Econ3319 (2022) Assn 3: Monopolistic Competition & Indices of Market Concentration

Question 1 : Monopolistic Competition Consider a city with many restaurants with a monopolistically competitive market structure with horizontal product differentiation as in class.1 Suppose that each restaurant sells meals (q) at price p where quantity units are in meals/time period and price units are in $/meal. Each firm’s demand curve has the form: �!(�) = � ( " # − � ∗ (� − �$), [1] * You do NOT need to use the above equation. I filled in the parameters for you. Where: S = total sales in entire market = 240,000,000 meals/y. n = total firms in the market P = price set by a representative firm PM = market price b = elasticity of demand parameter such that if b is bigger, demand is more elastic, so there is less price setting power. Treat each firm as a “representative firm” due to identical costs and due to facing identical residual demand curves given the output levels of the other firms. Due to this “symmetry”, each firm sells its variant at the equilibrium market price (P = Pmarket) at an output level that equals total market sales divided by the number of firms such that � = ! " . Each representative firm has a fixed cost of F = 32,000,000 $/year and a constant marginal cost of � = 16 $

You will not need to use the above equations and only need to know the total sales, fixed costs and marginal costs and the demand equations (below) to do this question as I have substituted in all the parameters. a) The model of monopolistic competition is a model of horizontal product differentiation. i) Give an example of how restaurants could horizontally differentiate their products and ONE example of how they could vertically differentiate their product. ii) In both the short run and long run equilibrium, it is assumed that all of the individual firm's prices are equal to the market price such that P = PM [2]. Substitute [2] into equation [1] above to find the demand for meals of a representative firm in equilibrium as a function of S and n. iii) List 3 fixed costs and 3 variable costs of restaurants. b) Given the number of firms in the market, suppose that each representative firm faces a demand for its meals with the following equation: qD(P) = 117,600,000– 3,600,000P For a representative firm, find the following: i) inverse demand, total revenue, total cost, & total profit equations as functions of the firm’s output (q). ii) Find the FOC for profit maximization and then solve for the firm’s profit maximizing quantity and price. iii) Check the second order sufficient condition to check that the stationary point is a maximum. iv) Calculate total variable profits and total profits (subtract out fixed costs). v) Will there be net entry to this market? Explain why or why not? Is this market in a long run equilibrium? c) Using graph paper, plot and label the firm’s demand curve, marginal revenue, marginal cost, and average cost (AC). Give your graph a title, label both axis with variable names and correct units. To help plot AC, use the following table. Representative firm’s output (q) (millions) AC(q) /loan unit d) At the profit maximizing allocation above, please label the following using a legend for totals. i) profit maximizing price & quantity. ii) total consumer surplus. iii) total variable costs. iv) total fixed costs. v) total profits (if any) vi) total variable profits (producer’s surplus). vii) total deadweight loss. viii) minimum and maximum profitable scale.

e) Calculate the following: i) number of firms in the market. ii) number of product varieties. iii) total fixed costs of the market as a whole. f) Suppose that some market entry or exit has occurred such that each representative firms demand function is now: �!(�) = 79,066,300 − 3,600,000�, Repeat part b through e for these new demand conditions. Use Fig. 2 for your graph or plot yourself on paper to scale. g) What happened to each of the following when market demand changed from that in c) to that in f). Explain briefly. i) the number of varieties of meals (also the number of firms in the market). ii) the market price. iii) the total fixed costs of the market. iv) average costs per unit output. h) In moving from the short run to long run situation, will consumers get closer or further from their preferred variety? (one sentence answer) i) Comparative statics: refers to changing one exogenous parameter while holding all other parameters constant (ceteris paribus) and finding how this affects equilibrium variables such as price and quantity. For the long run equilibrium, please indicate which exogenous variable is changed in the following scenario and how this changes the long run equilibrium price, quantity and number of firms. Explain your answer in terms of what is happening in the economy and show using the long run equilibrium P*, n* and Q* equations. Hint: You can look at lecture notes. Scenario: "Suppose covid damages the model people's taste buds so they become more indifferent between the different variety of meals sold at these restaurants." Problem 2: Market Concentration Indices Estimates of market shares by retail sales in the Canadian food sector (Delibashi, 2021) are reported below: 1) Loblaws/ Shoppers Drug Mart (27%), 2) Sobeys/Safeway (22%) 3) Metro/Jean Coutu (11%), 4) Costco (9%) 5) Walmart (8%), 6) Overwaitea Food Group (4%), 7) Co-ops (3%) (assume all are the same firm for simplicity), 8) Couch-Tard (2%), 9) North-West Company Inc. (1%), 10) Dollarama (1%) a) Calculate the following concentration ratios, C1, C2, C3, and C4 for market share (pg. 252 Cabral, 2nd ed., see index for pages for 1st edition). b) Calculate the Hirfindahl Index (HHI). c) Based on the Hirfindahl index (HHI) calculated in the previous question, categorize market concentration based on the following: highly competitive (2500) d) Explain why the HHI index calculated here may underestimate the market concentration of food retail in Canada. Hint: recall our discussion of the telecomm industry in Canada. Delibashi, A. (2021) Retail Foods, USDA retrieved from https://apps.fas.usda.gov/newgainapi/api/Report/DownloadReportByFileName?fileName=Retail Foods_ Ottawa_Canada_06-30-2021.pdf on Oct 31, 2022. Question 3: Brightspace Questions Once you have completed the assignment, please answer the Brightspace Quiz questions on the assignment. This will be found under Assessments >>Quizzes. I will announce when it is ready under Announcements.