1. A monopolist's marginal cost function is given by: MC = 4g + 20 where q is the quantity of good the monopolist produces. Fixed costs are 20, and the demand equation for the good produced is p+4q = 40, where p and q are price and quantity, respectively. Find expressions for total revenue and for profit, as functions of q. Determine the value of q which maximises the profit.
1. A monopolist's marginal cost function is given by: MC = 4g + 20 where q is the quantity of good the monopolist produces. Fixed costs are 20, and the demand equation for the good produced is p+4q = 40, where p and q are price and quantity, respectively. Find expressions for total revenue and for profit, as functions of q. Determine the value of q which maximises the profit.
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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![1. A monopolist's marginal cost function is given by:
MC = 4q+ 20
where q is the quantity of good the monopolist produces. Fixed costs are 20, and
the demand equation for the good produced is p+4q = 40, where p and q are price
and quantity, respectively.
-
Find expressions for total revenue and for profit, as functions of q. Determine the
value of q which maximises the profit.
2. Suppose the numbers x, y and z satisfy the following equations, where a is some
number:
x+y+z= 5-a
2x+y = 7-a
x-y-2z = 0.
Use a matrix method to determine the values of x, y and z, in terms of a. For what
values of a will x, y and z all be positive?
3. Suppose that a is a positive number and that the function f is given by:
f(x, y) = y¹ - 8a²y²
+1](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb3f5bf23-6bf1-455b-9ba2-e85cc337779c%2Fbf534cea-12b0-4781-b7bd-f00bd7f458d1%2Fwcxcimn_processed.jpeg&w=3840&q=75)
Transcribed Image Text:1. A monopolist's marginal cost function is given by:
MC = 4q+ 20
where q is the quantity of good the monopolist produces. Fixed costs are 20, and
the demand equation for the good produced is p+4q = 40, where p and q are price
and quantity, respectively.
-
Find expressions for total revenue and for profit, as functions of q. Determine the
value of q which maximises the profit.
2. Suppose the numbers x, y and z satisfy the following equations, where a is some
number:
x+y+z= 5-a
2x+y = 7-a
x-y-2z = 0.
Use a matrix method to determine the values of x, y and z, in terms of a. For what
values of a will x, y and z all be positive?
3. Suppose that a is a positive number and that the function f is given by:
f(x, y) = y¹ - 8a²y²
+1
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