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One cubic centimeter of water has a mass of (a) Determine the mass of of water. (b) Biological substances are water. Assume that they have the same density as water to estimate the masses of a cell that has a diameter of a human kidney, and a fly. Model the kidney as a sphere with a radius of and the fly as a cylinder long and in diameter.

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Texts: Please complete parts d and e. Thank you! (30 points) Consider a more general Cournot model. Suppose there are n firms. The firms simultaneously and independently select quantities to bring to the market. Firm i's quantity is denoted qi, which is constrained to be greater than or equal to zero. All of the units of goods are sold, but the prevailing market price depends on the total quantity in the industry, which is Q = Σqi. Suppose the price is given by p = a - bQ and each firm produces at marginal cost c. There is no fixed cost for the firms. The profit function for firm i is given by ui = p(Q)qi - cqi = (a - bQ)qi - cqi. Defining Q-i as the sum of the quantities produced by all firms except firm i, we have ui = (a - bqi - bQ-i)qi - cqi. Each firm maximizes its own profit.
  1. (5) Represent this game in the normal form by describing the strategy spaces and payoff functions. (Check the last slide on the lecture notes for an example)
  2. (10) Find firm i's best-response function as a function of Q-i. Graph this function. (Plot qi on the x-axis and Q-i on the y-axis)
  3. (10) Compute the Nash equilibrium of this game. Report the equilibrium quantities, price, and total output. (Hint: In equilibrium, all firms will produce the same output because the game is symmetric. So in equilibrium, assume that q1 = q2 = q3... = qn. Which implies Q* = (n - 1)q*. Substitute in the best response function to solve for q*)
  4. (5) Find the price at which output is sold in Nash Equilibrium.
  5. Bonus (5) What happens to the price in a Cournot model as the number of firms increases to infinity?
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Question Text
One cubic centimeter of water has a mass of (a) Determine the mass of of water. (b) Biological substances are water. Assume that they have the same density as water to estimate the masses of a cell that has a diameter of a human kidney, and a fly. Model the kidney as a sphere with a radius of and the fly as a cylinder long and in diameter.
TopicAll topics
SubjectPhysics
ClassClass 11