uestion 1. In this question we begin by constructing a competitive market for a good, and then compare the stcome when supply is controlled by a single-price monopolist. Suppose that the demand for units of some everage comes from households with the preferences over units of the beverage (x,) and expenditure on all her goods (x2) represented by the following utility function, U(x1,X2) = 800 In(x;) + x2 ach household has an exogenous income of I per period. The second 'good is referred to as a 'composite' pod and is an amount of money. We assume throughout that p2 = 1. i) Derive a household's ordinary demand functions, x, (p,, 1,1) and x,(P, 1, 1) when they are price-takers in the market for the beverage. How large does the exogenous income need to be
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- A manager of a nightclub realizes that demand for drinks is more elastic among students and is trying to determine the optimal pricing schedule. Specifically, he estimates the following average demand for his customer types: Under 25: q^r=18-5pOver 25: q=10-2p The two age groups visit the nightclub in equal numbers on average. Assume that drinks cost the club $2 to make. A) suppose that once again it is impossible to identify which group the customers belong. Suppose the manager lowers the price of drinks to equal to marginal cost and still wanted to attract both customers, what entry fee would the manager set?Consider a monopolist who is selling his blockbuster drug in two markets where one market is much larger than the other. Suppose the demand in the two markets is given by q1 = 30 − p1 and q2 = 3 − p2 (quantity is measured in millions of complete dosages and price is in your favorite currency) and the marginal cost of production and distribution is roughly the same and equal to 1 per unit (c=1). This problem asks you to compare equilibrium outcomes (prices, quantities, profits, consumer surplus, and consumer surplus per unit of output) when the monopolist can price discriminate across the two markets versus when it must set a uniform price. It then asks you to comment on some recent policy proposals. For each market separately, set up and solve the monopolist’s profit-maximizing problem. Specifically, write down/compute the following. Inverse demand and the profit functions. Equilibrium prices (), quantities () and profits () Consumer surplus () and consumer surplus per unit of…Suppose you are the owner of a movie theater. There are two types of customers: senior (‘s’) and non-senior (‘ns’). You know if a customer is a senior or non-senior and so you could use price discrimination with selection by indicators. The demand for movies is: Senior: qs = 30 − 3ps Non-Senior: qns = 15 − pns 1. Plot the total demand curve and the marginal revenue curve if the two types of consumers are as one. 2. Suppose that MC = 1 and that you can only set a single price. 2a. What is the optimal uniform price? 2b. What is the profit under uniform pricing? 2c. What is consumer surplus under uniform pricing?
- A firm is a profit-maximizing monopolist in the market of a patented computer software. As an economic analyst,you observe the following data:a) The monopoly’s price is set at $50 per copy.b) The monopoly’s total revenue is $300,000.c) The monopoly’s marginal cost at the profit-maximizing quantity is at $30 per copy.Based on the observed data, please determine the linear inverse demand function.Fill in the blanks. Suppose the inverse demand function is of the formwhere a, b are both positive constants, determine the value for a: 1 and b: 2 .Hint: a should be an integer, the answer for b should round to four decimal places.Suppose that a monopolist sells its product in two countries; Japan and Canada. The monopolist’s marginal cost is $60 and total fixed cost is $100. The direct market demand equations in the two countries are as follows:QJ = 200 − 2PJ and QC = 100 − 0.5PC;where the subscript J denotes Japan and the subscript C denotes Canada. Suppose that the monopolist cannot prevent resale, i.e, the monopolist must charge a single price for both countries.a) Derive the direct total market demand equation, QD = f(P).b) What would be the profit-maximizing quantity (Q*), price (P*), and profit (π*)? Please answer both a) and b). Thank you.Q62 Assume that Mattel is a monopolist that sells 8 units of a toy per day at a unit price of $16. If it lowers the price to $15, its total revenue increases by $37. This implies that its sales quantity increases by Multiple Choice 1 unit per day. 12 units per day. 2 units per day. 3 units per day. 4 units per day.
- A monopolist w11ishes to maximize total revenue. She produces two outputs, (x1, x2) and faces the following demands for her products, X1 = 20 – 2p1, and X2 = 20 – 4p2 Where p1 and p2 are, respectively, the prices of the two goods. To produce one unit of x1 the monopolist must use one unit of land and one unit of capital. And, to produce one unit of x2 requires two units of land and one unit of capital. The firm has available 10 units of land and 6 units of capital. Specify the firm’s short-run maximization problem. Set up the Kuhn-Tucker conditions for maximization (you do not need to solve). Assume that the solution is x*1 = 5 1/3 (i.e. 16/3) and x*2 = 2/3. Explain which constraints are binding and whether the Lagrange multipliers are positive or zero and what they mean.Consider a monopolist who produces perishable (non durable good) in two periods. The cost of production of one unit is c = 1/4. In both periods the monopolist faces a unit mass of costumers of two types θH = 1 and θL = 1/2. Each consumer needs only one unit of the good and gets a utility θ from buying it. Fraction of each type in the population is µ = 1/2. The discount factor is δ > 1/2. Suppose the monopolist cannot price discriminate between new and returning customers, what would be his prices and profits in the two periods? Suppose now the monopolist got a technology that allows him to track costumers, so that at period 2 he can distinguish new and returning customers, i.e. in period 2 he can charge price pN to a new customer and price pR to a returning customer. As in the class, assume there is not commitment to What would be the monopolists prices and profits in this case? What is the monopolist’s gain from the ability to price discriminate, explain the intuition behind…A golf club’s owner has commissioned a market study that estimates the average customer’s monthly demand curve for playing 18-hole golf game to be Q=50 – 0.5P, where Q stands for the number of 18-hole golf game, and P is the green fee. The marginal cost is given by MC=20. (1) Under two-part pricing strategy, what is the optimal amount of green fee to charge for one round of 18-hole golf game? (2) Under two-part pricing strategy, what is the optimal amount of membership due? (3) Under two-part pricing strategy, what is the size of the profit obtained from the average customer?
- Suppose a monopolist faces two markets withdemand curves given by D1(p1) = 200 − p1D2(p2) = 100 − 2p2Assume that the monopolist’s cost function is c(y) = y2 1. What is the optimal prices for the monopolist if it can charge different prices in these markets?2. What is the optimal price if the monopolist must charge the same price in each market?3. How much total consumers’ surplus changes between the two separate prices and the sameprice cases?. Let the demand curve for a monopolist’s product be P = 100 – 2Qd and the marginal cost of production be constant at MC = 10. Suppose that the firm considers moving from a uniform pricing strategy to a two-block tariff where the first block provides 15 units at a price of P1 = $70 and the second block provides an additional 15 units at a price of P2 = $40. How much does the monopolist’s profit rise with this scheme?Albert and Johny are the only sellers of Motorbikes in Ireland. The inverse market demand function for motorbikes is P(Y)= 200- 2Y . Both firms have the same total cost function: T(C)= 12Y and the same marginal cost: M(C)=12. Suppose now that the two firms decide to act like a single monopolist. What will the total quantity of Motorbikes sold in the market be and what will the equilibrium price be? Represent the profit maximisation problem on a graph and indicate the price and quantity at the equilibrium. Calculate the total profit made by the two firms when they act like a monopoly. Compare it with the total profit they were making in the Stackelberg oligopoly. For the two firms to be willing to agree to act as a monopoly, how should they split the quantity to produce between them? We assume that if they do not agree to act like a monopoly, then the market structure is the Stackelberg oligopoly studied above. We further assume that no money transfer is possible between the two…