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# AEC 3113 - Exam 1 AEC 3113

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This 13 page Study Guide was uploaded by Kate Martin on Sunday September 11, 2016. The Study Guide belongs to AEC 3113 at Mississippi State University taught by Dr. Randall Little in Spring 2016. Since its upload, it has received 2 views.

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Date Created: 09/11/16

EXAM I AEC 3113 – Introduction to Quantitative Economics September 22, 2015 Name: ___________________ 1. (12 points) Draw the demand and supply curves of a market for orange juice in equilibrium. Assume there is a hard freeze in South Florida. Show the expected effect of the freeze on the juice market on your graph. Explain the effect in the marketplace. 2. Assume a market for some good in which demand and supply are given by these functions, respectively: QD= 240 – 2.0P Q S -12 + 10.0P a. (6 points) Calculate the market clearing price and quantity, assuming the market operates without constraint. Illustrate graphically. 2 b. (4 points) Assume the government imposes a price floor of $25 per unit. Calculate the market response to this policy. Illustrate graphically. c. (4 points) Now assume the government imposes a price ceiling of $20 per unit. Calculate the market response to this policy. Illustrate graphically. d. (6 points) Derive the inverse demand and supply functions for this market. 3 3. (10 points) Using the supply and demand functions from Question 2, assume per unit tax of $21 is imposed on sellers. Calculate the effect of this tax. What is the incidence of this tax (how is it shared between producers and consumers)? What is the tax revenue generated? Illustrate graphically any effects of imposing this tax. 4. Given the following functions Total Cost: TC = 8,000 + 150Q – 20Q + 2.0Q 3 Price: P = 1,000 – 1.5Q a. (7 points) Derive: Total Revenue: Average Revenue: Fixed Cost: 4 Variable Cost: Average Total Cost: Average Variable Cost: Average Fixed Cost: b. (6 points) Derive and simplify this firm’s profit function. 5. A firm has the marginal cost function, MC = 0.25Q – 5Q + 30 and the marginal revenue function, MR = 100 – 0.5Q a. (9 points) At what output level does this firm maximize its profit? 5 b. (6 points) Explain the economic logic underlying the decision rule used in part a. 6. (10 points) Assume that you have $10,000 to invest today in a fund that earns 8 percent annual interest, compounded continuously. Suppose your goal is to have $100,000 in your account. How long will it take your account to grow to your target amount, if principal and interest are left untouched? 7. (10 points) A firm estimates its annual fixed costs are $300,000. It estimates its average variable costs are $40 per unit produced and sold. The market price for the good this firm produces is $80 per unit. How many items must the firm sell to breakeven? Given a target annual profit of $240,000, use Cost-Volume-Profit analysis to derive the number of units the firm must sell MONTHLY to meet its annual target, assuming sales are distributed uniformly throughout the year. 6 8. (10 points) Assume markets for two related goods are given by: For Good 1: Q D-G1= 240 – 2PG1– PG2 QS-G1= 12 + 10PG1 For Good 2: Q D-G2= 300 – PG2– 2PG1 QS-G2= -10 + 2PG2 Find the equilibrium prices and quantities in each market, for Goods 1 and 2. EXAM I AEC 3113 – Introduction to Quantitative Economics February 20, 2014 Name: ___________________ 1. (10 points) Draw the demand and supply curves of a market in equilibrium. Assume a decrease in demand – show that on your graph. List and discuss key changes that might cause such a shift. Explain the effect in the marketplace of such the shift have depicted. 2. Assume a market for some good in which demand and supply are given by these functions, respectively: QD= 810 – 2.0P Q S -90 + 10.0P a. (6 points) Calculate the market clearing price and quantity, assuming the market operates without constraint. Illustrate graphically. 2 b. (4 points) Assume the government imposes a price floor of $72 per unit. Calculate the market response to this policy. Illustrate graphically. c. (4 points) Now assume the government imposes a price ceiling of $68 per unit. Calculate the market response to this policy. Illustrate graphically. d. (4 points) Derive the inverse demand and supply functions for this market. 3 3. (10 points) Using the supply and demand functions from Question 2, assume per unit tax of $30 is imposed on sellers. Calculate the effect of this tax. What is the incidence of this tax (how is it shared between producers and consumers)? What is the tax revenue generated? Illustrate graphically any effects of imposing this tax. 4. Suppose your firm uses two inputs, X and Z, to produce output Y. Suppose also that you have $2,500 to spend each production period on some combination of inputs X and Z. Suppose also that input X costs $20 each time while input Z costs $50 per unit. a. (6 points) Formulate your firm’s budget constraint. Express your constraint as an equation for a straight line (clearly specify which input is the dependent variable and which is the independent variable). 4 b. (3 points) Illustrate the budget line graphically. c. (3 points) On your graph, clearly illustrate the effect of a $200.00 increase in your firm’s operating capital. d. (3 points) Assuming the original budget, suppose the price per unit of input X increases from $20 per unit to $25 per unit. Clearly illustrate the effect of this on your budget line. 5. (6 points) Completely specify the line that goes through the points (40,20) and (20,80). Identify an economic application of such a line. 0.45 0.5 6. Using the Cobb-Douglas production function, Y = f(X,Z) = 21X Z , a. (4 points) Express the natural logarithm of this production function. 5 b. (6 points) Derive the associated isoquant equation. 7. A firm has the marginal cost function, MC = 0.15Q – Q + 50 2 and the average cost function, AVC = 0.05Q – 0.5Q + 50 a. (4 points) What is the minimum supply price for this firm in the short run? b. (2 points) How much will this firm produce at that price? c. (3 points) Explain the economic logic underlying the decision rule used in part a. 6 8. (4 points) Assume that you have $15,000 to invest today in a fund that earns interest at an 8.5% annual rate, compounded continuously. What will your investment have grown to after 25 years? 9. (8 points) A firm estimates its annual fixed costs are $500,000. It estimates its average variable costs at $50 per unit produced and sold. The market price for the good this firm produces is $90.00 per unit. Given a target annual profit of $250,000, use Cost-Volume-Profit analysis to derive the number of units the firm must sell its target, assuming sales are distributed uniformly throughout the year. How many items must the firm sell to breakeven? 7 10. (10 points) Assume markets for two related goods are given by: For Good 1: Q D-G1= 4,500 – 2PG1– 2PG2 QS-G1= -20 + 5PG1 For Good 2: Q = 2,500 – 2P – P Q = -40 + 4P D-G2 G2 G1 S-G2 G2 Find the equilibrium prices and quantities in each market, for Goods 1 and 2.

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