DOC PREVIEW
UW-Madison ECON 101 - Answers to Homework

This preview shows page 1-2-3-4 out of 11 pages.

Save
View full document
View full document
Premium Document
Do you want full access? Go Premium and unlock all 11 pages.
Access to all documents
Download any document
Ad free experience
View full document
Premium Document
Do you want full access? Go Premium and unlock all 11 pages.
Access to all documents
Download any document
Ad free experience
View full document
Premium Document
Do you want full access? Go Premium and unlock all 11 pages.
Access to all documents
Download any document
Ad free experience
View full document
Premium Document
Do you want full access? Go Premium and unlock all 11 pages.
Access to all documents
Download any document
Ad free experience
Premium Document
Do you want full access? Go Premium and unlock all 11 pages.
Access to all documents
Download any document
Ad free experience

Unformatted text preview:

Economics 101 Answers to Homework #5 Spring 2009 Due 04/28/2009 in lecture Directions: The homework will be collected in a box before the lecture. Please place your name, TA name and section number on top of the homework (legibly). Make sure you write your name as it appears on your ID so that you can receive the correct grade. Please remember the section number for the section you are registered, because you will need that number when you submit exams and homework. Late homework will not be accepted so make plans ahead of time. Please show your work. Good luck! Problem One Suppose the total cost of production for a firm is given by the equation: 28 400.TC q q= + + This firm’s marginal cost equation is: 8 2 .MC q= + Market demand is given by: 100 .P Q= − a) Give the formulas for: fixed cost: FC = 400 This is the component of total cost that doesn’t vary with quantity. variable cost: 28VC q q= + This is the component of TC that depends on quantity. average total cost: 28 400 4008 .TC q qATC qq q q+ += = = + + average variable cost: 288 .VC q qAVC qq q+= = = + Now suppose this firm is operating in a perfectly competitive market (in which all firms have access to the same technology and hence face the same costs). b) What is the long run equilibrium price in this market? First we’ll find the equilibrium quantity supplied by a representative firm in the market. Since firms make zero profit in the long run, the price in the long run moves to the minimum point of ATC. MC = ATC at the minimum point on ATC. Set MC = ATC: 4008 2 8q qq+ = + + and solve for 20.Cq = Now we can find the long run equilibrium price by plugging q = 20 into either the MC or the ATC equation. Using MC: 8 2 20 48.CP = + × =c) Calculate the economic profit earned by a perfectly competitive firm in the long run. We actually don’t need to calculate anything. It is a fact that in the long run a perfectly competitive firm makes economic profit = 0. You can verify this is you want by calculating total revenue and total cost. You will find TR = TC which implies that economic profit = 0. Now suppose the cost equations given (and derived) above belong to a monopolist. d) What quantity will the monopolist produce? We know the monopolist chooses the quantity where MR = MC. To find this quantity we first need to derive MR from the market demand equation. Recall that the MR curve has the same vertical intercept as demand but slope that is twice as steep. Since demand can be expressed: 100 ,P q= − marginal revenue is: 100 2 .MR q= − Set MR = MC: 100 2 8 2 23.Mq q q− = + ⇒ = e) What price will the monopolist charge? The monopolist will charge the max. price consumers would pay for 23 units. This is given by the demand curve. Plug q = 23 into the demand curve to find: 100 23 $77.MP = − = f) What is the monopolist’s economic profit? The monopolist’s economic profit is TR – TC. 77 23 1771.TR= × = 28 23 23 400 184 529 400 1113.TC = × + + = + + = Economic Profit is therefore: 1771 1113 658.π= − =g) What is the monopolist’s producer surplus? Producer surplus is the area above the MC curve and below the market price. Here we can see this can be broken down into two parts. Area of top part: (77 54) 23 529.− × = Area of bottom part: 1(54 8) 23 529.2− × = So producer surplus is: 529 + 529 = 1058. Now consider a monopolist in a different market with costs: 2, 2 .TC q MC q= = Suppose market demand is given by: 100 .P q= − h) Give the formulas for: fixed cost: FC = 0, (All of TC depends on the quantity of output.) variable cost: 2VC q= (All of TC is variable cost.) average total cost: 2.TC qATC qq q= = = average variable cost: 2.VC qAVC qq q= = = i) What quantity will this firm produce? The firm will choose the quantity such that MR = MC. Using the market demand equation we can derive: 100 2 .MR q= − Set MR = MC: 100 2 2 25.Mq q q− = ⇒ =j) What price will consumers face in this market? The firm chooses the highest possible price (given by the demand equation). 100 25 $75.MP = − = k) Calculate the monopolist’s economic profit. First find: 25 75 1875.TR= × = 225 625.TC = = So profit is: 1875 625 1250.π= − = l) Calculate the monopolist’s producer surplus. Producer surplus is the area above the MC curve and below the market price. Here we can see this can be broken down into two parts. Area of top part: (75 50) 25 625.− × = Area of bottom part: 1(50) 25 625.2× = So producer surplus is: 625 + 625 = 1250. m) Looking back over this problem, under what conditions is a firm’s economic profit = producer surplus? In the special case that a firm has no fixed costs, economic profit = producer surplus.Problem Two A representative firm has an average total cost curve that is described by the equation: 10010.9qATCq= + + The firm’s marginal costs equation is: 210 .9MC q= + Market demand is given by: 125 .2Q P= − a) Sketch ATC, MC, MR (you need to derive this), and the market demand curve. Hint: to draw ATC you may want to plot points then connect the dots. Assume that the firm perceives that the market demand curve is the demand curve for the product they are producing. First derive MR using the fact that demand can be written: 50 2P q= − so 50 4 .MR q= − b) Suppose the representative firm is an unregulated monopolist. What quantity will they produce and what price will they charge? A monopolist chooses the quantity that equates MR and MC. To find this quantity set 250 4 109MR MC q q= ⇒ − = + and solve for 9.47.Mq = To find the price, plug 9.47Mq = into the demand equation: 50 2 9.47 $31.06.MP = − × = c) Is the monopolist’s chosen level of output allocatively efficient? Explain your answer. No. The marginal cost of the last unit is: 210 9.47 12.10.9MC = + × = This is less than the price. So, for the last unit produced, price > marginal cost. If more of the good were produced / consumed, surplus would increase (deadweight loss would decrease).d) Is there any way to regulate the firm to achieve allocative efficiency in the long run without government intervention beyond price regulation? Why or why not? No. Recall the concept of marginal cost pricing: the firm is


View Full Document

UW-Madison ECON 101 - Answers to Homework

Documents in this Course
Exam 1

Exam 1

8 pages

Exam 1

Exam 1

8 pages

Load more
Download Answers to Homework
Our administrator received your request to download this document. We will send you the file to your email shortly.
Loading Unlocking...
Login

Join to view Answers to Homework and access 3M+ class-specific study document.

or
We will never post anything without your permission.
Don't have an account?
Sign Up

Join to view Answers to Homework 2 2 and access 3M+ class-specific study document.

or

By creating an account you agree to our Privacy Policy and Terms Of Use

Already a member?