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# AEC 3113- Exam 2 AEC 3113

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This 9 page Study Guide was uploaded by Kate Martin on Tuesday October 4, 2016. The Study Guide belongs to AEC 3113 at Mississippi State University taught by Dr. Randall Little in Fall 2014. Since its upload, it has received 8 views.

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Date Created: 10/04/16

AEC 3113 EXAM II October 29, 2013 NAME: ______________________ (Show your work.) 1. Given the Total Utility function, U = 44.8Q6 a. (3 points) Find the MU function. b. (4 points) Evaluate each function, U and MU, at Q = 20 and 50. c. (4 points) Evaluate the curvature of this Total Utility function at Q = 20 and Q = 50. 2 3 2. A firm has the total cost function, TC = 800 + 20Q – 5Q + 0.4Q and faces a demand curve given by, P = 110 – 0.5Q a. (4 points) Set up and simplify this firm’s profit function. b. (5 points) Find the output at which this firm maximizes profit. c. (7 points) Calculate Total Revenue, Total Cost, Variable Cost, and Fixed Cost at that output level. d. (2 points) Calculate maximum profit. 3. Assume a firm operates in a perfectly competitive market. Given VC = 0.05y – 1.2y + 12y fixed cost, FC = $250, and output price, p = $25.00 per unit, a. (5 points) Find the profit maximizing output level. b. (4 points) Calculate maximum profit. 4. Using the cost information for the firm operating in a perfectly competitive market from Question 3, 3 2 VC = 0.05y – 1.2y + 12y and fixed cost, FC = $250, a. (5 points) Find the lowest output price this firm would be willing to accept and still produce. b. (4 points) At that price, how much output would this firm produce and sell? How much would its Total Revenue equal? c. (3 points) Calculate its variable costs at that output level. d. (5 points) Explain the economic significance of the price calculated in part a. 5. Suppose that demand in a certain market is given by Q D 1200 – 3P a. (6 points) Calculate the point elasticity of demand at the following prices, P = 100 and P = 250. b. (6 points) Explain a firm’s potential pricing strategy to increase total revenue, based on the elasticity of demand calculated at each price. 6. Given the production function, Y = 2.1x + 2.4x - 0.08x ,3 a. (3 points) Find the average product function. b. (3 points) Find the marginal product function. c. (4 points) At how many units of the variable input is average product maximized? d. (2 points) What does average product equal at its maximum? e. (4 points) At how many units of the variable input is output maximized? f. (2 points) What is the output maximum? 7. Assume a market that, before-tax, is defined by these (inverse) demand and supply functions: Demand: P = 570 – 3Q D Supply: P = –62 + Q S a. (4 points) What is the before-tax equilibrium price and quantity for this market? b. (5 points) Assume implementation of a tax paid by the suppliers in this market. Derive the per unit tax rate that maximizes tax revenue. c. (2 points) What is the total tax revenue, assuming implementat ion of that per unit tax? d. (4 points) Discuss the tax incidence of this tax – how is the burden of the tax shared? Introduction to Quantitative Economics EXAM II “REWRITE” Spring 2015 The Offer: You have the opportunity to “get back” up to one-half of the points you dropped on Exam II. For example, if you got a 60 on the exam, you could get up to 20 points back, giving a total Exam II score of 80 points. The Rules: The following guidelines apply: 1. You must rework the ENTIRE exam to qualify for any points. 2. You must get a given individual problem completely correct to earn back the possible points on that particular problem. Be thorough, use complete sentences, and carefully develop your answers. When solving problems, show your work – set up the problem, then go through the steps to solve. 3. No partial credit on individual problems will be given. 4. Your answers to all discussion questions must be typed. All solutions to the math problems must be neatly printed. Any graphs must be carefully and legibly drawn. Write only on the front of the page. 5. Your Rewrite must be handed in at the beginning of class, THURSDAY, April 16, 2015. No late papers will be accepted. 6. Failure to follow these directions carefully and completely will VOID this offer. DUE DATE: April 16, 2015 AEC 3113 EXAM II April 2, 2015 NAME: ______________________ (Show your work.) 1. Given the TR function, TR = 210Q – 1.5Q 2 a. (4 points) Find the AR and MR functions. b. (4 points) At what output is TR maximized? c. (3 points) Evaluate TR, AR, and MR at the output level derived in b. 2. (6 points) Given the function, y = 27x 0.4, find the first and second derivatives. 3. Assume a firm oper3tes in2a perfectly competitive market. Given VC = 2.4y – 48y + 260y fixed cost, FC = $500, and output price, p = $150, a. (6 points) Find the profit maximizing output level. b. (2 points) Verify your solution is a maximum. c. (5 points) Calculate maximum profit. 4. Assume a firm operates in a perfectly competitive market. Given VC = 2.4y – 48y + 260y fixed cost, FC = $500, a. (5 points) Find the output price below which this firm would be better off shutting down. b. (5 points) At that price, how much output would this firm produce and sell? c. (4 points) Calculate its variable costs and profit at that output level. d. (5 points) Explain the economic significance of the price calculated in part a. 5. Suppose that supply in a certain market is given by P = –20 + 0.5Q S a. (8 points) Calculate the point elasticity of supply at the following: Q = S40 and Q = S 240 b. (4 points) Comment on the type of elasticity of supply in the market at each. 6. Given the production function, y = f(x) = 25x + 4.5x – 0.25x , 3 a. (4 points) Find the average product and marginal product functions. b. (7 points) If it exists, find the input level (x) where the inflection point occurs. Comment on the function’s curvature prior to and beyond the inflection point. c. (8 points) At how many units of the input is average product maximized? Use the second derivative test to verify that your solution is at a maximum. What does average product equal at that input level? What does output equal at that input level? d. (6 points) At how many units of the variable input, x, is yield maximized? Use the second derivative test to verify that your solution is at a maximum. What is the yield maximum? 7. Assume a firm uses 144,000 widgets in its production process each year (12,000 each month). Also assume that the cost of placing an order for widgets is $105.00 per order, regardless of the size of the order, while the cost of holding a widget in inventory is $21.00 per year. a. (6 points) What is the economic order quantity for this firm? b. (3 points) How many orders will it place per year? c. (5 points) What is this firm’s Total Inventory Cost?

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