Need economics help with an Intermediate micro homework

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Intermediate Micro 1. A firm in perfect competition has the following cost functions: TFC = 3900 TVC = 2500 + 12*Q + Q2 a. Determine this company’s supply curve (you will need to do the slightest bit of calculus for this). b. Find this company’s shutdown price and quantity. c. Find this company’s breakdown price and quantity. 2. Let the market for bicycles be perfectly competitive. The market demand curve for bikes is given by Qd = 45,000 – 100*P. We will make no distinction between the short run and long run cost functions for the typical firm. The cost function for the typical bicycle manufacturer is TC = Q2 + 10,000, and is identical for all firms. In the various parts of this question you will be asked to solve for the equilibrium in this industry. A complete answer for each part should specify: the equilibrium price, the quantity produced by the typical firm, the total quantity of bicycles produced by the industry, the number of firms, and the total profit made by each firm. a. Initially let the number of firms in this industry be fixed at 100. Solve for the short run equilibrium. b. Now solve for the long run equilibrium. c. The market demand curve for bicycles now shifts to Qd = 40,000 – 100*P. Find the new short run equilibrium for the market for bikes. Was this an increase or decrease in demand? d. Find the new long run equilibrium for the new market demand curve from part c. 3. Comparing Competition and Monopoly. Let the market demand curve for widgets be P = 100 – Q/50, and let the marginal and average cost be constant at $20 per unit. a. Find the equilibrium price and quantity of widgets if this industry is perfectly competitive. Find the dollar amount of the total consumer surplus with competition. Is there any producer surplus in this equilibrium? b. Find the equilibrium price and quantity of widgets if the industry were controlled by a single monopolist. Find the dollar amount of the consumer surplus in equilibrium with monopoly, the amount of the profit (if any) this monopolist earns in equilibrium. Is there deadweight loss in the equilibrium with monopoly, compared with perfect competition? If so, find the dollar amount of the deadweight loss. 4. Our textbook states, and it was mentioned in class, that a monopolist would never operate in the inelastic portion of the market demand curve, given that the market demand curve were linear. This problem helps establish this relationship using some calculations. We will use the formula that the elasticity of demand, ed, equals the slope of the demand curve multiplied by the price and divided by the quantity, or ed = slope*(P/Q). Let the market demand for sweaters be P = 100 – Q. a. Find the marginal revenue curve for this demand curve. b. Suppose that a monopolist faces this market demand curve and has a marginal cost equal to a constant $30 per unit (the MC curve is horizontal at $30). Find the price and quantity of sweaters that maximize profit for the monopolist. Use the elasticity formula to calculate the elasticity of demand at the profit maximizing price and quantity. Is demand elastic or inelastic at this point? c. Now assume that the monopolist has a constant marginal cost of $0 per unit. In other words, this monopolist has discovered a large container box of sweaters on an island, and is the sole supplier of sweaters, but does not have to incur any costs to produce the sweaters. This represents the lowest possible cost for a monopolist. Find the price and quantity of sweaters that maximize profit for the monopolist, and then calculate the elasticity at this point. Is demand elastic or inelastic? d. Now let’s make the marginal cost curve for the monopolist more general. So MC is positively sloped but not necessarily linear. It turns out that whatever the shape of the MC curve, we only need to be concerned about the dollar value at which it intersects the MR curve. Let this dollar amount be C, and we know that C > 0. Solve for the profit maximizing quantity and price for this monopolist as a function of C. Then substitute these values into the elasticity formula. What can you say about the elasticity as a function of C? In particular, can you convince yourself that ed will be less than -1? Based on your solutions as a function of C, what do you think happens here if C > 100? 5. Traditional Monopoly. Let the cost function of a monopolist producing thingamajigs be C = Q2/20 + 4,000. Let the market demand curve for thingamajigs be Qd = 50 – Q/20. Solve for the price and quantity which maximize this monopolist’s profit. Also find the monopolist’s profit and the total consumer surplus in the thingamajig market.
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