Consider a city where the fixed cost of a transit system is $4,000 per hour. The...

 

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Consider a city where the fixed cost of a transit system is $4,000 per hour. The long-run marginal cost is constant at $1.00 per rider. The (hourly) demand curve is given by Q=(20,000 - 2000P)/(P+2) for 10> P>0, else 0. (a) Algebraically identify the inverse demand curve for this transit system, as well as the total and average cost curves. (b) Graph the (inverse) demand curve, the average cost curve and marginal cost line on a SINGLE graph with money on the vertical axis and ridership on the horizontal axis. Find all relevant intersections of the curves and note them on the graph. (c) What level of price and ridership yields the maximum amount of profits for the transit system? What is the profit per rider? Move on to the next part if this gives you trouble. (d) What level of price and ridership yields zero profit for the transit system under average cost pricing (P-AC). You will solve a quadratic that has two solutions; choose the larger of the two values (since a transit system would prefer to have more riders than fewer given same profit level). (e) What level of price and ridership is generated under marginal cost pricing (P-MC). Whatis the deficit per rider? (f) Suppose there is a 25% service cut, which reduces the fixed cost to $3,000 per hour. Note that will also reduce demand at any given point: Q=(3/4) [(20,000 - 2000P)/(P + 2)] for 10> P > 0, else 0. Repeat the parts above and comment on what happens. (g) Suppose the city internalizes the externalities from automobiles (through a gas tax, eliminatingstreet parking and/or uses congestion pricing.) How will this change the demandcurve and the price and ridership levels under AC and MC pricing? Consider a city where the fixed cost of a transit system is $4,000 per hour. The long-run marginal cost is constant at $1.00 per rider. The (hourly) demand curve is given by Q=(20,000 - 2000P)/(P+2) for 10> P>0, else 0. (a) Algebraically identify the inverse demand curve for this transit system, as well as the total and average cost curves. (b) Graph the (inverse) demand curve, the average cost curve and marginal cost line on a SINGLE graph with money on the vertical axis and ridership on the horizontal axis. Find all relevant intersections of the curves and note them on the graph. (c) What level of price and ridership yields the maximum amount of profits for the transit system? What is the profit per rider? Move on to the next part if this gives you trouble. (d) What level of price and ridership yields zero profit for the transit system under average cost pricing (P-AC). You will solve a quadratic that has two solutions; choose the larger of the two values (since a transit system would prefer to have more riders than fewer given same profit level). (e) What level of price and ridership is generated under marginal cost pricing (P-MC). Whatis the deficit per rider? (f) Suppose there is a 25% service cut, which reduces the fixed cost to $3,000 per hour. Note that will also reduce demand at any given point: Q=(3/4) [(20,000 - 2000P)/(P + 2)] for 10> P > 0, else 0. Repeat the parts above and comment on what happens. (g) Suppose the city internalizes the externalities from automobiles (through a gas tax, eliminatingstreet parking and/or uses congestion pricing.) How will this change the demandcurve and the price and ridership levels under AC and MC pricing?