Economics Output Maximization and Profit Maximization

What you are solving for in these problems is the optimal input combination based either on what I call Solution #1 and Solution #2; Solution #1 guarantees output maximization and Solution #2 guarantees profit maximization. Use them where appropriate. Use the optimization procedure to get answers not an Excel result.

1. The owner of the Hughes Car Wash believes that the relationship between the number of cars washed and the labor input is:
Q= -.8 + 4.5L - .3L2 where Q is the number of cars washed per hour and L is the number of people hours employed per hour.
The firm receives $5 for each car washed and the hourly wage rate for each person employed is $4.50. The cost of other inputs such as water is trivial and hence they are ignored.
a) How many people should be employed to maximize profit?
b) What will be the firm's hourly profit?
2. Find the optimal input combination for the following:
Q= 30X + 2XY -.5X2 -.5Y2 where Q is total output, X is worker hours, and Y is machine tool hours
Given that the price of X is $25.00 per unit of X and the price of Y is $40.00 per unit of Y and MR is $.50, find the optimal input combination for this production relationship.
3. In the Elwyn Company, the relationship between output (Q) and the number of hours of skilled labor (S) and unskilled labor (U) is as follows:
Q= 300S + 200U -.2S2 -.3U2
The hourly wage of skilled labor is $10.00 per unit and the hourly wage of unskilled labor is $5.00 per unit. The firm can hire as much labor as it wants at these wage rates.
A) Elwyn's chief engineer recommends that the firm hire 400 hours of skilled labor and 100 hours of unskilled labor. Evaluate this recommendation.
B) If the Elwyn Company decided to spend a total of $5,000 on skilled and unskilled labor, how many hours of each type of labor should it hire?
C) If the price of a unit of output is $10.00, how many hours of unskilled and how many hours of skilled labor should the company hire?

ProfitMaximizationProfitMaximization
1) Fill in the missing data for price (P), total revenue (TR), Marginal Revenue (MR),
total cost (TC), Marginal Costs (MC), profit (ð), and marginal profit (Mð)
in the following table (all units except Q are dollar

Question: A monopolist faces a marginal revenue function of MR = 20 - Q. The monopolist's marginal cost is $15 at all levels of output. How many units of output should the firm produce in order to maximize profits?

Is profitmaximization alone an appropriate goal for the firm? Why or why not? Who in a corporation is responsible for protecting and managing stockholders interest? How is profitmaximization different from maximizing shareholder wealth?

Market Equilibrium andProfitMaximization under Perfect Competition
The supply and demand equations for a hypothetical perfectly competitive market are given by
QS = -100 + 3P and QD = 500 - 2P.
a) Find the market equilibrium price algebraically.
b) In Excel, use the above equilibrium price and the cost data fro

Suppose the demand curve faced by a monopolist is:
q=p^-a where a>0
The total cost for the monopolist are C=sq
a) Find the profit maximizing level of output.
b) Specify the first and second order condition for profitmaximization.
c) What is the price elasticity of demand faced by this monopolist
d) What hap

It costs Dan's company C(x) = x^2 - 3x + 64 dollars to produce x items. The selling price (p) when x hundred units are produced is p(x) = (44 - x)/4. Determine the level of production (# of items produced) that maximizes profit.

In perfectly competitive market a firm typically has short run average total cost curve and marginal cost curve of:
ATC-100+Q+(100/Q)
MC=100+2Q
1. Assume the firm faces an output price of $110. How many units of output does firm produce
2. Consider that average total cost is minimized at 10 units of output, what would we

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 price and Q is the number of lockers rented per month.
a. What price wou