What price do farmers get for their watermelon crops? In the third week of July, a random sample of 40 farming regions gave a sample mean of x = $6.88 per 100 pounds of watermelon. Assume that σ is known to be $1.88 per 100 pounds.

(a) Find a 90% confidence interval for the population mean price (per 100 pounds) that farmers in this region get for their watermelon crop. What is the margin of error? (Round your answers to two decimal places.) lower limit $ upper limit $ margin of error $

(b) Find the sample size necessary for a 90% confidence level with maximal error of estimate E = 0.33 for the mean price per 100 pounds of watermelon. (Round up to the nearest whole number.) farming regions

(c) A farm brings 15 tons of watermelon to market. Find a 90% confidence interval for the population mean cash value of this crop. What is the margin of error? Hint: 1 ton is 2000 pounds. (Round your answers to two decimal places.) lower limit $ upper limit $ margin of error $

What price do farmers get for their watermelon crops? In the third week of July, a random sample of 40 farming regions gave a sample mean of x = $6.88 per 100 pounds of watermelon. Assume that σ is known to be $1.92 per 100 pounds.

(a) Find a 90% confidence interval for the population mean price (per 100 pounds) that farmers in this region get for their watermelon crop. What is the margin of error? (Round your answers to two decimal places.)

(b) Find the sample size necessary for a 90% confidence level with maximal error of estimate E = 0.43 for the mean price per 100 pounds of watermelon. (Round up to the nearest whole number.)
farming regions

(c) A farm brings 15 tons of watermelon to market. Find a 90% confidence interval for the population mean cash value of this crop. What is the margin of error? Hint: 1 ton is 2000 pounds. (Round your answers to two decimal places.)

What price do farmers get for their watermelon crops? In the third week of July, a random sample of 40 farming regions gave a sample mean of x = $6.88 per 100 pounds of watermelon. Assume that σ is known to be $1.94 per 100 pounds.

(a) Find a 90% confidence interval for the population mean price (per 100 pounds) that farmers in this region get for their watermelon crop. What is the margin of error? (Round your answers to two decimal places.)

(b) Find the sample size necessary for a 90% confidence level with maximal error of estimate E = 0.45 for the mean price per 100 pounds of watermelon. (Round up to the nearest whole number.)
farming regions

(c) A farm brings 15 tons of watermelon to market. Find a 90% confidence interval for the population mean cash value of this crop. What is the margin of error? Hint: 1 ton is 2000 pounds. (Round your answers to two decimal places.)

What price do farmers get for their watermelon crops? In the third week of July, a random sample of 41 farming regions gave a sample mean of x = $6.88 per 100 pounds of watermelon. Assume that σ is known to be $1.94 per 100 pounds.

(a) Find a 90% confidence interval for the population mean price (per 100 pounds) that farmers in this region get for their watermelon crop. What is the margin of error? (Round your answers to two decimal places.)

(b) Find the sample size necessary for a 90% confidence level with maximal error of estimate E = 0.41 for the mean price per 100 pounds of watermelon. (Round up to the nearest whole number.)
farming regions

(c) A farm brings 15 tons of watermelon to market. Find a 90% confidence interval for the population mean cash value of this crop. What is the margin of error? Hint: 1 ton is 2000 pounds. (Round your answers to two decimal places.)

Let the utility function be given by
u(x1, x2) = √x1 + x2.

Let m be the income of the consumer, P1 and P2 the prices of good 1 and good 2, respectively.
To simplify, normalize the price of good 1, that is P1 = £1.

(a) Write down the budget constraint and illustrate the set of feasible bundles using a figure.

(b) Suppose that m = £100 and that P2 = £10. Find the optimal bundle for the consumer. In other words, find the combination of x1 and x2 that maximizes the consumer’s utility when the prices are p2 = £10, p1 = £1 and her income is m = £100.

(c) Suppose still that m = £100 but now the price of good 2 has increased to p2 = £30. Find the optimal bundle for the consumer. In other words, find the combination of x1 and x2 that maximizes the consumer’s utility when the prices are p2 = £30, p1 = £1 and her income is m = £100.

(d) How can we explain the drastic change in demand for the goods when the price of good 2 increased from £10 to £30?

1. What is the price of an American-style call option assuming a 4% annual risk-free rate, a strike price = $150, and 3 years to maturity.  In each year the price can either rise by a factor of 1.3 or fall by a factor of 0.9.  The current price of the underlying asset is $100 and it pays no dividends.
2. Why is the price in part a different than you would get from inputting a 10% drift and 20% volatility into the Black Scholes equation?
3. What would be the price of an American-style put option on the same stock with the same maturity as in part a above?
4. What is the price of an American-style call option assuming a 4% annual risk-free rate, a strike price = $150, and 3 years to maturity.  In each year the price can either rise by a factor of 1.3 or fall by a factor of 0.9.  The current price of the underlying asset is $100 and it pays no dividends.
5. Why is the price in part a different than you would get from inputting a 10% drift and 20% volatility into the Black Scholes equation?
6. What would be the price of an American-style put option on the same stock with the same maturity as in part a above?

For two goods x and y, the individual’s preferences are measured by the utility function ?(?,?)= ?^0.5?^0.5, the price of good y is $10, income equals $100, and the price of good x increase from $5 to $10. Draw the price consumption curve for x and y and compute the slop of the price consumption curve. Show your calculation step by step.

The president of Doerman Distributors, Inc., believes that 30% of the firm’s orders come from first-time customers. A random sample of 100 orders will be used to estimate the proportion of first-time customers. Assume that the president is correct and p =0.30. What is the probability that the sample proportion will be between 0.25 and 0.35?

1. Consider the three stocks in the following table.  Pt represents price at time t, and Qt represents shares outstanding at time t. Stock C splits two-for-one in the last period.

Can you show work with steps and answer c please

                        P 0       Q 0     P 1      Q 1     P 2      Q 2

            A         80        100      85        100      90        100

            B         60        200      45        200      40        200

            C         110      200      120      200      60        400

c. Calculate the rate of return of the price-weighted index for the second period (t=1 to t=2).

One of Matt's favourite brands is offering a deal on its’ hooded jackets, which is sold at $100 a piece. The promotion claims that you can “get the second piece 50% off.” It means, if Matt buys a jacket for $100, he can buy the second jacket (of different colour) for 50% of the original tag price, $50. In addition, if Matt wants a third jacket, he has to pay $100 again, but now he has the privilege to purchase the fourth jacket for $50, etc. Assume the price for Other goods is $50 and Matt has an income of $1,000 to spend on both the jackets and Other goods.”

Draw Matt's budget constraint with jackets on the horizontal axis.