3. Imagine there is a monopolist with a cost function of C = 500 +5Q + ¹/4Q², and a demandfunction of P = 50 - ¹/₂Q.a. State the firm's fixed costs.b.Differentiate the cost function to find the marginal cost.c. Multiply the demand function by Q to find the revenue function.d. Differentiate to find the marginal revenue.e.f.g.h.i.Use the rule that maximum profit is when MC = MR to find the profit-maximising Q.Now use the demand function to find the market price at this Q.Use your results to find the firm's total revenue at this Q.Use the cost function to find the firm's total cost at this Q.Hence find the firm's profit.4. Taking the same firm:a. Find the firm's average cost function, by dividing the cost function by Q.b. Differentiate the average cost function you have found, and set the result equal to zero.C. Then solve for Q to find the level of Q at which average cost is minimised.d. Use the value for Q that you have just found in the average cost function, to compute theminimum average cost.Now use the demand function to find the quantity demanded if the good were sold at thatminimum average cost.f. Compare the results you found in parts (c) and (e). Comment on what you have found,thinking about market structure and minimum efficient scale.e.5. Again taking the same firm:a.Use graph paper to carefully hand-draw the firm's demand curve, MC curve, and MR curve.Your x-axis should show Q and go from 0 to 50. Your y-axis should show P (and C) and alsogo from 0 to 50. You will get credit for a neat diagram.b. Use dotted lines and shading to show the areas of consumer surplus, producer surplus, anddeadweight loss.c. Using the geometric rule that the area of a triangle is equal to height x width x ½2, find thearea of deadweight loss. You will get extra marks for using demand, MC and MR to beprecise about the height and width of the triangle. For example, MR = MC will give you thebottom point of the triangle (as this is where the two lines cross). Questions1. Consider the diagram below.a. Hand-draw the diagram, and show how the feasible frontier changes if there is animprovement in the technology of food production.b. If Angela is an independent farmer (so, she owns the land and starts at point C), use thec.d.concepts of income and substitution effects explain how the improvement might cause heroptimal labour supply to either fall or rise.Show both outcomes, using a different colour for each.Which outcome (fall or rise) seems more consistent with real-world data concerning labourhours and technology improvements?Bushels of grain12-4.500Angela's reservationindifference curve, IC,16Angela's hours of free timeAngela's best feasible indifference curvewhen an independent farmer, ICFeasible frontier: Angelaand Bruno combined242. Now imagine a different situation, where Angela is a worker on Bruno's land. Bruno has thebargaining power, so Angela is at point D. You are a benign ruler who wants to improve Angela'ssituation. Discuss the pros and cons of each policy below, taking into account economicefficiency, where Angela would end up, and any other effects you can think of.a. Improve Angela's reservation option, so that her reservation indifference curve is higher.Make a new law that workers can work a maximum of 7 hours each day.b.C. Create jobs in other industries, so that there is a shortage of workers in farming.

(A) Fixed cost is that part of total cost function which does not vary with quantity produced.Hence…

3. Imagine there is a monopolist with a cost function of C= 500 +5Q + ¹/4Q², and a demand function of P = 50 - ¹/₂Q. a. State the firm's fixed costs. b. Differentiate the cost function to find the marginal cost. C. Multiply the demand function by Q to find the revenue function. d. Differentiate to find the marginal revenue. Use the rule that maximum profit is when MC = MR to find the profit-maximising Q. Now use the demand function to find the market price at this Q. Use your results to find the firm's total revenue at this Q. Use the cost function to find the firm's total cost at this Q. Hence find the firm's profit. e. f. g. h. i. 4. Taking the same firm: a. Find the firm's average cost function, by dividing the cost function by Q. b. Differentiate the average cost function you have found, and set the result equal to zero.

3. Imagine there is a monopolist with a cost function of C= 500 +5Q + ¹/4Q², and a demand function of P = 50 - ¹/₂Q. a. State the firm's fixed costs. b. Differentiate the cost function to find the marginal cost. C. Multiply the demand function by Q to find the revenue function. d. Differentiate to find the marginal revenue. Use the rule that maximum profit is when MC = MR to find the profit-maximising Q. Now use the demand function to find the market price at this Q. Use your results to find the firm's total revenue at this Q. Use the cost function to find the firm's total cost at this Q. Hence find the firm's profit. e. f. g. h. i. 4. Taking the same firm: a. Find the firm's average cost function, by dividing the cost function by Q. b. Differentiate the average cost function you have found, and set the result equal to zero.

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

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
Suppose the inverse demand function for a monopolist's product is given by P=100-2Q and the cast function isC(Q)=10+2Q. What is the profit-maximizing price of the firm?A. $15 B. $51 C. $41 D. $32 And what is the profit-maximizing quantity of the firm?A. 24.5B. 18C. 20.5D. 16
3. Suppose a software monopolist faces two markets for its software, students and professionals. The demand curve of professionals is given by Qp = 200-2Pp and the demand curve by students is given by Qs = 150 - 3Ps. The firm's cost function is C(Q) = 400+5Q. (a) If the firm can price discriminate, what price should it charge in each market to maximize profits? How much profit does it earn? (b) If the firm cannot price discriminate, what price should it charge? Verify that it sells to both markets at this price. How much profit does it earn? Hint: If the firm cannot price discriminate, this means it must treat the two markets as a single combined market.
Suppose that a profit-maximizing monopolist faces a demand curve of P = 240 – 4Q, a marginal revenue ofP=240 – 8Q, a marginal cost of 8Q, and an average total cost of 4Q. a. What quantity will the monopolist supply? b. What price will the monopolist charge? c. How much revenue will the monopolist make at the profit maximizing quantity? d. What is the monopolist's total cost at the profit maximizing quantity? e. How much profit will the monopolist make?
part C D
The total cost of a monopolist is TC(Q)=5Q2+9Q+10. Her inverse demand function is P=146-3Q. You are told that her marginal revenue is 2*5Q+9 and and her marginal cost is146-2*3Q. You are also told that the firm will not shut down in the short run. Please find the profit of the monopolist.