Econ 244
Exercise #1. [11] rates] A monopolist has an inverse demand curve given by p-[y] = 12 y and a cost curve given by cur] = 3:2 Describe how to determine its prot-maximizing level of output, and compute it. Show your work: to receive full credit you should show how you compute the optimal quantity of output. Exercise #2. [15 pts.] You are the manager of a new amusement park that has monopoly power over the service it oers: roller master rides. You have gured that the park will attract LIEU people per day, and each person will take a: = E 50p rides, where p is the price of a ride. The marginal cost of a ride is essentially zero. (a) If admission to the par]: were free and you had to choose the prot maximizing price of a ride In\Exercise #3. [20 pts.] Your company has monopoly over product H. It sells it in the UK and in the US. The cost function for your firm is c(q) = 10q. Your marketing department has identified the UK and the US demand curves for H to be qUS 50,000 - 2,000pus qUK = 10,000 - 500pu K, where qus and quy represent the quantities demanded by US and UK consumers respectively, and pus and pox the (US dollar) prices charged for the product in the US and in the UK, respectively. (a) If you were to charge the same price in both countries, how many units of H should you sell, and what price should you charge in order to maximize your company's profits? (b) If you could charge different prices in the US and the UK what prices would you choose and how many units would you sell in the US and how many in the UK?Exercise #4. [20 pts.] A company sells product A in a competitive market. Its long-run cost function is given by c(y) = y' + 10 for y > 0 c(y) = 0 for y = 0. where y represents the quantity of good A. (a) What is the lowest price at which this company will supply a positive amount of product A in the long-run? (b) Suppose that the market price for A is p = 2v10, and that 100 firms are operating in this market in the long-run. What is the equilibrium market demand for the product? Part II Exercise #5. [17 pts.] The rental price of machinery K (measured in machine-hours) is $10 per hour, while the hourly wage rate for labor, L (measured in labor-hours), is $6. Find the cost function associated with the following technology: y = 10K + L, where k represents machinery (measured in machine-hours) and L labor (measured in labor-hours).Part I Exercise #6. [18 pts.] John likes books and restaurant meals. His utility function is u(rb, I'm) = (x5)"-2 (Im)04, where ; represents the quantity of books that John "consumes" in a month, and I'm the amount of restaurant meals that he consumes. Suppose that both books and restaurant meals are perfectly divisible goods. The relative price of books in terms of restaurant meals is 0.4, i.e., buying a book costs 40% of the price of a restaurant meal. The nominal price of a restaurant meal is $40. John's income is $1,000 per month. Compute the quantity of books and restaurant meals that John consumes in a month
