Question

The demand for a commodity of a company is given by the demand function: [3+2+1] p = (60 − q 10) 2 a) Find the elasticity of demand E(p). [3 marks] b) What price results in the maximum revenue? [2 marks] c) What is the maximum revenue? [1 mark]

Answer #1

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...

The demand function for a certain commodity at a sales
price of p dollars follows the function:
d(p)=22000e^-0.5p -1
a) Determine the sales price at which there will be no demand for
this commodity.
Construct the elasticity of demand function for this commodity.
Calculate and interpret
the elasticity at a sales price of $2.
Determine the maximum revenue generated by sales of this
commodity.

The demand function for a Christmas music CD is given by
q=0.25(225−p^2)
where q (measured in units of a hundred) is the quantity
demanded per week and pp is the unit price in dollars.
(a) Evaluate the elasticity at p=10. E(10)=
(b) Should the unit price be lowered slightly from 10 in order to
increase revenue?
yes no
(c) When is the demand unit
elastic? p=______dollars
(d) Find the maximum revenue. Maximum revenue =________ hundreds of
dollars

If the demand function for a commodity is given by p(q + 4) =
400 and the supply function is given by 2p – q – 38 = 0, find the
market equilibrium.

The demand function for a Christmas music CD is given by
q=D(p)=0.25(225−p2)where q (measured in units of a hundred) is the
quantity demanded per week and p is the unit price in dollars. (a)
Find the elasticity function E(p)= _________
(b) Evaluate the elasticity at 10. E(10)= ________
(c) Should the unit price be lowered slightly from 10 in order
to increase revenue? Yes or No.
(d) Use the elasticity of demand to find the price which
maximizes revenue for...

Suppose the cost of producing q unit is
c(q)=500-4q+q2 and the
demand function is given by p=14-2q
A) Develop the total revenue, total cost (if not given), and
profit functions. Explain these functions in few sentences.
B) Compute the point elasticity of demand.
C) Find the intervals where the demand is inelastic, elastic,
and the price for which the demand is unit elastic.
D) Find the quantity that maximizes the total revenue and the
corresponding price. Interpret your result.
E)...

1.A demand function given by: Q = 240 ‒ 3P. What is the price
elasticity of demand when the price is P = $10? You will have to
use the point elasticity formula. The price elasticity of demand at
this price is ___________
2.Consider the same demand equation, Q = 240 ‒ 3P. If a firm
sells at the unit elastic price on this demand curve, what is the
total revenue it will receive? The total revenue received at this...

(a) find the elasticity of the demand function q = (15000) /
(p^2 + 50) when the price is p = 10 Dollars.
(b) If the price increases, will the revenue increase or
decrease? Explain how you conlcuded this from your elasticity
value.

Suppose the quantity of good X demanded by consumer 1 is given
by: Q DX1 =62 – 3P X + 0.35I + 0.3P Y And the quantity of good X
demanded by consumer 2 is given by: Q DX2 = 10 – 2.5P X + 0.2I +
0.6P Y Answer the following questions and ensure that you show ALL
calculations.
(a) What is the market demand for good X? 3 marks
(b) Using the first demand function: (Q DX1 =...

(3)The demand (P) and total cost ( TC) functions for commodity Z
can be represented by the following equations:
P = 1400 – 7.5Q
TC= Q^3-6Q^2+140Q+750
(a)Graph the marginal revenue and marginal cost for Q = 0, 5,
10, 15, 20 and 25
(b)What is the profit maximizing output for this firm?
(c)Find the price the firm will sell its output.
(d)If the market clears, find the profit the firm could
earn.

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