3. Assume for simplicity that a monopolist has no costs of production and faces a demand curve given by Q = 150 – P (a) Calculate the profit-maximizing price-quantity combination for this monopolist. Also calculate the monopolisť's profit. (b) Suppose instead that there are two firms in the market facing the demand and cost conditions just described for their identical products. Firms choose quantities simultaneously as in the Cournot model. Compute the outputs in the Nash equilibrium. Also compute market output, price, and firm profits. (c) Suppose the two firms choose prices simultaneously as in the Bertrand model. Compute the prices in the Nash equilibrium. Also compute firm output and profit as well as market output.

Assume that two companies (A and B) are duopolists who produce identical products. Demand for the products is given by the following linear demand function: P=200− Q A − Q B where Q A  and Q B  are the quantities sold by the respective firms and P is the selling price. Total cost functions for the two companies are TC A =1,500+55 Q A + Q A 2 TC B =1,200+20 Q B +2 Q B 2 Assume that the firms form a cartel to act as a monopolist and maximize total industry profits (sum of Firm A and Firm B profits). In such a case, Company A will produce    units and sell at   . Similarly, Company B will produce    units and sell at   . At the optimum output levels, Company A earns total profits of    and Company B earns total profits of   . Therefore, the total industry profits are   . At the optimum output levels, the marginal cost of Company A is    and the marginal cost of Company B is   . The following table shows the long-run equilibrium if the firms act independently, as in the Cournot model…

Two firms (called firm 1 and firm 2) are the only sellers of a good for which the demand equation is Here, q is the total quantity of the good demanded and p is the price of the good measured in dollars. Neither firm has any fixed costs, and each firm’s marginal cost of producing a unit of goods is $2. Imagine that each firm produces some quantity of goods, and that these goods are sold to consumers at the highest price at which all of the goods can be sold. A Cournot equilibrium in this environment is a pair of outputs (q1, q2) such that, when firm 1 produces q1 units of goods and firm 2 produces q2 units of goods, neither firm can raise its profits by unilaterally changing its output. Find the Cournot equilibrium. Determine whether the price at which the goods are sold exceeds marginal cost.  

Question 1. In this question we begin by constructing a competitive market for a good, and then compare the outcome when supply is controlled by a single-price monopolist. Suppose that the demand for units of some beverage comes from households with the preferences over units of the beverage (x1) and expenditure on all other goods (x2) represented by the following utility function, U(x1,x2) = 800 In(x1) + x2 Each household has an exogenous income of I per period. The second 'good' is referred to as a 'composite' good and is an amount of money. We assume throughout that p2 = 1. (4 marks) Derive a household's ordinary demand functions, x1(P1, 1,1) and x2(P1,1,1) when they are price-takers in the market for the beverage. How large does the exogenous income need to be in order for the household to enjoy a positive amount of both 'goods'? i) (2 marks) Suppose there are 80 households who participate in the market for the beverage. Half of the households have an income of $1200 per period,…