I need help in understanding the formula's and to create them in long format.

Question 1

1. The demand curve is Q_d= 200 - P. Calculate the (point) price elasticity of demand when price is $24. Is demand elastic or inelastic?

Question 2

1. Suppose equilibrium price in the market is $30, and the marginal revenue is $20. What is the price elasticity of demand?

Question 3

1. The David Company's demand curve for the company's product is P = 2,000 - 20Q, where P = price and Q = the number sold per mont

a.Derive the marginal revenue curve for the firm.

b.At what output is the demand for the firm's product price elastic?

c.If the firm wants to maximize its dollar sales volume, what price should it charge?

Question 4

1. Rebel Sole is a rapidly expanding shoe company. The following is the demand estimate for its popular shoes. The estimate was done using 40 observations.

Q= 10 - 10P+ 4A+ 0.42I+ 0.25P_y

(3)(1.8)(0.7)(0.1)(0.1)

F= 93,s= 6,R₂= 93%

Q is quantity sold (in thousands), P is shoe price, A is advertising expenditure (in thousands), the numbers in parentheses are standard errors, I is disposable income per capita (thousands of dollars), and P_yis the price of related goods.

1. Evaluate the model based on F, R².
2. Test the significance of P_y.
3. If P = $5, A = $30,000, I = 50,000, and P_y= $6, calculate advertising elasticity.
4. Given the information in c. above, calculate the 95% confidence interval for Q.