Report

ECON 100 Tutorial: Week 5 www.lancaster.ac.uk/postgrad/murphys4/ [email protected] office: LUMS C85 Outline • Question 6 – 15 min. • Question 7 – 15 min. • Past Exam Multiple Choice questions - 15 min. • Suggested solutions for other questions will be included/added to slides so you can check your own answers. Tutorial 5 Worksheet Questions and Corresponding Textbook Page #’s • • • • • • • Question 1: pgs. 268 Question 2: pgs. 269-270 Question 3: pg. 270; Figure 13.2 Question 4: pgs. 275-276; Figure 13.4 Question 5: pgs. 269-271; Figure 13.2 Question 6: pgs. 271-275 Essay Question: pgs. 278-280 Question 1 Distinguish between the short run and the long run in production In the short run, fixed costs are fixed. In the long run, fixed costs can change or become variable. Question 2 Why does marginal product decline as total product increases? Diminishing marginal product is the result of diminishing marginal returns to the inputs of production. Question 3 Explain the relationship between the production function and the total cost curve. Use diagrams to help illustrate your answer and explain why the curves are shaped as they are. (See figure 13.2 for a detailed discussion) Question 3 Question 3 Question 3 Explain the relationship between the production function and the total cost curve. Use diagrams to help illustrate your answer and explain why the curves are shaped as they are. So the production function curve gets flatter while the cost curve gets steeper, but both because of diminishing marginal returns as Q increases. Question 4 Why does the marginal cost curve cut the average cost curve at its lowest point? • When MC < ATC, ∆ATC < 0 – When the cost of one more unit is below the average cost, it drags the average down • When MC > ATC, ∆ATC > 0 – When the cost of one more unit is above the average cost, it pulls the average up • As a result, MC = ATC at the minimum of ATC Question 5(a) Complete the following table. It describes the production and cost of hamburgers at a roadside stand. All figures are measured per hour. = Labor (L) = Quantity (Q) = Change in Output = Fixed Cost (FC) = (Q2 – Q1)/(L2-L1) = Variable Cost = TC (VC) = FC+VC Question 5(a) ctd. =Q =(Q2-Q1)/(L2-L1) =FC =VC =FC + VC 25+0= (6-0)/(1-0)= 25+5= (11-6)/(2-1)= 25+10= 15-11= 25+15= 18-15= 25+20= 20-18= 25+25= Question 5(b) Plot the production function. • Slope of the production function is the marginal product of labour (the change in output that results from a change in one unit of input) • MPL is diminishing and the slope of the production function gets flatter as a greater number of inputs are used Question 5(c) What happens to the marginal product of labour as more workers are added to the production facility? Why? It diminishes because additional workers have to share the production equipment and the work area becomes more crowded. Use this information about the marginal product of labour to explain the slope of the production function you plotted above. The slope of the production function is the change in output from a change of one unit of input, which is the marginal product of labour. Since it is diminishing, the slope of the production function gets flatter as a greater number of inputs are used. Question 5(d) & 5(e) d) Plot the total-cost curve. e) Explain the shape of the total cost curve. • The Total Cost curve begins at €25, due to Fixed Costs • As output increases, the curve gets steeper due to diminishing marginal product of labour Some useful equations for Q6 Total Cost TC = FC + VC Average Fixed Cost AFC = FC / Q Average Variable Cost FC (fixed cost) VC (variable cost) TC (total cost) AFC (average fixed cost) AVC (average variable cost) ATC (average total cost) MC (marginal cost) AVC = VC / Q Average Total Cost ATC = TC / Q or ATC = AFC + AVC Marginal Cost MC = (TC2 – TC1)/(Q2-Q1) Question 6 The information below is for Bastien’s blue jeans manufacturing plant. All data is per hour. Note the following abbreviations: FC (fixed cost), VC (variable cost), TC (total cost), AFC (average fixed cost), AVC (average variable cost), ATC (average total cost), MC (marginal cost). Question 6 Question 6(a) Plot AFC, AVC, ATC, and MC. Question 6(b) Explain the shape of each of the curves in part (a) • AFC ↓ as Q↑ • MC ↓ for the first four units, due to increasing marginal product of the variable input. • MC ↑ after the first four units, due to decreasing marginal product (MC is U-shaped) • AVC is U-shaped for the same reasons as MC • ATC ↑ at higher levels of production due to decreasing marginal product • At lower levels of production, ATC ↓ because AFC ↓ and because of increasing marginal product Question 6(c) Explain the relationship between ATC and MC. • When MC < ATC, ∆ATC < 0 – When the cost of one more unit is below the average cost, it drags the average down • When MC > ATC, ∆ATC > 0 – When the cost of one more unit is above the average cost, it pulls the average up • As a result, MC = ATC at the minimum of ATC Question 6(d) & 6(e) Explain the relationship between ATC, AFC, and AVC. ATC = AFC + AVC (also, ATC = TC / Q) Question 6(e) What is Bastien’s efficient scale? How do you find the efficient scale? Efficient scale is the quantity (output) that minimizes ATC. It is where MC = ATC. Why is the efficient scale important? For a firm that is a price-taker, ATR (Average Total Revenue) is fixed as Q varies, or we can say, ATR = P. If Average Profit = ATR – ATC and ATR is fixed at P, then in order for a firm to maximize profit, the must minimize ATC. So the efficient scale is the amount of output that a price-taking firm will produce. Question 7(a) Suppose utility depends on income (M) and the consumption of food (F) such that U=M+F and suppose that the price of a unit of money is £1 and the price of a unit of food is also £1. Imagine that income is £10. How much food is bought? What is the utility level of the household? HINT: Substitute the budget constraint M=10-F into the utility function then find the slope of this function (using the simple rule) and then solve for the value of F that makes the slope of U zero. Question 7(a) There are two ways we can approach this problem. We have a utility function: U=M+F Where M is money and F is food and the price of a unit of money and the price of a unit of food are both £1. Income is £10. We need to find how much food is bought and what is the utility level of the household. HINT: Substitute the budget constraint M=10-F into the utility function then find the slope of this function (using the simple rule) and then solve for the value of F that makes the slope of U zero. This is a standard constrained optimization problem. To solve it, we will take our budget constraint, M=10-F, and plug it in to the utility function, U=M+F, then take the derivative of that and set it equal to zero and solve for F. Step 1: plug in M=10-F into U=M+F U=10-F+F 1 = −1 + 2 Step 2: Set this equal to zero and solve for F. 0 = −1 + 1= 1 2 1 F = 2 1 F= 4 1 2 We solved for F, how much food is bought, now 1 we need to find the level of utility when F = . 4 Note, Utility is a function of both M and F (U=M+F), so we need to find M before we are able to solve for U. 1 4 To solve for M, we plug F= into the budget constraint: M=10-F M = 10 M = 9.75 1 4 1 4 Now, we have F= and M = 9.75 So, we can plug these in to the Utility function: U = M+F 1 4 U = 9.75 + U = 9.75 + U = 10.25 1 2 Question 7(b) Suppose the government is concerned with the poor nutrition of households with such low levels of income. It decides to give a voucher for 1 unit of food to such households. What happens to the amount of food that such a household will consume? And utility? In this scenario, the consumption of F rises to F + 1 (the amount of money spent on F) + (1 unit of F from the voucher) That changes our utility function from U = M+F to U=M+ +1 The budget constraint remains unchanged, because there is no change to our initial endowment or income of £10. So, the budget constraint is M=10-F. This is the same type of problem as in part (a), so we’ll use the same methods. We will take our budget constraint, M=10-F, plug it in to the new utility function, U = M + + 1. then take the derivative of that and set it equal to zero and solve for F. Step 1: plug in M=10-F into U = M + + 1 U=10-F+ + 1 1 = −1 + 2 +1 Step 2: Set this equal to zero and solve for F. 0 = −1 + 1= +1= 1 2 1 2 +1 F+1= 3 1 2 +1 1 4 F=4 This indicates to us, that given this consumer’s utility function and budget constraint, they would prefer to sell the £1 Food voucher and continue consuming at F=1/4. In this problem, we are supposed to assume that the vouchers cannot be sold, which limits us to a corner solution where the consumer spends all of their income on M (M= 10) and none of their income on Food (F = 0) and that they then only consume 1 unit of food, which they get from the £1 food voucher. Now, if we have F= 0 and M = 10 We can plug these in to the Utility function: U=M+ +1 U = 10 + 0 + 1 U = 10 + 1 U = 11 Question 7(c) Suppose the government gives £1 instead of a £1 food voucher. In this scenario, The amount of F does not change, but rather M is increased by £1. So, M=£11. Our budget constraint now becomes 11 = M + F The utility function is still U = M+F. We use the same methods as in parts (a) and (b), 1 and should find that F = , M = 10.75 and U = 11.25 4 Question 7(d) Draw a picture of what the above shows. What important principle does this show? a) When we have an income of £10, U = 9.75. b) When we receive a £1 non-transferrable food voucher in addition to our £10 income, U = 11. c) When we receive £1 in cash in addition to our £10 income, U = 11.75. So, this suggests that based on this particular utility function, we get a higher utility from cash than from a food voucher (in-kind transfer). Question 8 Scherer (Journal of Economic Literature 2001) tells the story of a famous German music publisher – Hartel – who calculated the cost of printing music (using engraved plates – it was 1796) and used his analysis to determine his production decisions. Hartel figures that fixed costs of a page, F, was 900 pfennigs. And the marginal cost of printing subsequent copies of the same page was 5 p. In those days music publishers bought compositions, did their own printing, and sold to the public. People bought the latest music to play themselves - there were no ipods (or even “gramophones”). The publishers had to decide on what price to charge the public. Some useful equations for Q6 Q8 Total Cost TC = FC + VC Average Fixed Cost AFC = FC / Q Average Variable Cost FC (fixed cost) VC (variable cost) TC (total cost) AFC (average fixed cost) AVC (average variable cost) ATC (average total cost) MC (marginal cost) AVC = VC / Q Average Total Cost ATC = TC / Q or ATC = AFC + AVC Marginal Cost MC = (TC2 – TC1)/(Q2-Q1) Question 8 Hartel figures that fixed costs of a page, F, was 900 pfennigs. And the marginal cost of printing subsequent copies of the same page was 5 p. From this statement, we know that: FC = 900 and MC = 5 In this case, because MC is constant, AVC = MC = 5. Part (a) says to graph TC, ATC, AVC, and MC; we can find equations for each of these, which can then be graphed by plotting points. Because AVC = VC/Q, then VC = AVC(Q), so VC = 5Q We know that TC = FC + VC, so we can find our total cost: TC = 900 + 5Q Average total cost (ATC) is TC/Q: ATC = 900/Q + 5 AVC is MC Question 8(b) Would it make sense for a composer to award a printing contract to just one firm, or to use more than one? Why? Answer: Since MC and AVC is constant, ATC falls with Q indefinitely, just like AFC. So it makes sense to use just one publisher no matter how many (or few) copies you think you might sell rather than having two publishers paying the fixed costs. Question 8(c) Hartel thought he could sell 300 copies of a good piece of music for about 15p per page. What is the most he would have been prepared to pay a good composer – per page? Answer: This changes our cost function. Our new cost function equals our old cost function plus the cost paid to the composer. Let the cost paid per page be w, so: TC = 5Q + 900 + wQ In a competitive market: Profit = 0 So, TR - TC = 0 TR = 15Q so, 15Q – (5Q + 900 + wQ) = 0 If Q = 300, 15(300) – (5(300) + 900 + w(300)) = 0 So, 4500 – (1500 + 900 + 300w) = 0 Or, 4500 – 2400 – 300w = 0 Hence, 2100 = 300w And, w=7 Past Exam Essay Question (2011) Show how short and long run cost curves (total, average and marginal) can be derived from a firm’s production function (where output depends on just two inputs). What properties would we expect those cost functions to have? If this firm operated in a competitive industry how would its output respond to an increase in demand? Next Week • Exam 1 is next Friday. – 20 Questions from Caroline – 10 Questions from Ian – You will have 50 minutes, starting at either 4 or 5 pm. • We will do more practice Multiple Choice Questions during tutorial • Tutorial 6 Worksheet on Moodle Practice Multiple Choice Questions Please note: Tutors are not given “solutions” to past exams. The answers in my slides are suggestions only. Note: to view suggested answers, you will need to either click on the animations tab or view in slideshow mode. Practice Multiple Choice Questions All of the following shift the supply curve of a good to the right except a) an advance in the technology used to manufacture the good. b) an increase in the price of the good c) a decrease in the wage of workers employed to manufacture the good. d) subsidizing workers employed to manufacture the good Practice Multiple Choice Questions, ctd. If the quantity of available housing in the UK is less than the quantity of houses demanded, then UK house prices: (a) Will not change. (b) Will fall, thus clearing the market. (c) Will rise, thus clearing the market. (d) Will either fall or remain unchanged. Practice Multiple Choice Questions, ctd. With an inferior good, a price change: (a) Leads to opposing income and substitution effects (b) Creates a large income effect (c) Produces a large substitution effect (d) Leads to conspicuous consumption Practice Multiple Choice Questions, ctd. Which one of the following statements regarding indifference curves is correct? • (a) Indifference curves are normally drawn as concave to the origin. • (b) The further to the left an indifference curve lies, the more total utility it yields to the consumer. • (c) Indifference curves normally slope downwards from right to left. • (d) None of the above Practice Multiple Choice Questions, ctd. When goods X and Y are being consumed, a consumer is in equilibrium when: • (a) The marginal rate of substitution equals the slope of the isocost curve • (b) MUx/MUy = Py/Px • (c) The indifference curve touches the budget line • (d) All of the above Practice Multiple Choice Questions, ctd. • 10. According to the law of diminishing marginal utility, the additional satisfaction that you get from consuming beer decreases: • (a) As the price of beer falls • (b) As you get older • (c) As your income rises and you can substitute beer with whiskey • (d) With every additional unit of beer that you consume Practice Multiple Choice Questions, ctd. Which one of the following would shift the demand curve of a normal good to the right? a) An increase in the price of that good. b) A decrease in the price of that good c) A fall in income d) A decrease in the price of a complement to the good Practice Multiple Choice Questions, ctd. If an increase in consumer incomes leads to a decrease in the demand for a good, then it must be the case that the good is: a) a normal good b) an inferior good c) a complementary good d) a substitute good Practice Multiple Choice Questions, ctd. • 6. If the price of a good is above the equilibrium price, • a) there is a surplus and the price will rise. • b) there is a shortage and the price will fall. • c) there is a shortage and the price will rise. • d) there is a surplus and the price will fall Practice Multiple Choice Questions, ctd. • 7. An increase (rightward shift) in the demand for a good (whose supply curve is upward sloping) will tend to cause • a) an increase in the equilibrium price and quantity. • b) an increase in the equilibrium price and a decrease in the equilibrium quantity. • c) a decrease in the equilibrium price and an increase in the equilibrium quantity. • d) a decrease in the equilibrium price and quantity. Practice Multiple Choice Questions, ctd. The price of a good increases by 10% and the quantity demanded falls by 20%. This indicates that demand is a) elastic b) inelastic c) unit elasticity Δ d) perfectly elastic Practice Multiple Choice Questions, ctd. 16. The shut down condition for a perfectly competitive firm in the long run is: a) Average total costs are greater than marginal costs b) Average variable costs are greater than marginal costs c) Average total costs are less than marginal costs d) Average variable costs are less than marginal costs Practice Multiple Choice Questions, ctd. • 1. When goods X and Y are being consumed, a consumer is in equilibrium when: • (a) The marginal rate of substitution equals the slope of the isocost curve • (b) MUx/MUy = Py/Px • (c) The indifference curve touches the budget line • (d) All of the above Practice Multiple Choice Questions, ctd. When two goods are complements of each other: (a) The cross price elasticity of demand is negative (b) The cross price elasticity of demand equals zero (c) The cross price elasticity of demand is positive (d) The cross price elasticity of demand may be either positive or negative Practice Multiple Choice Questions, ctd. All the following will cause the demand curve to shift to the left except: (a) A reduction in income if the good is normal (b) An increase in the price of a complementary good (c) An increase in the price of a substitute good (d) An increase in income if the good is inferior Practice Multiple Choice Questions, ctd. If the price elasticity of demand for bubblegum is 2.0 and bubblegum prices increase by 15 percent. The quantity demanded changes by: (a) (b) (c) (d) 15 percent 20 percent 3 percent None of the above 30 percent Practice Multiple Choice Questions, ctd. • 9. Considering any linear downward sloping demand curve, lower prices along the demand curve are associated with: • (a) Lower absolute price elasticities • (b) Lower quantities demanded • (c) Different points of unit elasticity • (d) Higher absolute price elasticities