Simon spends his income, $100, on food (f) and video games (v) with prices p_f= 7 and p_v = 1. Assume that f ≥ 0, v ≥ 0. His preferences are given by u(f, v) = f^0.7 *v^0.3 . Paul’s Marshallian demand is . (a) (11, 23) (b) (5, 65) (c) (10, 30) (d) (10, 25)

Consider the production function q=5L^(0.3) K^(0.5) The marginal product of labor is MPL=1.5L^(-0.7)K^(0.5) . Assume that capital is fixed at in the short run.

1. Derive the formula for the short-run total product and graph it. (Hint: Substitute in the production function

2. Derive the formula for the short-run average product of labor (Hint: Divide the short-run total product by)

Ms. Maple is considering two securities, A and B, and the relevant information is given below:  

Suppose Ms maple wants to have a portfolio, which pays 20% expected return. What are the weights of securities A and b in this new portfolio. What do these weights means?

Suppose marginal product of labor (MPL) = 0.3*K and wage = $ 2 while the marginal product of capital (MP_K) = 0.7*L and price of capital = $ 1.

(a) What the marginal Rate of technical substitution between labor and capital at L = 50 and K = 100?

(b) What is the relative wage ratio?

(c) Is the input allocation L=50 and K=100 optimal?

Reaction time is normally distributed, with a mean of 0.8 sec and a standard deviation of 0.1 sec. Find the probability that an individual selected at random has the following reaction times. (Round your answers to four decimal places.)

(a) greater than 1 sec


(b) less than 0.7 sec


(c) between 0.7 and 1 sec

Systolic blood pressure for a group of women is normally distributed, with a mean of 118 and a standard deviation of 9. Find the probability that a woman selected at random has the following blood pressures. (Round your answers to four decimal places.)

(a) greater than 133


(b) less than 111


(c) between 111 and 125

Health experts’ estimate for the sensitivity of coronavirus tests, as they are actually used, is 0.7. They also think the specificity is very high. Suppose specificity is 0.99 and that the health experts’ estimated sensitivity is correct (0.7).

a. In a population where 20% of the population is infected with the coronavirus, what is the probability that a person who tests positive actually is infected?

b. Continued. What is the probability that a person who tests negative actually is not infected?

c. If the prevalence of infection in the tested population is 0.8 (in other words, if 80% of people tested have the infection), what is the probability that a person who tests positive actually is infected?

d. Continued. What is the probability that a person who tests negative actually is not infected?

(a) (7 points) Is there evidence, at 5% significance level, to show that the mean diameter of these two plants are different? Write down the hypotheses, test statistic, P-value and your conclusion.

Use exponential smoothing with trend adjustment. Consider T₁ = 2, F₁ = 12, α alpha = 0.2 , delta = 0.3

PART (A) What is your forecast for period 3?

Part (B) What is the related MAD for your forecast?

Uber Inc purchased a car for $23,500. The car has a salvage value of $3,900 and is estimated to be in use for 150,000 miles. What is the accumulated depreciation at the end of Year 2 assuming mileage used in year 1 was 16,380, year 2 was 16,930, and year 3 was 22,440? $_______

devise a system for you and three friends, at rest with you, to synchronize your clocks if your clocks are too large to move and are separated by hundreds of miles. 2. Can you think of an experiment to verify length contraction directly? Explain.  has to be approximately 500 words.