You work for a drug manufacturing company that holds a patent on Hair Grow, the world most effective drug for restoring hair. Your job is to analyze the pricing and investment decisions facing the firm. Your marketing group estimates that Hair Grow has the following demand curve:

P = 101-0.00002Q

where P is measured in dollars and Q is measured in the number of pills a year. You have this patent for another five years.

a. Your marginal cost for producing a Hair Grow pill is $1. What is the profit-maximizing price and quantity? What is your profit?

b. Suppose that your production facility can only produce 1,200,000 pills per year. What is your optimal price and quantity given the production constraint? What are your profits (assume there is no fixed cost)?

c. Assume that your production capacity is currently 1,200,000 pills as in (b). Now, suppose that you could increase the capacity of your plant to 3,000,000 pills per year for a cost of $30,000,000. However, the construction of the new plant takes a full year, and during the year while your factory is under construction, you have to shut down the production facility, and cannot produce Hair Grow. Should you undertake the investment (for simplicity, assume you can borrow the funds for the expansion at a 0 percent interest rate)?

Solution Preview

a.Your marginal cost for producing a Hair Grow pill is $1. What is the profit-maximizing price and quantity? What is your profit?

Given
Marginal Cost=MC=$1
P=101-0.00002Q

Total Revenue=P*Q = 101Q-0.00002Q^2
Marginal Revenue=MR=dTR/dQ = 101-0.00004Q

Put MR=MC for profit maximization
101-0.00004Q = 1.00
Q= 2,500,000

P=101-0.00002*2500000 =$51.00

Total Revenue=P*Q=51*2500000=$127,500,000
Total Cost=1*2500000=$2,500,000 (assume zero fixed costs)

Profit =127,500,000-2,500,000=$125,000,000

b. ...

Solution Summary

Solution describes the steps to find out optimal output and price level in the given case. It also calculates optimal profit and profit in case maximum production capacity is 1,200,000 pills.

The demand curve for tickets at an amusement park is:
Q = D(p) = 1400 - 46p, p > 0
The marginal cost of serving a customer is $11.
Using calculus and formulas (but no tables or spreadsheets) to find a solution, how many tickets will be sold at the profit-maximizing price?
Round the equ

Supposing the demand for a gas station is given as PD = 2.06 - .00025QD. The marginal cost is $1.31 per gallon. At his current $1.69 price, he sells 1,500 gallons per week. Is this price-output combination optimal?

Please refer problem 3 from the attached file for graph.
The accompanying graph (bottom of this page) summarizes the demandand costs for a firm that operates in a monopolistically competitive market.
a. What is firm's optimaloutput?
b. What is firm's optimalprice?
c. What are the firm's maximum profits?
d. What ad

Please refer attached file for graph.
Answer the following questions on the basis of the monopolist's situation illustrated in the following graph.
a.At what output rate andprice does the monopolist operate?
b.In equilibrium, approximately what is the firm's total cost and total revenue?
c.What is the firm's economic pr

Currently the total cost is given by TC = 100 + 10Q +Q^2 for sale shoe manufacturing company. The demand equation is given by P =-5Q +130. How many units should the company produce to maximize its profit? What is the price that company charges? What are the profit, total revenues, and total cost of the company?

1. Use the "graph attached" What is the firm's Total Revenue at the profit maximizing level of output
32
0
16
8
14
Not enough information
2. Use the "graph attached" What is the firm"s Total Profits at the profit maximizing level of output?
0
32
16

The demand for speciality glue is given as follows: P = 1200 - 6Q, where P is price per 100 pounds of specialty glue produced and Q is the amount produced and sold in hundreds of pounds. The marginal cost of producing glue for the entire glue industry is as follows: MPC = 700 + 2Q. Let the production of speciality glue result in

Tyvex LLC produces professional quality color laser printers. The market for professional color laser printers is monopolistically competitive. Assume that the inverse demand curve faced by Tyvex (given its competitors' prices) can be expressed as
P = 5,000 - .2Q
and Tyvex's total costs can be expressed as
TC = 20,000,000

As manager of Citywide Racquet Club, you must determine the best price to charge for locker rentals. Assume that the (marginal) cost of providing lockers is 0.
The monthly demand for lockers is estimated to be: Q= 100-2P where P is the monthly rental priceand Q is the number of lockers rented per month.
a. What price wou

(see attached for full problem description)
1
Global Corp. sells its output at the market price of $9 per unit. Each plant has the costs shown below:
What is the profit at each plant when operating at its optimaloutputlevel?
2
Suppose that you can sell as much of a product (in integer units) as you like at