# Math

Could someone work this question out so I understand it. Thanks

The marginal price dp/dx at x units of demand per week is proportional to the price p. There is no weekly demand at a price of \$100 per unit [p(0)=100], and there is a weekly demand of 8 units at the price of \$60.83 per unit [p(8)=60.83].

A)find the price demand equation. Give an exact answer in simplified form. Round all decimal values to the nearest hundreth.

B)At a demand of 25 units per week, what is the price? Round to the nearest cent.

1. 👍
2. 👎
3. 👁
1. dp/dx = k p
dp/p = k dx
ln p = kx + C
p = e^(kx+C) = c e^kx
p(0)= + 100
so
100 = c e^0 = c
so
p = 100 e^kx
p(8) = 60.83
60.83 = 100 e^(k*8)
ln(.6083) = 8 k
k = -.06214
so
p = 100 e^(-.06214 x)

if x = 25
p = 100 e^-(.0214*25)
p = 100 * .5857
p = \$58.57

1. 👍
2. 👎

## Similar Questions

1. ### Math help

You buy clothing at a sale. You buy sneakers at 2/3 of their original price of \$60, a sweater at 7/10 of its original price of \$35, and a jacket at 5/6 of its original price of \$45. Answer each question and show all your work. a.

2. ### Economics

you are hired as the consultant to a monopolistically competitive firm. The firm reports the following information about its price, marginal cost, and average total cost. Can the firm possibly be maximizing profit? If the firm is

3. ### Calculus

The price-demand and cost functions for the production of microwaves are given as p=235−x40 and C(x)=14000+70x, where x is the number of microwaves that can be sold at a price of p dollars per unit and C(x) is the total cost (in

4. ### Economics

50. In both monopolistic competition and non-price-discriminating monopoly, isn't the marginal revenue curve lies below the demand curve? 51. A monopolistically competitive firm is producing an output level where marginal revenue

1. ### Economics

3. Suppose a firm has a constant marginal cost of \$10. The current price of the product is \$25, and at that price, it is estimated that the price elasticity of demand is -3.0. a. Is the charging the optimal price for the product?

2. ### Economics

The market for fertilizer is perfectly competitive. Firms in the market are producing output, but they are currently making economic losses. a. How does the price of fertilizer compare to the average total cost, the average

3. ### managerial econ

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

4. ### Math

1. The towns population increased from 80,000 to 90,000 in ten years. What was the percent of increase? I didn't understand this one. 2. A \$15 item on sale for \$12 is marked down what percent? 20% 3. If Jenna buys and item for 40%

1. ### Micoreconomics

As a general rule, profit-maximizing producers in a competitive maket produce output at a point where: A) Marginal cost is increasing B) Marginal cost is decreasing C) marginal revenue is increasing D) Price is less then marginal

2. ### Economics/Algebra

A monopolist has a constant marginal and average cost of \$10 and faces a demand curve of QD = 100 - 10P. Marginal revenue is given by MR=100-.20P. a. Calculate the monopolist's profit maximizing quantity, price, and profit. b. Now

3. ### Microeconomics

Monopolistic Competition A monopolistically competitive market could be considered inefficient because: A. Marginal revenue exceeds average revenue B. Price exceeds marginal cost C. Efficient scale is realized in the long run, but

4. ### economics

Suppose a monopolist faces an inverse demand function P=100-1/2Q, and the monopolist has a fixed marginal cost of \$20. How much more would the monopolist make from perfect price discrimination compared to simply producing where