Final Exam Study Guide
Final Exam Study Guide ECON 1011
Popular in Principles of Economics I
Popular in Economcs
One Day of Notes
verified elite notetaker
verified elite notetaker
verified elite notetaker
Alice Wei Tian
verified elite notetaker
verified elite notetaker
verified elite notetaker
This 22 page Study Guide was uploaded by SophieSol on Thursday December 10, 2015. The Study Guide belongs to ECON 1011 at George Washington University taught by Yezer, A in Fall 2015. Since its upload, it has received 281 views. For similar materials see Principles of Economics I in Economcs at George Washington University.
Reviews for Final Exam Study Guide
Report this Material
What is Karma?
Karma is the currency of StudySoup.
You can buy or earn more Karma at anytime and redeem it for class notes, study guides, flashcards, and more!
Date Created: 12/10/15
8 PPF’s —Linear 1. Bo Peep has a 20 acre ranch and 8 employees. She can produce 30 pounds of lamb chops per acre or 50 pounds of pork chops per acre. Draw Peep’s PPF. Given this PPF, what is Peep’s opportunity cost of pork chops? If lamb chops are $6 per pound and pork chops are $3 per pound, what will Peep produce? a. Write the production function equations a. Do this by thinking what two things constitute the whole. So she gets 30lbs lamb chops/acre. This means that if you multiply 30 by the amount of acres you have designated to lamb chops, you will get the total amount of lamb chops. Therefore: b. L = 30AL c. We do the same thing for pork chops: she gets 50lbs pork chops/acre and multiplying 50 by the amount of land assigned to pork chops would give us the total amount of pork chops. So… d. P = 50AP b. We need to determine the total amount of acreage for both lamb chops and pork chops, or in other words, we need to combine these functions into an equation. Note that the two letters that the production functions have in common are “A,” which indicate that Acres is what we start with. So, a. A = A L A P b. We need to isolate the L and APvariables in the production functions in order to plug them in. i. L = 30A L A L L/30 ii. P = 50AP AP P/50 c. Now to plug and chug! a. A = L/30 + P/50 b. But A is equal to 20 acres (see problem question) so: i. 20 = L/30 + P/50 d. If we decide that lamb chops will be the independent variable (x- axis) and that pork chops will be the dependent variable (y-axis) then we isolate the variable P, as though it is “y” in a “y = mx + 1,00 b” equation. Note that it doesn’t matter which variable plays the role of “y” or “x,” unless we are told in the question which to 0900 put on which axis. a. P = 1,000 – 5/3 L our PPF 800 i. We can graph this with the mindset of 1,000 being the y-intercept and -5/3 being the slope 700 600 Pork 500 400 Chops 300 200 100 100200300400 500600700 Lamb Chops e. You can find the opportunity cost by looking at the absolute value of the slope in the equation of the variable you are looking for. It is 5/3 L, so if you want to find the opportunity cost of one lamb chop, you look for the slope with “L” and know that it is 5/3 pork chops. To get the opportunity cost of the other variable, you take the reciprocal. So the opportunity cost of one pork chop would be 3/5 lamb chop. f. When there is a question about money, you automatically know to find the equations for the iso-revenue lines. Revenue is R, so we know that we have a total “R” comprised of revenue from lamb chops and revenue from pork chops. We get $6/lb of lamb chops and 3$/lb of pork chops. So, a. R = 6R L 3R P b. Because P is our “y-variable,” we solve for P and get i. RP= R/3 – 2RL 1. What always confused me with this was that there is not really a “y-intercept,” because of the R. What I had to learn was to only look at the slope, which is 2. In a linear PPF, the iso- revenue lines will intersect at one of the two corner points of the graph, so start at the y- 1,200 intercept of the PPF line and draw a new line using the slope of the iso-revenue line. The 1,100 one that is the furthest away from the origin is what gives us our answer. 1,00 0900 800 700 Furthest out iso- 600 500 revenue line. This Pork tells us that she will Chops 400 produce 600 lbs of 300 Lamb Chops and 0 200 pork chops 100 100 200 300 400 500 600 700 Lamb Chops 2. Original Growth Lumber makes wood products out of large trees growing on 10,000 acres of mountain land. Original Growth can turn 1 tree into 50 studs (stud is 8 foot long and 2” by 4”) or 75 boards (boards are ¾ inch thick). Flatlands Forest Products uses smaller trees grown on a 20,000acre tree farm and can turn 1 tree into 20 studs or 40 boards. Assuming each producer can process 30 trees per day: Find the equations of the PPF’s for OGL and FFP and plot the PPF’s. What is OGL’s opportunity cost of studs? What is FFP’s opportunity cost of studs? Which has the lower opportunity cost of studs? Which has a comparative advantage in producing studs? a. OGL: a. Studs per tree: S = 50TS S/50 = TS b. Boards are B = 75TB B/75 = TB c. Total trees per day = 30 = T = TS + TG d. Substitution: T = 30 = S/50 + B/75 i. Solve for S: S = 1500 – (2/3)B. ii. This is the PPF equation e. Plot the PPF with S on the vertical axis f. The slope is –(2/3) so the opportunity cost of a board at OGL is 2/3 of a stud. The B intercept is 30 (75) boards per tree = 2,250 boards/day. b. FFP: a. S = 20TS S/20 = TS b. B = 40TB B/40 = TB c. Total trees per day = 30 = T = TS + TG. d. Substitution: T = 30 = S/20 + B/40 i. Solve for S: S = 600 – (1/2)B ii. This is the PPF equation e. The slope is –(1/2) so the opportunity cost of a board is ½ of a stud and the B intercept is 1,200 boards/day. c. OGL has an absolute advantage in production because than can make more of both studs and boards than FFP. d. Comparative advantage depends on opportunity cost of studs which comes from the slope of the PPF. At OGL they take 30 trees and produce either 1, 500 studs or 2,250 boards per day. At FFP they use 30 trees and produce either 600 studs or 1,200 boards. a. Opportunity cost of boards at OGL is (2/3) of a stud b. Opportunity cost of boards at FFP is (1/2) stud. i. Clearly boards cost less at FFP and hence FFP has a comparative advantage in board production! PPF’s —Non-Linear 7a. Figure 1 shows the PPF 90 for Neptune Boats which can 80 produce either sailboats (S) or 70 powerboats (P). Assume that 60 sailboats sell for $100,000 50 and that powerboats sell for 40 $50,000 each. Neptune maximizes 30 revenue by producing 55 20 sailboats, 65 powerboats 10 and earning $8,750,000 0 in total revenue. 0 10 20 30 40 50 60 70 80 90 100 110 120 Powerboats The slope of the isorevenue line ispowerboasailboat 50,000/100,000 = (1/2) Isorevenue lines with this slope are shown by the dashed lines on the figure. Tangency between the PPF and isorevenue line with slope = 1\2 occurs when 65 powerboats and 55 sailboats are produced. Total revenue = 65 (50,000) + 55 (100,000) = 3,250,000 + 5,500,000 = $8,750,000 Supply and Demand 1. The demand for doughnuts in Flabtown is given by: Q = 4,000 - 5DP where P is the price in cents and Q is doDghnuts demanded per day. If the current price 40 cents, how many doughnuts will be sold? What is total expenditure? a. Substitute 40 for P and find: Q = 4,000 – 50(40) = 4,000 – 2,000 = 2,000. Total expenditure = price x quantity and hence PQ = 2,000 (40 cents) = 80,000 cents = $800. If the price rises to 60 cents, how many doughnuts will be sold? What is expenditure? b. Substitute 60 for P and find: Q = 4,000 – 50(60) = 4,000 – 3,000 = 1,000. Total expenditure = price x quantity and hence PQ = 1,000 (60 cents) = 60,000 cents = $600. Assume the supply of doughnuts to Flabtown is given by Q = -2000 + S 100P; Q iS doughnuts supplied and P is price in cents/donut. Find the market-clearing price and quantity. c. Set Q S Q D d. -2,000 + 100P = 4,000 – 50P i. Adding 2,000 to each side and adding 50P from both sides of the equation gives: 150P = 6,000, or P = 6,000/150 = 40 cents per doughnut. e. Market clearing price: 40 cents f. Market clearing quantity: 2,000 Assume a price ceiling at 30 cents per doughnut. What would you observe in the market? g. Substitute 30 cents into both supply and demand functions. i. Q D 4,000 – 50(30) = 4,000 – 1,500 = 3,500 ii. Q S -2,000 + 100 (30) = -2,000 + 3,000 = 1,000 h. A price ceiling at 30 cents per doughnut should produce excess demand. i. 1,000 doughnuts will be produced and sold. The excess demand is 2,500 doughnuts 2. The short run market demand curve for apples in Appletown is given by: A = 2,000 500AP where A is pounds of apples purchased per day anA P is the apple price in dollars. What is the “choke price” of apples? If apples are provided “free” how many pounds will be consumed daily? a. To find the choke price from a demand curve, set quantity = 0 and solve for P b. In this case set A = 2,000 500 P = 0, and P = 2,00/500 = 4 $/pound is the A A choke price. c. Apple consumption when “free” is found by setting A = 0 and solving for A which means: A = 2,000 500 P = 2,000 500(0) = 2,000. A The short run market supply curve for apples in Appletown is A = 1,000 + 1,0A0 P . Note the supply curve is only defined in the first quadrant (i.e. for values of A ≥ 0.) What is the short run market clearing price of apples in Appletown? How many pounds of apples will be sold per day? 1. Set short run quantity demanded equal to short run quantity supplied: a. A = 2,000 500 P = 1,000 + 1,000 P A A i. This implies that 1,500AP = 3,000 orAP = 3,000/1,500 = $2 per pound. ii. Substitute into either demand or supply to get quantity: A = 2,000 500(2) = 1,000 pounds of apples per day. Now impose a price ceiling of $2.50 per pound on apples. How many pounds of apples will be sold per day? a. The market clearing price is $2. Therefore a price ceiling of $2.50 has no effect Own Price Elasticity 1. The own price elasticity of demand for doughnuts is 2. Due to failure of the wheat crop (there is some wheat in doughnuts) the price of doughnuts rises by 30%. You then expect doughnut consumption to change by ____% and revenue to change by about______% a. E = %∆Q/%∆P. b. Substitute for E and %∆P and solve for %∆Q as follows: c. 2 = %∆Q/+30% or %∆Q = 60%. d. %∆R ≈ %∆P + %∆Q = + 30% + ( 60%) = 30% 2. When the price of doughnuts fell by 20%, total revenue from doughnut sales fell 10%. This implies that the quantity of doughnuts changed by ___% and that the own price elasticity of demand for doughnuts is ____. a. %∆R ≈ %∆P + %∆Q = ( 20%) + %∆Q = 10% or %∆Q = + 10% b. E = %∆Q/%∆P c. Substitute for %∆P and %∆Q d. Solve for E: e. % = 10%/ 20% = 0.5 3. Price rose by 10% but total revenue fell 10%. Is this possible? What does this imply for the own price elasticity of demand? a. %∆R ≈ %∆P + %∆Q = 10% = (10%) + %∆Q or %∆Q = 20% b. You know own price elasticity = E = %∆Q/%∆P c. Substitute for %∆P and %∆Q d. Solve for E: % = 20%/ 10% = 2 4. When the price of “J phones” fell from $250 to $150, the number of J phones sold per month rose from 5,000 to 15,000. What does this suggest about the own price elasticity of demand for J phones? a. E = [(Q – Q )/(Q + Q )/2]/[(P – P )/(P + P )/2] = [(15,000 – 2 1 2 1 2 1 2 1 5,000)/(15,000 + 5,000)/2]/[(150 – 250)/(150 + 250)/2] = [(10,000)/(10,000)]/[(-100)/(200)] = /[-1/2] = -2.0 and demand is quite elastic. Marginal Utility and Marginal Product 1. Jack shops at Tracy’s and purchases 12 cups for $4 each and 4 dishes for $12 each. At the same time, Jill shops at Sacks and purchases 8 dishes for $12 each and 4 cups for $6 each. If Jack and Jill are neighbors and happen to meet, what, if any, exchange might they consider? a. Jack: a. MU /MC = D /P C D b. 4/12 = 1/3 b. Jill: a. MU /MC = D /P C D b. 6/12 = ½ c. Jack values cups at 0.33 dishes and Jill values cups at 0.5 dishes d. Jill’s cups are worth more than Jack’s e. Jill will be willing to send Jack up to 3 dishes f. Jack values 6 dishes at 9 cups so he has a gain from trade of 3 cups. 2. Yizhi uses land, labor, and tractors to grow corn. Currently, the annual rental price of land is $500/acre, annual wages for farm workers are $8,000, and annual rent per tractor is $1,000. If the marginal products of land, labor, and tractors are: MP LAND= 2,000, MP LABOR= 24,000, and MP TRACTORS= 2,000 bushels of corn per year. Is he minimizing the cost of producing given output? Assuming that Yizhi is a price taker in both factor and product markets, how might he adjust her input mix? a. MC = $/MP i. MC Land= $500/2,000= $0.25 ii. MC Labor $8,000/24,000 = $0.33 iii. MC Tractors$1,000/2,000 = $0.50. Land is the cheapest and tractors are the most expensive, so Yizhi should hire more land and get fewer tractors Adding Horizontally 1. Assume that Big BMI is a town with 1000 high income households and 1000 low income households. The weekly demand for doughnuts by the typical high income household is given by DH = 20 10 P whereHD is number demanded per high income household per week and P is the price of doughnuts in dollars per doughnut. The low income household demand for doughnuts per week is L = 10 5 P. Plot these demand curves on a graph and add them horizontally to get the market demand for doughnuts in Big BMI. Assume that the supply of doughnuts in Big BMI is given by D = 5,000 + 20,000 P, where D is total doughnut supply and P is price in $/doughnut. Note that, if P = 0.25, D = 0 which means that there is no willingness to supply any doughnuts at prices below $0.33. Plot the supply of doughnuts in Big BMI on the market diagram and find the market clearing price and quantity produced. The find the weekly consumption of doughnuts by the typical high and low income family. Who determines the price, and quantity of doughnuts and the distribution of doughnuts in Big BMI? High Income Household Low Income Household Market in Big BMI $2 S 1.80 1.60 1.40 1.20 1.00 0.80 0.60 0.40 0.20 H L D 0 5 10 15 20 1 2 3 4 5 6 7 8 9 10 11 5000 10000 15000 20000 25000 30000 Doughnuts per week Plot the demand curves of individual high and low income consumers and add horizontally multiplying consumption of the individual by 1000 in each case. Note that the choke price is $2 for both groups so adding horizontally is quite easy. Market demand has a choke price at $2 and at P = 0 market demand is 10 (1000) + 10 (1000) = 30,000. Supply is 0 at price < $0.25 and it is plotted on the market diagram Market clearing price = $1, quantity = 15,000 and this implies that each high income household consumes 10 doughnuts per week, low income households 5 per week. It is possible to add horizontally algebraically by simply multiplying the quantity demanded by each group by the number in that group so market demand is: 1000 [ 20 – 10P ] + 1000 [ 10 – 5P ] = 30,000 15,000 P Equating this to market supply, find the market –clearing price: 30,000 15,000 P = 5000 + 20,000P 35,000 = 35,000 P or P = $1 2. Now assume that 1,000 more high income households move into Big BMI. There is no change in the individual household demand curves but there is a new market demand curve. Find that curve, and determine the new market price, total doughnut sales, and consumption by high and low income households. How have the new arrivals change the welfare of the households who previously lived in Big BMI? Who determined the changes in price, quantity, and the distribution of doughnuts High Income Household Low Income Household Market in Big BMI $2 S 1.80 1.60 1.40 1.20 1.00 0.80 0.60 0.40 0.20 H L D 0 5 10 15 20 1 2 3 4 5 6 7 8 9 10 11 5000 10000 15000 20000 25000 30000 Now add horizontally but multiply individual high income demand by 2000 and get the solid demand curve on the market diagram (the original demand curve is show by dots). Price = $1.22 and sales are about 19,500. Note that the growth in the community has caused a rise in price of doughnuts that makes the initial residents worse off, they consume fewer doughnuts at the higher price of $1.22 rather than $1. It is possible to add horizontally algebraically by simply multiplying the quantity demanded by each group by the number in that group so market demand is: 2000 [ 20 – 10P ] + 1000 [ 10 – 5P ] = 50,000 25,000 P Equating this to market supply, find the market –clearing price: 50,000 25,000 P = 5000 + 20,000P 55,000 = 45,000 P or P = 55,000/45,000 = 11/9 = $1.22 Weird Marshallian Cross Examples In the past, GWU has provided free flu shots for 3 hour periods on a given day, and time to students and faculty at 4 different locations around campus each fall. What would you expect to see at these events? Describe the situation with a Marshallian cross diagram. Let’s say that 2 of these events are held at convenient locations and times and the other two are not. Illustrate this on a Marshallian cross diagram. If GWU charged a fee for the shots, what would change? $/shot S shotsssuming 3 hours of operation) Line Convenient Line Inconvenient D Conveniebnt D Inconvenient We have two demand curves. One is demand of inconvenience and the other is demand of convenience. The convenient curve should be above the inconvenient one (think that when demand increases, the line shifts up or right). If GWU charged a fee for the shots, the lines would be shorter. As the fee rises the lines would disappear Complex Graphs and Example Problems 1. Output of J phones J phones/day Figure 1 and workers at the J phone plant is giv1,000 in Figure 1. Please plot the average and 900 marginal product curves of labor. 800 Find the marginal product of labor 700 Slope = 20 = AP Labor when the number of workers is 600 20, 50, and 80. Assuming that workers500 Slope =12 = AP Labor are paid $300 per day, find the margina400 cost of J phones when the number of 300 Slope = 16 = AP Labor workers is 20, 50, and 80. 200 100 10 20 30 40 50 60 70 80 90 Workers Per Day MP is slope of TP at each number J phones/L Of workers. Slope at 20 = 600/30 = 2026 Slope at 50 = 300/30 = 10 24 Slope at 80 = 100/30 = 3.3 22 Average Product AP is slope of a ray from the origin 20at Shows the ratio Q/L. 18 AP(20) = MP(20) = 20 16 AP(50) = 800/50 = 16 14 Marginal Product AP(80) = 966/80 = 12 12 10 Note that MPLabor actually a series 8 Of “steps” at 20, 10, 3.3 6 MP = AP when labor is ≤ 30 4 Then MP falls to 10 and AP 2 begins to decline slowly 0 10 20 30 40 50 60 70 80 90 2. Now assume that workers are the ONLY input in the production of J phones. Draw the total, average, and marginal cost curves implied by the total product curve above. The wage of labor is $300/worker. Total cost is TC = WL = 300L Total Cost in Hundreds of $ 300 Total Cost 270 Slope = AC = 2700/1000 = 2.7 240 Plot total cost on the vertical axis a210 output on the horizontal axis and you see180 that the total cost curve, in this case with150 only one input is just the total prod120 curve with the axes reversed! We made 90 this point in class. When total product is 60 steep, total cost is shallow because M30 and MC vary inversely! 100 200 300 400 500 600 700 800 900 1,000 $/J-phone J-phones per day 0.35 90 Marginal cost = Wage/MP Labor If the wage = 1, the MC = 1/Labor 75 So when L ≤ 30, MC = 300/20 = 15 When 30 < L ≤ 60, MC=300/10=30 60 MC When L > 60, MC = 300/3.3 = 91 So MC is a step function because MP 45 Is a step function. Whenever MP is constant, MC is constant. 30 AC AC = TC/Q = WL/Q = L/Q and you (when Q ≤ 600, MC=AC=15) See that AC is just the inverse of 15 AP in this case. But in general, AC varies inversely with AP. 0 When L ≤ 30, AC = 300/AP = 15 = MC 100 200 300 400 500 600 700 800 900 1,000 When 30 < L ≤ 60, AC rises because J-phones per day MC > AC, and similarly when 60 < L, AC rises further as shown. $ Figure 1 TS 3. The graph on the right shows the 1000 short and long run total cost curves 900 TC L for Han’s bicycles. Based on these 800 curves, total fixed cost = 250 700 short run average cost is minimized 600 when output = 33 bicycles. Long 500 run average cost is minimized when 400 output = 52 bicycles. 300 Note, AC Linimum = 800/50= 16 200 Note, AC Sinimum = 666/33= 22 100 10 20 30 40 50 3. Using the space provides on Figure 2 Bicycles/day carefully draw the short and long run 35 Figure 2 MC S AC S average and marginal cost curves for 30 AL Han. If she is a price taker 25 And the market price of bicycles = $ 20 20 In the short run, he will produce 31 bicycles 15 In the long run, he will produce 56.bicycles 10 MC L 5 10 20 30 40 Draw AC aL a “happy face” win a minimum at 52. Draw AC tangent So AC at 22 and Lith a minimum at 33. Then MC is drawn through the minimum of AC and MC is drawn cutting L L S MC Lrom below at 22 and through the minimum of AC at 33. Short run output is found by equating P = 20 = MC atSan output of 33 (this just happens to be the minimum of AC ) and lSng run output is found by equating P = 200 = MC at an output of 56. L
Are you sure you want to buy this material for
You're already Subscribed!
Looks like you've already subscribed to StudySoup, you won't need to purchase another subscription to get this material. To access this material simply click 'View Full Document'