. Explain these questions.This question is complete.

A management consulting firm produces reports for clients using highly skilled consultants (H) and moderately skilled analysts (M). Its production function is f(H,M)=H0.5M 0.5. The wage rate for consultants is $360/hour and the wage rate for analysts is $90/hour.

a) What returns to scale property does this production function exhibit? Show this mathematically.

b) Show that the isoquant associated with producing 6 reports is given by H=36/M (or H=36M-1) . Using simple calculus, provide an expression for the marginal rate of technical substitution (the slope of the isoquant).

c) What is the marginal rate of technical substitution when 3 analysts are employed (and 6 reports are produced)? What does this imply about how many consultants could be substituted for 1 analyst and still produce the same number of reports?

d) State the cost minimization problem of the firm mathematically. How many consultants and analysts will the firm employ to produce q reports if its objective is to minimize costs? In other words, solve for H*(q) and M*(q).

e) Derive an expression for the firm's long-run cost function.

f) The management consulting industry in New York City is very competitive as it easy for experienced executives to start their own boutique consultancies. Given that firms will enter the industry until economic profits are driven to zero, what will the price of a report be in the longrun?

I really need to understand this so if you could be as clear as possible that would be great. Thanks!!

c. Graph an indifference curve that shows the bun- e. Connect the dots to create Josd's budget con- dles of X and Y for which U = 6 and U = 8. Is straint. What is the slope of the budget constraint? the "more is better" assumption satisfied for X f. Divide the price of fireworks by the price of and Y? music. Have you seen this number before while 7. Kelly's utility function is given by U= 3X + 21, working on this problem, and if so, where? where MU, = 3 and MU, = 2. R. Suppose that a holiday bonus raises Jose's in- a What is MRS ,? come temporarily to $360. Draw Jose's new b. What is MRS,, when X = 1 and Y - 57 When budget constraint. X = 2 and Y = 2.57 h. Indicate the new bundles of music and fireworks c. Draw a sample indifference curve. that are feasible, given Jose's new income. 8. Andrea loves to eat burritos with hot sauce, In fact, 1 1. Suppose that only one person in the world sells ice she cannot enjoy a bumto (8) unless it has three cream. She employs a strange pricing policy: You can servings of hot sauce (H ). She gets no additional en- buy I ice cream cone for $1, but if you buy 2 cones, joyment from more than three servings per burrito. you have to pay $2 each. If you buy 3. you have to Thus, her utility function is (= min [ B.- H ). Graph pay $3 each, cic., so that if you buy 10, you have Andrea's indifference curves for U= 1 and U= 2. to pay $10 each. You have $100 dollars to spend on ice 9. Suppose John's utility function is 4XY, where X is cream comes and chocolate milk, and chocolate milk consumption of beer and I is consumption of pizza. costs $1 per unit Draw your budget constraint. This For this utility function, the marginal utility of X is strange ice cream pricing, where buying more costs given by MU, = 41, the marginal utility of F is given you more, is called a quantity surcharge. by MU,= 4X. 12. John enjoys ordering out for pizza and renting mov- I Suppose Y= 3. Calculate John's utility for X - 2, ies online. He makes $30 each week at a part-time 3, 10, and I1. For a given level of Y, does good X job. If movies cost $2 per rental and pizza costs display diminishing marginal utility? $7.50 per slice. graph John's budget constraint. Then illustrate the effects of each of the following b. Suppose X - 3. Calculate John's utility for Y = 2. events; 3, 10, and 11. For s given level of X, does good F display diminishing marginal utility? a. John's mother finds a coupon good for one free pizza and gives it to John. C. Find three different bundles containing X and Y' that give John 48 wils of satisfaction. Plot the The company John rents movies from sponsors theme bundles and connect them with an indiffer. holiday weck promotion: Rent the first five move coe curve. What happens to the marginal rate ies at their regular price, and all movies after the of sbalitution between X and Y' as consumption of fifth are half off. X' increases? C. John's favorite plaza place increases the price of 4. Does the principle of diminishing MAS depend pizza from $7 50 to $10. on the diminishing marginal utility of X and 17 13. Good X sells for $4, and good F sells for $2. At your 10. Jose gets satisfaction from both music and fireworks. current level of consumption, the marginal rate of Jon's income is $340 per week. Music costs $12 per substitution between X and Fisd. CD, and fireworks cost $8 per bag. I Draw an indifference curve and budget constraint It Graph the budget constraint Jose faces, with that reflects the facts given above. (Mar: You music on the vertical axis and fireworks on the will have to choose an linkial income level and horizontal suit an initial bundle of X and F.) I Jost spends all his income on music, how b. Are you maximizing your utility? much music can be affordt Plod a point that c. If you are not maximizing your utility, are you illustrates this scenario, buying low much X or too much IT Explain. c.IT hard spends all his incommon fireworks, him 14. Andre gets utility from playing laver tag and read- many bags of fireworks can be afford? Plot a ing books. Each week. Andre spends his entire $100 point that Illustrates this scenario paycheck in both pools, One hour of laver rag cous If Joad spends half his income on fireworks and $30: s bick costs $10. half his income un music, how much of each a. Graph Andre's budget constraint. Put books on can be allland? Hot s point then illustrates this the horizontal axis and hour of laser tag on the vertical unit.3. Forward rate. Suppose the following spot rates are available: 5.0% for one year, 6.0% for two years, 6.5% for three years, and 7.0% for four years. Suppose you want to borrow $20 million for two year, starting one years from today, what would be a fair rate for the forward contract? 4. Dividend discount model. The common stock of XYZ is selling for $17.00. The firm pays dividends that are expected to grow at a rate of 3.60% indefinitely. (a) If the current dividend is $1/share, what is the implied required rate of return of XYZ's equity? (b) If the expected next year dividend is $1/share, what is the implied required rate of return of XYZ's equity? (c) What do you estimate the price of XYZ stock to be after 10 years (at t = 10)? 5. Growth opportunities. The firm XYZ has projected earnings per share (EPS) for the next three years as listed in the following table. The firm plan to payout a fraction of EPS as dividend, with the payout ratio listed in the table. Starting from year 4, the firm will maintain a constant payout ratio of 80%. Suppose the firm XYZ's return on equity is 15%, and the required rate of return is 10%. Year 1 2 3 4 EPS/$ 2.1 3.5 5.0 ? Grow at 9 =7% Payout ratio 20% 40% 60% 80% Constant 80% Dividend ? ? ? Grow at g =7% (a) What are the expected dividend payments in the first three years? (b) What is the expected EPS and expected dividend in year 4? (c) What is the growth rate of expected dividend after year 4? (d) What is your estimation of current stock price using DDM