Perpetual plastic plant makers cost $200 each. The number of plants that your firm expects to produce each year for each level of capital stock is as follows:

Machines: 0 1 2 3 4 5

Plant Production: 0 250 400 500 565 600

The plants sell for $1 each and your firm faces no other costs. The real interest rate is 10% and the depreciation rate of capital is 15%. There is a 20% tax on your firm's revenues from selling these plants. Use these numbers to answer the following 4 questions: 1. What is the firm's tax-adjusted user cost of capital? 2. What is the marginal product of capital for the fourth machine? 3. How many machines should the firm buy? 4. What is the profit after deducting taxes, interest, and depreciation?

In a small open economy

Sd = $20 billion + ($100 billion)?r

Id = $30 billion - ($100 billion)?r

Y = $70 billion

G = $20 billion

r w = 0.04

5. Calculate the current account balance.

6. Calculate net exports.

7. Calculate desired consumption.

8. Calculate absorption.

A country has the per-worker production function yt = 5kt 0.5, where yt is output per worker and kt is the capital-labour ratio. The depreciation rate is 0.2 and the population growth rate is 0.05. The saving function is St = 0.2yt, where St is total national saving and Yt is total output.

9. What is the steady-state value of the capital-labour ratio?

10. What is the steady-state value of output per worker?

11. What is the steady-state value of consumption per worker?

In a university class that includes 120 students, mostly non-traditional, the Mean age is 32, with a standard deviation 12 students, and with a normal distribution. Six of these students are international students. 1. What is the probability that, if one student is picked at a random, he/she be a teenager (12 to 19 years old)? You need to (somewhat] critically think about this before tackling it!! 2. What is the probability that if ONE student is selected at random, he/she will be an international student? 3. What is the probability that if ONE student is selected at random, his/her age be between 28 to 30 years old? 4. What is the probability that if on student is selected at random, his/her age be between 28 to 36 years old? 5. Suppose we select, at random, a sample of 9 students from this class. What is the probability that the MEAN age of that sample will be more than 38 years old? Show your work! Write the relevant Formula and the graph!The diameter of steel rods manufactured on two different extrusion machines is being Investigated. Two random samples of sizes /1=13 and /2=16 are selected, and the sample means and sample variances are x1 = 8.73, 51 = 0.32, X2 = 8.68, 52 =0.40, respectively. Assume that the data are drawn from a normal distribution. Construct the following (using only Table VI of Appendix A): (a) A 90% two-sided CI on 71 / 02. Round your answers to 3 decimal places. CI: [ (b) A 95% two-sided Cl on 1 / 02. Round your answers to 3 decimal places. CI: [ Which of the following is a true statement regarding the widths of the 90% and 95% CIs? 1. The width of the 95% CI is larger because we have more confidence in the 95% interval. 2. The width of the 95% CI is larger because there is a greater probability that it contains the true ratio of standard deviations. 3. The 90% CI is better since it has smaller width than the 95% CI. 4. The 95% CI is wider because it is 5% more likely to contain the true ratio of standard deviations.A casualty insurance company has 1000 policyholders, each of whom will independently present a claim in the next month with probability .05. Assuming that the amounts of the claims made are independent exponential random variables with mean $800, use simulation to estimate the probability that the sum of these claims exceeds $50,000