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13:13 BEEM015_2021MidTerm (1 of 2) Answer Both Questions "" """s are permitted.'l'hisis an open boolt exam. 2 of 2 thewppliedW/a 1] Suppose there are two rms selling a homogenous good, which can be produced with a constant marginal and average cost of 1. The two rms are located at either end of a line of unit lengthI [0, 1]. Consumers are uniformly distributed over the line with mass 1. Denote x as the position of a consumer item the start of the line at position B. Each rm can set a price p, where t E {1.2}. If the consumer purchases from rm 1 then the utility of the consumer is given by: u = r pl 2x lithe consumer purchases from rm 2 the utility of the consumer is given by: u = r p2 - 2 -i- 2): Each consumer purchases 1 unit so long as their utility is non-negative from whichever firm gives them the highest utility and othemise does not purchase (for a utility of zero]. i} Characterise the prices and prots of the two firms at equiiibrlum for the case where r = 6. [30 Marks} ii] Describe how your answer would change in the case where I" = 3. [2!] Marks] 2] Two mts compete Ecmrnot style in quantities. Inverse demands for the two firms are given by m = a In - deg :02 = a 'iz - do Where I] s d S l. The marginal costo'i production is zero. i} Calculate the quantities of output by the two rms and the associated prots where choices are made simultaneously. [:5 Marks] ii] Calculate th e quanties of output by the two firms where choices are made sequentially with rm 1 acting as a leader and making a choice which is observed by firth 1 before firm 2 makes a choice. [There is no requirement to calculate prots in this case}. [2:] Marks] Characterise the difference in choices by rm 1 between the simultaneous choice situation analysed in part i) and the sequential choice situation analysed in part ii) as the value at d is increased from 0 to 1. {15 Marks] End of Paper