Elucidate price and output determination under Cournot and Stackelberg models of Oligopoly.
Price and output determination in oligopolistic markets, where a small number of large firms dominate, is a complex task due to the interdependence of the firms' decisions. Two prominent models used to analyze oligopolistic behavior are the Cournot and Stackelberg models. Both models offer insights into how firms in an oligopoly set prices and determine their output levels, taking into account the strategic interactions among them.
### Cournot Model:
The Cournot model is named after the French economist Augustin Cournot, who introduced it in 1838. This model assumes that firms compete by simultaneously choosing their output levels, taking the output decisions of their rivals as given. The key features of the Cournot model include:
1. Number of Firms: There are two or more firms in the market, each producing a homogeneous product.
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Explain the concept of a Homothetic production function. Given a production function
where q represents total production, L and K stands for labour and capital respectively, and A is the technology coefficient. What are the returns to scale for such a production function?
(b) “Homothetic production function includes Homogeneous production function as a special case.” Justify this statement.
(a) How would you differentiate a Static game from a Dynamic game? (b) Consider the following game.
i) Can Backward induction be applied in this game to find a solution?
(ii) What will be the Subgame Perfect Nash equilibria for the given game?
Consider a market for energy drinks consisting of only one firm. The firm has a linear cost function: C(q) = 4q, where q represents quantity produced by the firm. The market inverse demand function is given by P(Q) = 24 − 2Q, where Q represents total industry output. Based on the given information answer the following:
(i) What price will the firm charge? What quantity of energy drinks will the firm sell?
(ii) Now suppose a second firm enters the market. The second firm has an identical cost function. What will be the Cournot equilibrium output for each firm?
(iii) What is the Stackelberg equilibrium output for each firm if firm 2 enters second?
(iv) How much profit will each firm make in the Cournot game? How much in Stackelberg?
(v) Which type of market do consumers prefer: monopoly, Cournot duopoly or Stackelberg duopoly? Why?
Elucidate price and output determination under Cournot and Stackelberg models of Oligopoly.
Raj expects his future earnings to be worth Rs 100. If there is some unfortunate event, his expected future earnings will be Rs 25. The probability of an unfortunate event to occur is 2/3 , while that of things remaining fortunate is 1/3 . Suppose his utility function is given by U(Y) =
Differentiate between a Hicksian and a Walrasian demand function? Do they ever intersect? Explain.
(b) Consider a Cobb-Douglas utility function
U (X,Y)= X1/5 Y4/5
where X and Y are the two goods that a consumer has an option to consume at per unit prices of PX and PY, respectively. Assume income of the consumer to be Rs M. Determine (a) Uncompensated demand functions for goods X and Y
(b) Compensated demand functions for goods X and Y
(a) Consider an Edgeworth box that describes a two-person, two-commodity exchange scenario. Explain how trade takes place between the two individuals starting from the initial endowment position. What is the significance of the slope of the ray passing through a Pareto optimal point and the endowment point? (b) Consider a pure-exchange economy of two individuals (A and B) and two goods (X and Y). Assume both the individuals are endowed with 2 units of good X and 1 unit of good Y each.
where Xi and Yi for i = {A, B} represent individual i’s consumption of good X and Y respectively. Determine the aggregate excess demand functions for each good.