Homework 2 l. The demand for Saperavi (a grapefwine specialty of the country of Georgia) can be represented by P=100-2Q, where Q is bottles of Saperavi demanded per year and where P is the price per bottle (in US. dollars). The supply curve for Saperavi can be represented by P=40; Saperavi is produced in a \"constant-cost competitive industry.\" a. (3 points) Graph the Saperavi market. Find the equilibrium price and quantity. b. (4 points) What is the elasticity of demand at the equilibrium price and quantity? What is the elasticity of supply at the equilibrium price and quantity? Please explain. Is the elasticity of demand in the elastic or the inelastic range? c. (8 points) The government is interested in discouraging alcohol consumption by imposing a per-bottle tax (t) on Saperavi. Even more than discouraging alcohol consumption, however, the government also likes to collect tax revenue. Find the per-bottle tax t that results in the highest government revenue. Amend your earlier graph to indicate the equilibrium prices and output associated with this revenue-maximizing tax. d. (5 points) At the new (post-revenue-maximizing tax) equilibrium, is the elasticity of demand in the elastic or the inelastic range? How can you tell, even without a calculation? Now, please calculate the elasticity of demand at the new equilibrium. 2. The demand curve for (vegan) chocolate can be represented by P = 1,200-10Q, where P is the price per ton (in US. dollars). The private marginal cost of production in the chocolate industry is given by lOQ. But chocolate production causes a nauseating odor to sweep over the city in the vicinity of chocolate factories, so the social marginal cost of production, taking the odor into account, is lSQ. a. (4 points) Assuming that the market for chocolate is competitive, what will be the outcome (and in particular, the quantity of chocolate produced)? Please include a graph. b. (4 points) What is the socially efcient output of chocolate? (Please update the graph from part a.) c. (8 points) What is the Pigovian per-unit (i.e., per ton of chocolate) tax? (Again, please illustrate this on the graph, too.) Can you calculate the dead-weight loss of this Pigovian tax? 3. An industry consisting of two rms is nevertheless behaving in a perfectly competitive fashion. Each firm has a constant marginal cost equal to 4. Demand for the good produced by the industry is represented by Q=60-4P. a. (4 points) Graph the market for this industry. What is the equilibrium output and price? The rms now merge, with the result that the marginal cost curve of the new (merged) rm is constant at MC=2. Simultaneously, however, the merger results in the single nn now behaving as an ordinary monopolist. h. (8 points) What is the new price and quantity? Please either add this situation to the graph of part (a) or provide a new graph for the merged rm. c. (6 points) A regulator has only two choices. She can either approve the merger, in which case the outcome is as in part (b), or she can void the merger, in which case the outcome is as in part (a). If the regulator is interested in maximizing overall surplus (efciency), should she allow or void the merger? Please explain carellly. 4. The President of the University of Chicago was himself a student in the College some decades ago, and he is feeling nostalgic. So, he introduces a new policy, one that mandates that vegan shakes be sold at the C-Shop on Wednesdays for only $1 per shake, well below the usual (market) price of $5 per shake. After the introduction of the mandated dollar-shake Wednesday, long lines form for shakes on Wednesdays! a. (8 points) Who wins and who loses from the imposition of the new College rule? Please explain carellly. h. (6 points) Starting with the situation when the mandate is in place, is there something better, a policy change that brings about (more-or-less) a Pareto improvement? Please explain. 5. a. (8 points) Residents of Hyde Park are charged a xed weekly fee of $6 for reJse collection. They are allowed to put out as many cans as they wish. The average household disposes of three cans per week in this way. Now, suppose that Hyde Park changes to a \"tag\" system. Each can of refuse to be collected must have a tag attached to it. The tags cost $2 each, but the xed weekly fee is eliminated. What effect will the introduction of the tag system have on the total quantity of trash cans put out for collection? Please explain. 1:. (8 points) Light bulbs come in a variety of wattages and prices, with higher watt bulbs generally selling for a higher price. Currently (hahl), the average bulb sold has 100 watts and sells for $1. If the government adopts a 50 cent per bulb tax on all light bulbs, what do you think will happen to the average price and wattage? Explain