Question 4 (20 minutes) The province wishes to improve our environment and accordingly will subsidise your municipality $ 2 for every $1 you spend on sewage facilities up to a maximum of $ 1920. Your income is $ 1,200. The price of sewage facilities (Y) is $ 12 and the price of non-sewage facilities (X) is $ 4. Carefully draw the new budget line labelling all points of interest. Sewage facilities (Y) 300 280 230 260 165 240 180 220 200 180 160 50 140 100 120 100 200 80 40 20 0 20 10 60 80 100 120 140 160 180 200 220 240 260 280 300 Non-sewage facilities (X)'1 \\ / At what point, are relative prices unaffected? Give the co-ordinates " v1 0 Y and C9 3 X (i.e. at what point do you obtain the maximum grant) How much better off are you with the conditional grant? g g, U}? ___I S [ I Q l f / o o ] v s o I g a What is the amount of the conditional grant? i / 9 O O M 5; ISOunihog 361 P3 all i xl'oo = 1100 3 With an unconditional grant of the same dollar amount, how much better off would you be compared to the conditional grant? IS, Lab): (f) At the current levels of employment of factors K and L, MPK = 30 and MPL = 15. Given that the price of K is $20 and the price of L is $ 5, the firm should use more capital even though capital is more expensive. MERS = MPL 15 The firm should K MPK 30 reduce the use of PL _ 5 capital and use more PK = 20 labour since MPL > PL MP K PK True or false false MPLS MPK (g) If there are increasing returns to scale and pecuniary diseconomies, then the slope of the long run average cost curve can be upward or downward sloping. AC CA IRS P D indeterminate LRAC Qty. True or false True (h) The greater the extent to which two factors are substitutable, the lesser the convexity of the isoquant. K if factors are perfectly substitutable , there is Constant MITRS ( no convexity ) True or false rue +(1) With cartels the greater the difference between price and average cost the greater the incentive to cheat. Price mc Me greater Po inclusive to cheat is greater difference bi P& MC P > MC Qty. True or false False (m) If the price is below my average cost, I should shut down in the long run but not necessarily in the short run. Price MC ATC AVC PSo Qty. True or false True(d) The long run average cost curve is U shaped because up to a certain point you have excess K/ L and thereafter excess L/ K. K LRAC Truce, because efficiency decreases 12 K due to increased labour in the 6 Acn. MPL Quantity True or false True (e) The long run expansion path for a firm must be horizontal. K In S. R we cannot make changes in K. 40 so it is horizontal in SR 20 But in L. R. we can change k, not horizontal in LR True or false false (e With a typical production function, diminishing MP is reached before the diminishing average product. TP at A, diminishing MP at b, diminishing AP a Qty. of input MP AP a Qty. of input b True/ False_ There C MP Diminishing\f(15 minutes) Question 6 Suppose in a perfectly competitive industry, the typical firm has a long run total cost curve expressed by: (1) TCi = 6qi -4qi2+ q3 where qi is the firm's output. AC MC S LRAC Price 2- Firm Qty . Industry Qty. Q - 800 What output will the firm produce in the long run? 2 What is the firm's long run per unit cost? $ 2 What is the optimal size for the firm? 9 = 2 Assuming free entry and exit for this industry and if the industry market demand curve is given by Px = 4002 - 5 Qx What will be the long run equilibrium, specifically (i) industry price $ 2 ii) industry output 800 (iii) number of firms in the industry 400 Industry output 1800 Firm output 2(20 minutes) Question 3 In St. Catharines there are three restaurants, A, B and C with the attributes and prices given below. Illustrate the efficiency(attribute) frontier. Which restaurant(s) will you as a consumer with $ 100 income select? Assume the restaurant meals are totally divisible and that you can attend more than one. Brand Attributes per meal Price # of [Cuisine, Decor] per meal meals Art's (A) [5,1] $20.00 5 25 6 5 D Bob's (B) [2,2] $10.00 10 206 20 D Cindy's (C) [ 1,71 $25.00 28D Cuisine 360 28 26 24 22 20 18 16 14 12 10 AA Bal scale 2 6 8 10 12 14 16 18 20 22 24 26 28 2 30 Decor(15 minutes) Question 5 Pottsville Dress Corporation which was designed to produce 50 dresses using 120 capital and 180 labour. The price of capital (K) is $10 and the price of labour is $10. Suppose the price of labour increases to $30. In the long run the company has two choices, reduce output or maintain output. Illustrate the long run adjustment if the budget is maintained. Next illustrate the long run adjustment if the output is maintained at 50 units. For both options what is the new cost of producing a dress compared to the original cost? Capital 300 280 20 260 240 55 220 50 200 180 160 140 120 100 80 60 40 20 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300 Labour MAiz - Ahmedlestion 8 Mc = $ 20 + Q centralized cartel consisting of two firms has an industry demand of P = 220 - 2Q. TR = 2209 - 2Q2 he firms have identical cost curves given by TCi = 20qi + qi2. MR - 220 - 4Q AC P mci = 20+ 29 MC . 2 /2 Typical firm Industry 1) What is the cartel's profit maximizing output? MR = MC 2 20 - 40 = 20 + 0 200 3 50 40 = 8 2) What is the cartel's profit maximizing price? P = 220 - 40(2) P= 140 1 3) The cartel allocates the output to two members. What is the individual firm's profit? TRi = Piqi = 140 x 20 - [ 20(20) +2027 Thi 4) If the cartel broke down and the firms competed, what would their price be? when P= MC Answers: 220 - 28 = 20+ 8 30 - 20 8 5 202 = 662/3 NW 5 3Question 7 The bridge linking the island of Pottsville to Texas is a monopoly bridge owned by Pottsville Bridge Corporation. The hourly demand and total cost given by the following: P = 100 - 2.0 Q TR = PQ = 1008 - 282 MR = 100 - 4Q TC= 40 Q MC = 40 where P is the price (that is the toll charged) and Q is the number of cars crossing. 1) What price (i.e. toll) would maximize the monopolist's profits? To maximize MR = MC Price Profit 100 - 48 = 40 Mc = 40 100 - 40 = 49 P 100- 20 60 = Q MR Q = 15 P= 100- 28 = 100- 2(15) Qty P = 70 $4 70 (3 marks) 2) How many bridge crossings would be purchased? That is, what is the profit- maximizing output? 15 (2 marks) 3) What are the monopolist's profits at this price? $ 450 (2 marks) Profit = TR- TC = PQ - 409 = 70 x 15 - 40x 15 = 450 4) The government wishes to regulate the price that is charged. At what level should the price be set to achieve the same number of bridge crossings as would be the case under perfect competition? P-MO $ 40 (3 marks) 10 0 - 20 = 40 100 - 40 = 29 100 - 2(30 ) Q = 30 P = 40 5) What will be the number of bridge crossings at the regulated price? 30 (3 marks) 6) What are the monopolist's profits in this situation? 0 _(2 marks) Profit = TR - TC excess profits = 30X40 - 40 ( 30 ) O(i) If an American and Canadian firm use the same technology to produce 10 cars but the Canadian firm uses a higher capital to labour ratio, capital must be more expensive in the US. K high Low 20 cars True US L True or false can (j) If the total product of labour is given by TPL = 48L + 9L2 -L3 and the price of the product produced is $ 10, the maximum wage I would be willing to pay for 4 labour would be $ 260. MPL MPC = STP c = 48 + 181 - 3L2 = 48 + 18 ( 4 ) - 3 ( 4 ) 2 48+ 72 - 48 72 - 72 W = VMPc 1 = 4 = 10(72 ) = $720 willing True or false false 3 MPC to pay (k) At R, the producer is getting less value per dollar from capital (K) than from labour (L). at R M P L > PL K MP K PK R MPL MPk PL P k getting less $value S from k True or falseQuestion 2 (15 minutes) Assuming decreasing returns to scale, illustrate the long run average cost curve under the following factor price conditions. Carefully explain your answer. For the cost curves which have the same slope (either negative or positive) explain why the slopes are different. Neither pecuniary economies or diseconomies, that is, all firms pay the same for inputs AC (A) 13.1 1 CD - upward sloping Qty b Pecuniary economies, that is, larger firms pay less for their inputs. AC OCA DCD : COLA inderterminate t Qty C Pecuniary diseconomies, that is, larger firms pay more for their inputs. AC 2 CD upward sloping ( 2 ) CD steeper than a. QtyB ar and C Selected restaurant(s) 4. 5 and 2 5 Number of meals from each restaurant B C = 45 meals x 10 2. 2 X 2 1 0 = $45 100- 45 =$55 25 2:2 meals B If you could only select one restaurant which would it be? B Because It is on a highle indifference wive ". gives the most well being What would restaurant B have to lower its price to for you to select only it? $ 9.08 Why? we need B 22 C attributes Price 2 BuShould 100 = $9.09 meal 3 /1 meals be 9. 08. or was to select only it? What percentage amount would restaurant B have to improve both their food and cuisine for you 22 - 20 x 100 = 1010 % 20(40 minutes) Question 1 - 12 True/ False and explain (a) If my total utility increases at an increasing rate, I must be addicted to the product. TU TV should start to decrease after a certain point, but if it does not , then the consumer isa Qty addicted True or false The (b) Given the diagram below, good X is an economic bad. Y It is an economic good 100 120 because the moufference cause increased from 100 60 . 120 X True or false False (c) Consumers are more health conscious today than they were 20 years ago. Therefore the 2021 indifference curve is flatter now than twenty years ago. Junk food If healthres, willing to give up more junk to get I more realtury food becomes AX steeper 2000 2021 Healthy food True or false falseOriginal cost of a dress $ 60 TC 120 ( 10 ) + 180 ( 10 ) Q = 3000 50 New cost of a dress if continue with your original budget $ 150 origual Budget = 3000 30 0 0 K 1. 10 2 0 130 producing 300 10 0 [ 207 If the firm wishes to maintain its output, what will be the new cost of a dress in the short run and in the long run? (a) New cost of a dress, after the price increase of labour, if there is not enough time to Point change K, that is in the short-run. 1= 180 $ 132 K = 12 0 T C = P KK + PL G = 10 ( 120 ) + 30 ( 180 ) = 6600 50 (b) New cost of a dress, after the price increase of labour, if there is enough time to change all inputs (long-run) $ 126 Point F TC = PKK + PIL 1 = 150 = 1 10 ( 180) + 30 (.150 ) 1 =180 = 1800+ 1500 = 6300 50I = $/200 Py = $12 PX = $4 grant $2 1 1 at J value 1200 + 1920 = 3120 3 260 12 120D If$1200 spent in non sewage 8 x = 120%% = 300 300 sopatent ano fostoe von bien max amount to spend 1920 on y to ger max 960 grow spent on non sewages 1200 - 960 (x ) Su ytho bol 8x = 240 60 at J , spent grant y val 960 + 1920 2880 240 12 1 2 Xval 1200 - 960 60 4 12DO+ 19 20 3120