The following questions are of micro economics. Please help me with better understanding.
2. You have collected the following data on output and total variable costs: \" m m m a. b. Identify the range of output exhibiting increasing returns (increasing MP} and the range exhibiting diminishing returns {decreasing MP}. Cmrent xed costs for the company equal $136,5U. Draw two graphs, both with Q on the horizontal axis: one graph shows WC and TC, and the other shows AVG, AC, and MC. Suppose that the government imposes a $T5, property tax hike on all businesses; how will that affect your two graphs; is, which cost curves will be affected and how? Suppose instead that the government consist your production process to he polluting, and iruposes a $35!} tax per unit produced (replacing the property tax in the previous question)- How does this tax increase compare to the property tax increase, in terms of the effect on your company's cost curves? Tfour boss says "either of these taxes is going to force us to change our production levels." Given what you know about optimization analysis, how would you respond? EXERCISE 3 Suppose that a firm has the production function f(r1, (2) = 201 + loge (2 + 1) (a) Does the marginal product of factor 1 increase, decrease, or stay constant as the amount of factor 1 increases? Does the marginal product of factor 2 increase, decrease, or stay constant as the amount of factor 2 increases? (b) This production function does not satisfy the definition of increasing returns to scale, constant returns to scale, or decreasing returns to scale. How can this be? Find a combination of inputs such that doubling the amount of both inputs will more than double the amount of output. Find a combination of inputs such that doubling the amount of both inputs will less than double output.1. This quration concerns surplus and the effect of taxes. Use the sue information as in Problem Set 46, and suppose N = 400. (a) Draw market demand and supply function on a single figure, and denote the equilibrium outcome. Label the areas that represent consumer surplus and producer surplus (b) Calculate the value of consumer surplus and producer surplus in this case. (c) Recall that producer surplus represents the sum of profits and fixed costs across all firms. Does your answer to (b] align with the implications of 2(e) from Problem Set #6? (d) Suppose a unit tax of : = 0.2 is imposed on each piece of output sold, so that consumers pay p+ # when the price is p. What is the new market demand function? (e) Solve for the new equilibrium outcome after the tax is imposed. (f) On a new figure, draw the old and new demand functions and the supply function, and denote the old and new equilibrium outcomes. Carefully label the areas that represent consumer and producer surplus, tax revenue, and deadweight loss imposed by the tax. (g) Calculate consumer surplus, producer surplus, tax revenue collected, and the deadweight loss after the tax is imposed. As a check on your work, the sum of these four values should equal market surplus before the tax is Imposed. (h) On the figure you drew in (d), carefully draw a line segment separating the portion of the tax effectively paid (or borne) by consumers vs producers, then calculate these values. Who pays more of the tax? Carefully explain why 2. This question concerns the market outcome when there is an unregulated monopolist pro- ducer. The firm can produce output y according to cost function Cly) = by" +2. Consumers in the market demand a total of D(p) = 4 - p units when the price is p. (a) If the firm sells y units at a price of p. how much revenue will it generate? (b) The price at which the monopolist can sell a quantity of output y is determined by the price at which consumers are willing to buy that quantity. This is the "inverse demand e(e) The most efficient way for the firm to produce output & when average total cost is minimized- the long run competitive equilibrium, Find the level of y that minimize ATC. Could this level of output ever be achieved? Explain. (f) Show that the firm's profit at the competitive outcome would be w = -]. What would happen in the long run if the firm had to operate at the competitive price? (x) Would a second firm enter this market to compete with the monopolist? What would happen if it did? You don't need to do all of the math, just explain. 5. The previous question established that this market is a natural monopoly. This question concerns price regulation of the monopolist. Use the same Information as before. (a) Suppose the government mandated that the monopolist firm set its price at the compet- itive level p'. Explain why this is a terrible idea (see answer to 4(1), and explain). (b) Suppose instead that the government set the price at po where the monopolist earns zero profit. This occurs where the demand function crosses average total cost, Find po and the corresponding quantity yo, and explain why this is where profit will be zero. (e) Calculate consumer surplus under the price regulation from 5(b) (it might help to draw a picture). Producer surplus is 2; how do we know this without doing any calculations? (d) Suppose the government gave a lump sum payment T to the monopolist firm, and then mandated that price is set at p". What is the smallest value of T that would fix the problem from S(a)? Explain. (c) Calculate consumer surplus if the price is set at p" (it might help to draw a picture). If consumers had to collectively pay a lump sum tax of 7, what is the largest value of T that would make them prefer the competitive price with the tax to the monopolist price Im with no tax? Is it feasible to achieve the competitive price? Explain. (f) What consideration(s) have we not mentioned in this discussion of regulation? Why would price regulation be more difficult in the real world than described here? e w ] 811. Suppose that the market for hotel rooms (one-night stay) has the following supply and demand schedules: Price of a Quantity demanded Quantity supplied room (thousands) (thousands) $150 100 10 $160 90 15 $170 80 20 $180 70 25 $190 60 30 $200 50 35 $210 40 40 $220 30 45 $230 20 50 $240 10 55 $250 0 60 a) Using this information, draw the demand curve and the supply curve for hotel rooms. b) What is the equilibrium price and quantity for rooms? c) Assume the government levies a tax of $30 per night. What is the price that consumers will pay for a room now? d) What is the price that hotels will receive when someone stays for a night? e) Illustrate the effect of this tax in your diagram from part a. f) Calculate the government revenue raised by this tax. diagram. g) Is the market efficient. with the $30 excise tax? Explain. Illustrate your answer with a
