Monsanto controls about 75-100% of the commercial seed market, so one is safe to
ID: 1136686 • Letter: M
Question
Monsanto controls about 75-100% of the commercial seed market, so one is safe to conclude they behave like a monopoly. Suppose that the inverse demand function for commercial seeds looks like this P=3000-5Q, where Q is the quantity sold and it represents bushels of seeds of about 5 tons. Let the total cost function for Monsanto be TC=12,500-500Q.
Set up the profit function.
What is the profit maximizing condition for this Monopoly? Given the profit maximizing condition, how many bushels will it produce?
What will the market price and profits for Monsanto given its production choice?
Suppose that, because of the economic crisis there is an overall reduction in demand such that now P=2000-5Q. How will that affect the operations for Monsanto. Will it produce more? Less? Will price change? How about profits?
What is a Nash Equilibrium? What is a prisoner’s dilemma? The prisoner’s dilemma, when played only once, always ends up in a Nash Equilibrium. Does that mean that a Nash Equilibrium always implies a prisoner’s dilemma? Explain.
Suppose that the Karaoke machine industry is a duopoly. The two firms there, Akai and Baku both facing an industry inverse demand function of P=100-QA-QB. Currently each firm has a marginal cost of $40 and no fixed costs.
Set up the profit function for each firm
What are the reaction functions resulting from the first order condition? Provide a brief intuition for the relationship of output between these two firms
Given the reaction functions, what is the equilibrium for this oligopoly? (i.e.: what are quantities, prices and profits in equilibrium?)
Look into the industry of your choice. What market structure (or structures) do you see? Perhaps along the supply chain, there are different types of markets. In a few sentences, explain what can be determining that market structure.
Explanation / Answer
P = 3000 - 5Q
TC = 12500 - 500Q
(a) Profit (Z) = Revenue (TR) - TC = (P x Q) - (12500 - 500Q) = 3000Q - 5Q2 - 12500 + 500Q
Z = 3500Q - 5Q2 - 12500
(b) Profit is maximized when dZ/dQ = 0.
dZ/dQ = 3500 - 10Q = 0
10Q = 3500
Q = 350
(c) When Q = 350,
P = 3000 - (5 x 350) = 3000 - 1750 = 1250
Profit (Z) = (3,500 x 350) - (5 x 350 x 350) - 12,500 = 1,225,000 - 612,500 - 12,500 = 600,000
(d) New demand function: P = 2000 - 5Q
Profit (Z) = Revenue (TR) - TC = (P x Q) - (12500 - 500Q) = 2000Q - 5Q2 - 12500 + 500Q
Z = 2500Q - 5Q2 - 12500
Profit is maximized when dZ/dQ = 0.
dZ/dQ = 2500 - 10Q = 0
10Q = 2500
Q = 250 (So quantity will fall by (350 - 250) = 100 units)
P = 2000 - (5 x 250) = 2000 - 1250 = 750 (Price will fall by (1250 - 750) = 500)
Profit = (2,500 x 250) - (5 x 250 x 250) - 12,500 = 625,000 - 312,500 - 12,500 = 300,000 (Profit will fall by (600,000 - 300,000) = 300,000).
NOTE: As per Answering Policy, first 4 parts have been answered.