Question

Assume that the demand function for tuna in a small coastal town is given by p = 20,000 q1.5 (200 ≤ q ≤ 800), where p is the price (in dollars) per pound of tuna, and q is the number of pounds of tuna that can be sold at the price p in one month.

(a) Calculate the price that the town's fishery should charge for tuna in order to produce a demand of 400 pounds of tuna per month.

(b) Calculate the monthly revenue R (in dollars) as a function of the number of pounds of tuna q. R(q)

(c) Calculate the revenue and marginal revenue (derivative of the revenue with respect to q) at a demand level of 400 pounds per month.

Answer #1

1. In a small college town, the demand for delivery pizza is
given by QD = 800 - 32P, where QD is the
number of pizza demanded each week. What is the firm's marginal
revenue function?
2. In a small college town, the demand for delivery pizza is
given by QD = 800 - 32P, where QD is the
number of pizza demanded each week. At what Q does MR = 0?
3. In a small college town, the demand...

1. The cost function C and the price-demand function
p are given. Assume that the value of
C(x) and p(x) are in dollars. Complete the
following.
C(x) = x^2/100 + 6x + 1000; p(x) = x/20+25
(a) Determine the revenue function R and the profit
function P.
R(x)
=
P(x)
=
(b) Determine the marginal cost function MC and the
marginal profit function MP.
MC(x)
=
MP(x)
=
3. Determine the derivative for the given single-term function.
When appropriate,...

The demand function for a particular brand of LCD TV is given
by
p = 2400 − 30x
where p is the price per unit in dollars when
x television sets are sold.
(a) Find the revenue function.
R(x) =
(b) Determine the number of sets that must be sold in order to
maximize the revenue.
sets
(c) What is the maximum revenue?
$
(d) What is the price per unit when the revenue is maximized?
$ per unit

The demand for a particular commodity when sold at a price of p
dollars is given by the function D(p) = 4000e −0.02p .
(a) Find the price elasticity of demand function and determine
the values of p for which the demand is elastic, inelastic, and of
unitary elasticity.
(b) If the price is increased by 3% from $12, what is the
approximate effect on demand?
(c) Find the revenue R(p) obtained by selling q units at p
dollars per...

A certain item can be produced at a cost of $10 per unit, the
demand equation for this item is p=90-.02q, where p is the price
per unit in dollars and q is the number of units. a) Give the cost
function C, the revenue function R, and the profit function P.
b) use a derivative to determine the number of units that would
produce the maximum profit and what that profit would be. Verify
using the second derivative test

The cost function C and the price-demand function
p are given. Assume that the value of
C(x)
and
p(x)
are in dollars. Complete the following.
C(x) =
x2
100
+ 7x + 3000;
p(x) = −
x
40
+ 5
(a) Determine the revenue function R and the profit
function P.
R(x)
=
P(x)
=
(b) Determine the marginal cost function MC and the
marginal profit function MP.
MC(x)
=
MP(x)
=
Here is a picture of the problem:
https://gyazo.com/b194ec1a9b7787b8b81ad12388ff915e

The demand for tickets to an amusement park is given by
p=70−0.04q, where p is the price of a ticket in dollars and q is
the number of people attending at that price.
(a) What price generates an attendance of 1500
people? What is the total revenue at that price? What is the total
revenue if the price is $20?
(b) Write the revenue function as a function of
attendance, q, at the amusement park. Use the multiplication sign
in...

Calculate the price and cross-price elasticities of demand for
coconut oil. The coconut oil demand function (Buschena and Perloff,
1991) is Q = 1,200 − 9.5p + 16.2pp + 0.2Y, where Q is the quantity
of coconut oil demanded in thousands of metric tons per year, p is
the price of coconut oil in cents per pound, pp is the price of
palm oil in cents per pound, and Y is the income of consumers.
Assume that p is initially...

A
doughnut shop determines the demand function q=D(p)= 300/(p+3)^5
for a dozen doughnuts where q is the number of dozen doughnuts sold
per day when the price is p dollars per dozen.
A.) Find the elasticity equation.
B.) Calculate the elasticity at a price of $9. Determine if
the demand elastic, inelastic, or unit elastic?
C.) At $9 per dozen, will a small increase in price cause the
total revenue to increase or decrease?

1. Demand for gasoline in a small town is given by P=5-0.05Q
where P is in dollars and Q is in 1000s of gallons per week. If
there are only 3 gas stations in very close proximity to each other
in the center of town, and consumers view them as perfect
substitutes, answer the following questions:
a) If all firms share a constant MC=$2 per gallon, what will be
the equilibrium price and quantity in the market?
b) Suppose that...

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