Cournot Duopoly Homestore, Inc. and Store-It, Inc. are the only two manufactures of large plastic storage containers. Because the product of these two companies are considered the same, the companies represent a duopoly with an undifferentiated (i.e. homogeneous) product. Each company seeks to maximize profit, incurring a constant marginal cost of $10 per container (MC=$10). Assume there are no fixed costs, and because MC is constant, average variable cost (AVC) is also equal to $10. The (inverse) market demand for containers is given by the function P = 100 - 3Q, where P is in dollars and Q is in millions of containers per year. Because there are only two companies in this market, total quantity in the market is given by Q = QH+ Qs, where Q is the number of containers Homestore produces (in millions) and Qs is the number of containers Store-It produces (in millions). Assume the companies simultaneously choose how many containers to produce, which means the market is a Cournot duopoly. Use this information to answer Part A below (NOTE: There are also parts B and C to this problem). PART A: a. What is the reaction function for each firm? NOTE: Complete the expression for each reaction function by specifying (in the respective box) the constant term and the slope value associated with the other firm's quantity. NOTE: Round every answer (constant and slope values) to two decimal places (i.e. two places to the right of the decimal). Q = Qs = Constant - Slope Value x Qs X QH b. In equilibrium, how many containers (in millions) will each company produce? NOTE: "in millions" means you can omit the last six digits (i.e. use values from above). Homestor e Output: Store-It Output: c. What is the market price? Market Price: d. What is the profit (in millions) of each company? NOTE: "in millions" means you can omit the last six digits (i.e. use values from above). Homestor e Profit: Store-It Profit: PART B: Suppose Homestore and Store-It acted as a cartel. e. In this case, and assuming each company produced the same amount, how many containers would each company produce? Productio n by each company: f. What would be market price in this case? Market Price: g. What would be the profit (in millions) of each company? Homestor e Profit: Store-It Profit: PART C: Suppose Homestore were able to make its quantity decision before Store-It, so that Store-It made its decision after observing what Homestore did (thus, the market would reflect a Stackelberg--or "first-mover"-- duopoly). h. In this case, how many containers (in millions) would each company produce? Homestor e Output: j. What would be the profit (in millions) of each company? Homestor e Profit: i. What would be market price in this case? Market Price: Store-It Output: