Problem Set #2 – ECON 100B, Spring Quarter 2021 Name:______________________ Due: April 20, 2021 at 11:00pm ------------------------------------------------------------------------------------------------------------------------------Note: In order to receive credit, you must show your work. 1) Suppose you are operating a discount movie theater and want to increase profits by charging adults and kids different prices. Assume there are no variable costs, just fixed costs to show the movie. You estimate the inverse demand function for kids to be: p1(y1) = 4 – 0.05y1 You estimate the inverse demand function for adults to be: p2(y2) = 9.6 – 0.08y2 a) How many kids will watch a movie? What price will you charge kids? b) How many adults will watch a movie? What price will you charge adults? 2) Suppose the smartphone market has two firms, Samsung and Apple. Apple is the quantity (Stackelberg) leader in this market. The inverse market demand for smartphones is p(y) = 820 – 2y Firm costs are Samsung: c(y) = 20y Apple: c(y) = 20y a) What is the total quantity of phones produced in the market? How is this total quantity split between Samsung and Apple? 1 b) Suppose Apple decides it wants to produce more and increases output by 1. How do Apple’s profits change? (Hint: when firm 1 increases its output, then firm 2 will also change its output according to its reaction function) 3) Suppose there are two firms who are Cournot duopolists in the wine business. The inverse demand for wine is given by p(y) = $300 – 0.2y. One firm has marginal costs of $45 and the other firm has marginal costs of $30. What is the total output produced in the market? 2 4) The inverse demand function in an industry is p(y) = 20 – y. The marginal cost of a unit of output is $8. a) What will total profits be if there is one firm in the market (monopoly)? b) What will total profits be if there are two Cournot duopolists (simultaneous decision on quantity)? c) What will total profits be if there are two firms where one is a quantity leader (Stackelberg model)? 3
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