Deriving maximum value and minimum value functions: an example

See the attached file as equations are contained within the Word file. Consider the following function: (see file) where a > 0 is a parameter. 1. Find the first order condition for a critical point of this function. 2. Is this a maximum or a minimum or an inflection point? 3. Solve for x* (a), the maximizer of the function f (x; a) :Also find y* (a), the maximized value of y as a function of a 4. Find (see file) and (see file) 5. Now use the FOC from 1 and the implicit function theorem to find 6. Use the envelope theorem to find . Why does this theorem allow you to simplify your calculations with respect to point 4?

Demand curve for oil changes at Jiffy Lube

The demand curve for oil changes at Jiffy Lube is P = 15 - 0.15Q. Q is the number of oil changes performed each week and P is the price of the oil change. Jiffy is thinking about raising their price of $9 per oil change, however, they do not want to if the raise will cause revenue to decrease. Should they raise the price above $9 and if so why? Also, say the demand for oil changes increase to P = 22 - 0.22Q, at what price should Jiffy increase the oil change prices? Why or why not?

Utility maximizing choice

If Fred is on a set salary and can only eat ham and drink tea. He drinks 4 bottles of tea and eats 10 lbs of ham. The price of tea is $10 per bottle and $4 per lb of ham. The last bottle of tea added 50 units to Fred's utility and the last lb of ham added 40 units. Would you consider that Fred was making a utility-maximizing choice and if so why or why not? If not, what should he do and why?

Present value

THE PRESENT WORTH OF AN ALTERNATIVE THAT PROVIDES INFINITE SERVICE IS CALLED IT'S? A. NET PRESENT VALUE B. DISCOUNTED TOTAL COST C. CAPITALIZED COST D. PERPETUAL ANNUAL COST

Industry structure is often measured by computing the Four-Firm Concentration Ratio.

Industry structure is often measured by computing the Four-Firm Concentration Ratio. Suppose you have an industry with 20 firms and the CR is 30%. How would you descripbe this industry? Suppost the demand fo the product rises and pushed up the price for the good. What long-run adjustments would you expect following this change in demand? What does your adjustment process imply about the Cr for the industry? Consider the industry has 20 firms but the CRfor the industry is 80% instead of 30%. How would you describe this industry? What are some reasons why this industry has a high Cr while the other industry had a low CR? Is it possible for smaller firms to thrive and profit in such an industry... click for more