 = 1.1 [Reservation price]
Consumer surplus (CS) = Area between demand curve & equilibrium price = (1/2) x (1.1 - 0.6) x 10
= (1/2) x 0.5 x 10
= 2.5
(b) This is known as first degree price discrimination policy. In this case, total profit equals entire consumer surplus lying between reservation price and marginal cost.
If P = 0.1, Q = 22 - (20 x 0.1) = 22 - 2 = 20
Profit = (1.2) x (1.1 - 0.1) x 20 = (1/2) x 1 x 20 = 10
Note: First 2 graded questions are answered.
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