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marginal cost coincides across plants. Intuitively, this indicates that the monopolist does not have further incentives to move production from one plant to another. Exercise #7 - Price discrimination with linear costs Consider a monopoly facing inverse demand function p(q) = 100 - q, and total cost TC(q) = 4q. a) No price discrimination. Assume that price discrimination is illegal. What are the monopolist's optimal output, price and profits? b) First-degree price discrimination. For the remainder of the exercise, consider now that the monopolist can practice price discrimination. In addition, assume that this firm has enough information to practice first-degree (perfect) price discrimination. What are the monopolist's optimal output, price and profits? c) Two block pricing. Assume that the monopolist offers price discounts (i.e., two blocks of units, each sold at a different price per unit). What are the monopolist's optimal output, price and profits? d) Comparison. Compare the monopolist's profit under each of the above pricing strategies, and show that the profits in part (b) are the highest, followed by those in (c), followed by those in part (c), and by those in part (a). Exercise #8 - Third-degree price discrimination with convex costs Consider a monopolist facing two groups of costumers, 1 and 2, with inverse demand functions P1 (q) = a1 - bq and P2(q) = a2 - bq, respectively, where a, > a2 > 0 and b > 0. The monopolist has convex cost function TC(q) = c(q)? where c > 0. a) Set up the monopolist's profit-maximization problem for each group of customers. b) Find its profit-maximizing output and price for each group of customers. ) Assume that a, = taz, where t > 1. Evaluate your above results using a, = taz, and determine how the output difference across groups of customers, and the price difference, are affected by a larger value of t. d) What would happen if t = 1, so the inverse demand functions coincide for both groups of customers?1. (BASED ON problem 10.4, page 262 in the text, and problem 11.2, page 281) Consider the town of Tuftsville, where everyone lives along Market street, which is 1 miles long. There are 1000 people living evenly spread along Market street, and every day they each buy an ice cream cone from one of two stores located at either end of the street (Soulman's at one end [x=0], Norman's at the other [x=1]). Customers value their travel time at $2.50 per mile of travel, and buy from the cheapest store for them, including the price and the travel cost. Norman has invested in a more efficient freezer, so his MC per cone is 1, while Soulman's MC is 2. Customers each have a maximum willingness to pay for their Daily cone of $10. a) If Norman changes p_n and Soulman charges p_s, which is the location, x, of the customer who is indifferent between going to the two shops? b) If Norman charges $2 and Soulman charges $3 per cone, how many will they each sell in a day? C) What are the equilibrium prices and quantities for the two shops? If each has daily fixed costs (in addition to marginal costs) of $100, what are each firm's profits? d) Qualitatively (just explain - you don't have to do the math), if the situation were sequential, so that Soulman announces his price first, how would you expect the firms' respective prices, quantities, and profits to change? AExercise #7 - Price discrimination with linear costs Consider a monopoly facing inverse demand function p(q) = 100 -q, and total cost TC(q) = 4q. a) No price discrimination. Assume that price discrimination is illegal. What are the monopolist's optimal output, price and profits? b) First-degree price discrimination. For the remainder of the exercise, consider now that the monopolist can practice price discrimination. In addition, assume that this firm has enough information to practice first-degree (perfect) price discrimination. What are the monopolist's optimal output, price and profits? c) Two block pricing. Assume that the monopolist offers price discounts (i.e., two blocks of units, each sold at a different price per unit). What are the monopolist's optimal output, price and profits? d) Comparison. Compare the monopolist's profit under each of the above pricing strategies, and show that the profits in part (b) are the highest, followed by those in (c), followed by those in part (c), and by those in part (a).Problem 20-3 (Algo) For tax purposes, "gross income" is all the money a person receives in a given year from any source. But income taxes are levied on "taxable income" rather than gross income. The difference between the two is the result of many exemptions and deductions. To see how they work, suppose you made $60,000 last year in wages, $10,000 from investments, and were given $5,000 as a gift by your grandmother. Also assume that you are a single parent with one small child living with you. Instructions: Enter your answers as whole numbers. a. What is your gross income? b. Gifts of up to $12,000 per year from any person are not counted as taxable income. Also, the "personal exemption" allows you to reduce your taxable income by $3,650 for each member of your household. Given these exemptions, what is your taxable income? c. Next, assume you paid $700 in interest on your student loans last year, put $2,000 into a health savings account (HSA), and deposited $4,000 into an individual retirement account (IRA). These expenditures are all tax exempt, meaning that any money spent on them reduces taxable income dollar-for-dollar. Knowing that fact, what is now your taxable income? d. Next, you can either take the so-called standard deduction or apply for itemized deductions (which involve a lot of tedious paperwork). You opt for the standard deduction that allows you as head of your household to exempt another $8,500 from your taxable income. Taking that into account, what is your taxable income? e. Apply the tax rates shown in the table below to your taxable income. Federal Personal Income Tax Rates, 2013" (1) (2) (3) (4) Average Tax Rate Total Taxable Marginal Tax Rate, Total Tax on Income Highest Income in on Highest Income % Bracket in Bracket, % (3) + (1) $1-$17,850 10 $ 1,785 10 $17,851-$72,500 15 9,983 14 $72,501-$146,400 25 28,45 19 $146,401-$223.050 28 49,920 22 $223,051-$398,350 33 107,769 27 $398,351-$450,000 35 125,847 28 $450,001 and above 39.6