In the Melitz (2003) model, competition takes the form of free entry of firms to the market at a setup cost and with uncertainty about their marginal cost, implying that in the equilibrium the setup cost to enter the market must equal the firm's _____ profit.
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In the Melitz (2003) model, competition takes the form of free entry of firms to the market at a setup cost and with uncertainty about their marginal cost, implying that in the equilibrium the setup cost to enter the market must equal the firm's _____ profit.
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- Assume the demand for a companys drug Wozac during the current year is 50,000, and assume demand will grow at 5% a year. If the company builds a plant that can produce x units of Wozac per year, it will cost 16x. Each unit of Wozac is sold for 3. Each unit of Wozac produced incurs a variable production cost of 0.20. It costs 0.40 per year to operate a unit of capacity. Determine how large a Wozac plant the company should build to maximize its expected profit over the next 10 years.If the number of competitors in Example 11.1 doubles, how does the optimal bid change?In the financial world, there are many types of complex instruments called derivatives that derive their value from the value of an underlying asset. Consider the following simple derivative. A stocks current price is 80 per share. You purchase a derivative whose value to you becomes known a month from now. Specifically, let P be the price of the stock in a month. If P is between 75 and 85, the derivative is worth nothing to you. If P is less than 75, the derivative results in a loss of 100(75-P) dollars to you. (The factor of 100 is because many derivatives involve 100 shares.) If P is greater than 85, the derivative results in a gain of 100(P-85) dollars to you. Assume that the distribution of the change in the stock price from now to a month from now is normally distributed with mean 1 and standard deviation 8. Let EMV be the expected gain/loss from this derivative. It is a weighted average of all the possible losses and gains, weighted by their likelihoods. (Of course, any loss should be expressed as a negative number. For example, a loss of 1500 should be expressed as -1500.) Unfortunately, this is a difficult probability calculation, but EMV can be estimated by an @RISK simulation. Perform this simulation with at least 1000 iterations. What is your best estimate of EMV?
- A European put option allows an investor to sell a share of stock at the exercise price on the exercise data. For example, if the exercise price is 48, and the stock price is 45 on the exercise date, the investor can sell the stock for 48 and then immediately buy it back (that is, cover his position) for 45, making 3 profit. But if the stock price on the exercise date is greater than the exercise price, the option is worthless at that date. So for a put, the investor is hoping that the price of the stock decreases. Using the same parameters as in Example 11.7, find a fair price for a European put option. (Note: As discussed in the text, an actual put option is usually for 100 shares.)A stock market advisory service offers three investments portfolios for one of its customers. All portfolios have the same investment cost. Portfolio U contains speculative stocks, which aim for capital gain through price appreciation. Portfolio V is made up of stocks of stable companies that pay good dividends overt the long run. Portfolio W comprises stocks with a moderate potential for growth and a moderate yield of dividends. The customer has enough money to invest in only one of these three portfolios for a period of one year. The net return on investments will depend on whether the economy during the period will be in a stage of inflation, recession, or depression. The net potential gains or losses (in thousands) are calculated as follows:Based on current dividend yields and expected capital gains, the expected rates of return on portfolios A and B are 11 % and 14 %, respectively. The beta of A is 0.8 % while that of B is 1.5. The T-bill is currently 6 %, while the expected rate of return of the S&P 500 index is 12 %. The standard deviation of portfolio A is 10 % annually, while that of B is 31 % , and that of the index is 20 %: If you currently hold a market index portfolio, would you choose to add either of these portfolios to your holdings? Explain. If instead you could invest only in bills and one of these portfolios, which would you choose, and why? Investor Y, who put K1 in large stocks (the S & P 500 portfolio) on December 31, 1925, and re-invested all dividends in that portfolio, would have ended on December 31, 2003, with K1992.80.
- Consider a consumer that lives only for two periods. He works in period 1 (and gets income Y1) and moves up the corporate ladder in period 2 (and gets income Y1 < Y2). This consumer has the usual preferences over time: u(C1) + βu(C2) Assume once again that a consumer cannot borrow, but can borrow and immediately sell some MacGuffins, and in the next period, the consumer must buy back the MacGuffins to return to the lender. Assume that MacGuffin t r a d e s a t P1 > 0 in the first period and is expected to trade at P ̃2 in the second period. Write down the new budget constraint. Would a consumer borrow a MacGuffin? What is the condition on the P ̃2? Is P ̃2 a fair price of a MacGuffin? Could the consumer be better off with a MacGuffin?The daily demand for a product in a shop can assume one of the following values: 100, 120, or 130 items with probabilities 0.2, 0.3 and 0.5. The owner of the store is thus limiting the alternatives to stocking one of the indicated three levels. If the owner stocks more that it can be sold in the same day the remaining items must be disposed at a discount price of 55 cents per item. Assume that the owner pays 60 cents per item and sells it for 100 cents, find the optimal stock level.You are thinking of starting Peaco, which will produce Peakbabies, a product that competes with Ty's Beanie Babies. In year 0 (right now), you will incur costs of $4 million to build a plant. In year 1, you expect to sell 80,000 Peakbabies for a unit price of $25. The price of $25 will remain unchanged through years 1 to 5. Unit sales are expected to grow by the same percentage (g) each year. During years 1 to 5, Peaco incurs two types of costs: variable costs and SG&A (selling, general, and administrative) costs. Each year, variable costs equal half of revenue. During year 1, SG&A costs equal 40% of revenue. This percentage is assumed to drop 2% per year, so during year 2, SG&A costs will equal 38% of revenue, and so on. Peaco's goal is to have profits for years 0 to 5 sum to 0 (ignoring the time value of money). This will ensure that the $4 million investment in year 0 is paid back by the end of year 5. What annual percentage growth rate g does Peaco require to pay back…
- Suppose that $100 is invested at the beginning of a year. Which (if either) of the following methods of growing the investment results in a larger amount at the end of the year? (i) The investment grows at an interest rate of 4% per year, compounded continuously.(ii) The investment grows at an instantaneous growth rate of 4% per year. method (i) method (ii) Both methods produce the same amount.I own a single share of Wivco stock. I must sell myshare at the beginning of one of the next 30 days. Each day,the price of the stock changes. With probability q(x), theprice tomorrow will increase by x% over today’s stock price(x can be negative). For example, with probability q(5),tomorrow’s stock price will be 5% higher than today’s. Showhow dynamic programming can be used to determine astrategy that maximizes the expected revenue earned fromselling the share of Wivco stock. Assume that at thebeginning of the first day, the stock sells for $10 per share.As the Quality Sweaters problem is now modeled, if all inputs remain fixed except for the number mailed, profit will increase indefinitely as the number mailed increases. This hardly seems realistic—the company could becomeinfinitely rich. Discuss realistic ways to modify the model so that this unrealistic behavior is eliminated.