A firm's demand function is Q = 16 - P and its total cost function is defined as TC = 3 + Q + 0.25Q² Use these two functions to form the firm's profit function and then determine the level of output that yields the profit maximum. What is the level of profit at the optimum?

A firm's demand function is Q = 16 - P and its total cost function is defined as TC = 3 + Q + 0.25Q² Use these two functions to form the firm's profit function and then determine the level of output that yields the profit maximum. What is the level of profit at the optimum?

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter2: Mathematics For Microeconomics

Section: Chapter Questions

Problem 2.2P

See similar textbooks

Related questions

Q: Nana sells homemade yoghurt tubs at 75 pesos per tub. Suppose x bottles of sanitizer are produced…

Q: Consider a firm with the following production function: f(x1,x2) = If the input prices are 2 and 4…

A: We are going to use Marginal rate of technical substitution ( MRTS) concept to answer this question.…

Q: Consider a market served by identical firms with the cost function C(q) = 722 + (q² / 200). The…

A: In economics, market equilibrium refers to a condition in which economic factors such as supply and…

Q: onsider a competitive firm that has the cost function, TC(Q) and faces the demand P = P(Q), that is,…

A: Since, you have asked a question with multiple parts, we will be answering the first three parts for…

Q: Given a firms demand function Q-90+2P=0 and it's average cost function AC=Q²-8Q+57+2/Q. Find the…

A: Given Information Demand function Q-90+2P=0 Average cost function AC=Q²-8Q+57+2/Q

Q: The total revenue curve of a firm is R (q) = 40q - 12q2 and its average cost A(q) = 1/30q2 - 12.85q…

Q: The inverse demand function for a commodity is given by p=41-0.33q and the cost of producing that…

A: Introduction The technique of maxima and minima can be used to determined the level of output at…

Q: Write out the total cost and total revenue functions in terms of Q.

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: The demand function for a firm is p = 320 – 3.2x, and the cost function is C(x) = 100 + 80x –…

A: (i) Demand Function p = 320 - 3.2x Cost Function C(X) = 100 + 80x - 1.6x2 Profit = Revenue - Cost…

Q: A price-taking firm's variable cost function is VC = 20', where Qis its output per week. It has a…

A: Fixed cost of a firm is defined as the cost of a firm that does not change with change in the…

Q: A firm's demand function is Q = 16 – P and its total cost function is defined as TC = 3 + Q +…

A: Profit depends on total revenue and total cost of a firm. Profit is a difference between total…

Q: Each of the 8 firms in a competitive market has a cost function of C= 5+q°. The market demand…

A: A Perfectly competitive firm has a constant price at all levels of output. Profit is maximized at…

Q: 20Q, where C is the total cost, F is a fixed cost, and Q is the level of output. The inverse demand…

A: Answer According to the question it is given that : Cost function (C) = F + 20 Q And, the inverse…

Q: Question: The price - demand equation and the cost function for the production of HDTV s are given…

A: Given x=9000-30pandx=15000+30xx=9000-30pp=900030-x30⇒P=300-x30We know that demand x and price…

Q: A firm has the following demand and average total cost functions: Q = 30 − P ATC =7/Q− 6 +1/2 Q…

A: Q = 30 − P P = 30-QATC =7/Q− 6 +1/2 Q Total Revenue (TR) = PXQ = 30Q-Q2 Total Cost (TC) = ATCXQ TC…

Q: Suppose that the demand functions facing a n product firm are as follows: Q, = 40 – 2P, + P2 %D Q2 =…

A: The following problem has been answered as follows:

Q: A firm’s production function is Q = 10 + 30L - .5L2+ 30K – K2, and its competitive demand function…

A: Given production function :- Q = 10 + 30L - 0.5L2 + 30K - K2 PQ = $40 PL = $6 PK = $12 K = 10

Q: Define Q to be the level of output produced and sold, and assume that the firm’s cost function is…

A: Since you have posted a question with multiple subparts, we will solve the first three subparts for…

Q: A firm’s price and cost equations are given by P = 200 - 0.2Q and TC = 1,000 + 40Q, respectively.…

A: According to question given that price(demand ) equation and total cost equation, using both we can…

Q: A firm has the following demand and average total cost functions: Q = 30 − P ATC =7/Q− 6 +1/2Q…

A: The total revenue of a firm is the total payment it receives from the sale of goods and services.…

Q: firm’s production function is Q = 10 + 30L - .5L2+ 30K – K2, and its competitive demand function is…

A: Answer A firm’s production function is Q = 10 + 30L - 0.5L2 + 30K – K2 MPL = = 40 - L At…

Q: A firm's demand function is Q = 16 - P and its total cost function is defined as TC = 3 + Q + 0.25Q2…

A: P = 16 - Q TR = PQ = 16Q - Q2 Profit (Z) = TR - TC = 16Q - Q2 - 3 - Q - 0.25Q2 = 15Q - 1.25Q2 - 3…

Q: A commodity has a demand function modeled by p = 106 − 0.5x and a total cost function modeled by…

A: In a firm that wants to maximize its profits levels, it becomes vital to determine the levels of…

Q: A local newspaper currently has 84,000 subscribers at a quarterly charge of $30. Market research has…

A: The measure that depicts expenses that are being incurred for carrying out day-to-day transactions…

Q: Match each graph with the function it best represents-a demand function, a revenue function, a cost…

A: Graph a = Demand function, decreases, increases Graph b = Cost function, increase linearly Graph c =…

Q: A firm's demand function is given by p 234 - 5q, where p and q denote the price and quantity,…

A: Given Demand function p=234-5q .....(1) Where p and q denote the price and quantity…

Q: The total revenue curve of a firm is R (q) = 40q - 12q2 and its average cost A(q) = 1/30q2 - 12.85q…

A: Total revenue, R (q) = 40q - 12q2 Average cost, A(q) = 1/30q2 - 12.85q +20 + 400/q

Q: In a given market the inverse demand function is P = 170 - Q per year. The interest rate is r= 0.05…

A: Meaning of Monopolistic Competition: The term monopolistic competition refers to the situation…

Q: A firm's demand function is Q = 16 - P and its total cost function is defined as TC = 3 + Q+ 0.25Q²…

A: The main objective of every firm is to maximize its profits. Profits are the excess of revenue…

Q: Suppose that the cost required for a company to produce r units of its product is a linear function…

A: Note: I have solved the question completely as we are expected to solve it properly. Answer: (a).…

Q: A firm’s demand function is P= 60 − 0.5Q If fixed costs are 10 and variable costs are Q + 12 per…

A: Profit is the amount which a producer earns over and above of all the costs. We can calculate profit…

Q: The total revenue curve of a firm is R(q) = 40q − 12q2 and its average cost A(q) = 1/30q2 − 12.85q +…

A: Solution - Given in the Question - Total Revenue curve of a firm R(q) = 40q -12q2…

Q: A company manufacturing laundry sinks has fixed costs of $100 per day but has total costs of $2,500…

A: The total cost is the cost incurred for using the factors of production to produce a good. Costs…

Q: Based on market research, a film production company in Ectenia obtains the following information…

A: Here we calculate the following blanks by using the given information so the calculation of the…

Q: What is the demand function and cost function based on the set of data below? Price Quantity Profit…

Q: A firm's demand function is Q = 16 – P and its total cost function is defined as TC = 3 + Q + 0.25Q2…

A: Equilibrium in economics is the state of stability and balance. Any deviation from this level will…

Q: Firm 1 and firm 2 compete with each other by choosing quantities. The market demand is given by if…

A: Here demand function=P=400-Q=400-q1-q2 cost function of firm1=TC1=40q1 cost function of…

Q: The figure deplcts the demand curve for Beautiful Cars, and the marginal cost and Isoprofit curves…

A: Demand curve is a graphic representation of the relationship between price of the product and the…

Q: Consider a firm whose total cost function is 2q 3 – 6q2 + 13q. a. If the price of a unit of output…

A: a.

Q: Find an expression for the profit function given the demand function 2Q + P = 24 and the average…

A: 2Q + P = 24 P = 24-2Q AC = 48/Q + 4

Q: A price-taking firm's variable cost function is C = Q3, where Q is the output per week. It has an…

A: Given, Variable cost (VC): C = Q3 Fixed cost (FC) = $1,024 Marginal cost (MC) = 3Q2 Price (P) = $192

Q: The profit function of a good is given by the following: n = -5Q2 + 631Q – 3255 where P is the price…

A: The relationship between the quantity demanded a commodity (dependent variable) and the price of the…

Q: The price-demand equation for the production of bluetooth speakers is: p = 250 - 1/20x, for 0 is…

A: Profit function: π =TR -TC; where π is profit, TR is total revenue and TC is total cost Revenue…

Q: A firm's demand function for a certain good is given by P=100e1. Its total cost function is…

A: A firm's output is maximized at the point where: Marginal Revenue (MR)=Marginal Cost (MC) MC curve…

Q: For output levels of 1, 2, 3, 4, 5 and 6 units, a competitive firm's total costs are $142, $172,…

A: Profit maximize when MC = MR MC is marginal cost and calculated by MC = (TCn - TCn-1)/(Qn - Qn-1)…

Q: The total revenue curve of a firm is R(q) = 40q − 12q2 and its average cost A(q) = 1/30 q2 − 12.85q…

A: total revenue (TR) is defined as the total quantity(q) of commodity produced multiplied with its…

Q: Which of the following statements is correct with respect to profit maximization? PLEASE EXPLAIN…

A: In economics, an individual will enter into a transaction if he is able to generate profit from it.…

Question

Q 1.
(B)
A firm's demand function is
Q = 16 - P and its total cost function is
defined as TC = 3 + Q + 0.25Q? Use
%3D
these two functions to form the firm's
profit function and then determine the
level of output that yields the profit
maximum. What is the level of profit at
the optimum?

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 2 steps with 1 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, economics and related others by exploring similar questions and additional content below.

Similar questions

A firm has a linear demand function for its product. When the price of the product isSh.220, the quantity demanded is 40 units. When the price increases to Sh.240, thequantity demanded becomes 30 units. In addition, the firm’s marginal cost function isgiven by:MC = 40q – 2q2 + 2Fixed cost = Sh.5 millionWhere q = quantity demanded, MC = marginal cost (Sh. million)Evaluate the level of output that maximizes profits.
A 62 metre length of rope is cut into pieces whose lengths are in arithmetic progressionwitha common difference of d metres. Given that the lengths of the shortest and thelongest pieces are 0.5 and 3.5 metres respectively, find d.(C) For a firm’s product, the demand function isp = 72 2 0.04qand the average cost function isc¯ =500q+ 30 At what level of output would profit be maximized?
A company manufacturing laundry sinks has fixed costs of $100 per day but has totalcosts of $2,500 per day when producing 15 sinks. The company has a daily demand functionof q = 360 − p, where q is the number if laundry sinks demanded and p is te price ofa laundry sink. ) If production increases continuously, what is likely to be the average cost per sink? How many laundry sinks will the company need to produce in order to maximise it′s profits? What is the maximum profit?
If demand function is given by P = 40 - 2Q then what is the procedure to get marginal revnue ?
Revenue and Cost The total weekly revenue functionfor a certain digital camera is given by R = 550xdollars, and the total weekly cost function for thecameras is C = 10,000 + 30x + x2dollars, where xis the number of cameras that are produced and sold.a. Find the profit function.b. Find the number of cameras that gives maximumprofit.c. Find the maximum possible profit.
he total revenue curve of a firm is R(q)=40q−12q and its average cost A(q)=130q−12.85q+20 +400q,where q is the firms output. i. Derive an expression C(q) for the firms total cost function. ii. Derive an expression Π(q) for the firms profit function. iii. Is the rate of change of profit increasing or decreasing when the ouput level of the firm is 10 units? iv. Determine the level of output for which the firms profit is maximized. v. What is the firmss maximum profit?
Revenue and Cost The total revenue function for LED TVs is given by R = 1050x dollars, and the total cost function for the TVs isC = 10,000 + 30x + x2dollars, where x is thenumber of TVs that are produced and sold.a. Which function is quadratic, and which is linear? b. Form the profit function for the TVs from thesetwo functions.c. Is the profit function a linear function, a quadraticfunction, or neither of these?
for a firm with price in excess of average total cost, the presence of ecomonics profits implies that the firm should increase output in the short runeven if the price is below marginal cost . true or false explain
4. Assess which of the following is true and which is false.A firm’s profit equation is given by π = -100 + 160Q – 20Q2. Therefore,a) The firm’s fixed cost is 100.b) The firm’s fixed cost is 40 and variable cost is 20.c) Marginal profit is Mπ = 160 – 20Q.d) The firm’s profit-maximizing output is Q = 4.e) Marginal profit is Mπ = 160 – 40Q and it is positive for quantities that are lower than theprofit-maximizing quantity.
) A company manufacturing laundry sinks has fixed costs of $100 per day but has totalcosts of $2,500 per day when producing 15 sinks. The company has a daily demand functionof q = 360 − p, where q is the number if laundry sinks demanded and p is te price ofa laundry sink. Find a function for the average cost of this company. (c) If production increases continuously, what is likely to be the average cost per sink? (d) How many laundry sinks will the company need to produce in order to maximise it′s profits? (e) What is the maximum profit?
A toy manufacturer makes miniature trucks. The pricep(in dollar) and the demandx(numberof miniature trucks) are related by the equation 6000−600p=x. The total cost for the sametoy manufacturer to producexminiature trucks can be modeled byC(x) = 8x+ 450.(a) (10 points) Express the pricepin terms of the demandx. Find the revenueR(x) if themanufacturer sellsxminiature trucks in a month and find the domain of this function.(b) (10 points) Graph the cost and revenue functions on the same coordinate system for 0≤x≤6000.(c) (10 points) What is the minimum number of trucks the toy manufacturer must sell tobreak even?(d) (10 points) FindP′(300) and interpret the result.(e) (10 points) What is the exact profit from the sale of the 301stminiature truck?
Now suppose firm X undertakes a process innovation that reduces its marginal cost ofproduction from $20 to $15. The fixed cost of undertaking this process innovation is F > 0. Is this atough commitment or a soft commitment? Why? For what values of F would it make sense for firm Xto make this commitment?