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Problem Set #2 - Noor - Fall 2019 Problem Set #2 – UN 1105 – Noor – Fall 2019 1 UN 1105: Principles of Economics Problem Set #2 – October 3 Fall 2019 Waseem Noor (section 3) Problem Set Guidelines • You will receive 4 assigned problem sets through the semester and together they account for 15% of your grade. This problem set is due at the beginning of lecture on Thursday, October 10. No late assignments will be accepted. • A physical copy of the problem set should be handed in at the beginning of class. Please staple the physical copy if there are multiple pages and put your name and UNI on all the pages. • In addition, a scanned PDF copy of the problem set should be uploaded by 10a on Thursday, October 10 before the lecture. Be sure to scan all the pages, not just the first page. The system will close at 10am and will not accept submissions after that time. Problem sets will be returned during your recitation session. • Students can work on problem sets in groups of maximum three people, but each student should write up his/her own solution, and list all the names of the people in a group. • TA’s will read and grade all the problems sets, so please write legibly. All graphs should have units and axes clearly labelled. If they cannot read the answers they will not be able to give you credit. • It goes without saying that copying your solutions from others is considered cheating and will be sanctioned. (please read Columbia’s policy on academic integrity at https://www.college.columbia.edu/academics/academicintegrity ). Solutions to the problem sets will be discussed during recitations. Problem Set #2 – UN 1105 – Noor – Fall 2019 2 1) Silvio runs a pastry shop. The following table shows the total number of cupcakes produced as a function of the number of workers put into making them. Number of Workers Cupcakes 0 0 1 10 2 25 3 35 4 44 5 52 6 58 7 62 8 63 9 62 a) Graph Silvio’s cupcake production function against number of workers. b) What happens to the marginal product of labor as the amount of labor input increases? c) What happens to the marginal product of labor after 8 workers are hired? Why does this happen? 2) Chengzhi is running a firm in a competitive market. The firm always makes the choice to maximize its profit. The figure below shows cost curves for the firm. The x-axis is quantity of output. a) If the market price is $3.25, how much does Chengzhi choose to produce? What are her total revenues, total costs and profits? Draw the total revenue, total cost and profit on a separate graph. b) If the market price of the product is $3.25, what is her fixed cost? Indicate how you calculate the amount. Would the fixed cost change if the market price changes to $1.75? c) If the market price is $1.50 how much would she produce? If the price drops further should she continue to produce? If the price increases to $1.75 should she continue to produce? d) Draw out the short run supply curve for Chengzhi’s firm. Problem Set #2 – UN 1105 – Noor – Fall 2019 3 3) Omer is running a firm in a competitive market. The firm always makes the choice to maximize profits. The figure below shows the marginal cost (circles) and the average variable cost (crosses) of his firm. At a price of $1700, the AVC and MC are the same. a) Draw out the short run supply curve for Omer’s firm. b) If the market price of the product is $5,000, what is the firm's producer surplus? If the market price of the product is $3,400, what is the firm's producer surplus? If the market price is $1,700 what is the firm’s producer surplus? c) Is producer surplus same as profit? Explain. 4) Raquel runs a perfectly competitive firm selling cupcakes. Her firm has the following cost functions: Total cost: TC(q) = $10,000 + $100q + $10q2, Marginal cost: MC(q) = $100 + $20q, where q is the number of cupcakes a) What is the Average Total Cost, Average Fixed Costs and Average Variable Cost functions? Draw out the three curves along with the marginal cost curve on one graph. b) If Raquel’s firm faces a market price of $900 per unit, how much will she produce at the profit maximizing point? c) In the short run, what are profits and producer surplus at the profit maximizing level of output? 5) Jean- Baptiste makes homemade pastries. His fixed input in the short run is the mixer. In the long run, he can choose a spatula, hand mixer, or a stand mixer. The following table shows the short-run fixed cost (FC) and variable cost (VC) of weekly production using each different level of the capital input. Output of pastries FC ($) spatula mixer VC ($) spatula mixer FC ($) hand mixer VC ($) hand mixer FC ($) stand mixer VC ($) stand mixer 10 5 40 30 20 200 5 20 5 80 30 40 200 10 50 5 200 30 100 200 25 100 5 400 30 200 200 50 200 5 800 30 400 200 100 500 5 2000 30 1000 200 250 Problem Set #2 – UN 1105 – Noor – Fall 2019 4 a) If Jean-Baptiste makes 10 pastries per week, which type of capital input (spatula mixer, hand mixer or stand mixer) should he choose? If he wants to make 100 pastries per week, which level of capital input should he choose? If he wants to make 500 pastries per week? b) Draw out the short-run average total cost curve for a spatula mixer. On the same graph draw out the average total cost curve for a hand mixer and stand mixer. c) What does the long-run average total cost curve look like for Jean-Baptiste’s firm? 6) Suppose the market for Columbia sweatshirts is competitive and has ten buyers and ten sellers. The following table shows the reservation values for both buyers and sellers. Buyer Reservation Value of Buyer ($) or Willingness to Pay Seller Reservation Value of Seller ($) or Willingness to Accept Aaron 15 Kelly 1 Bob 14 Lina 2 Cain 13 Max 4 Dana 12 Newt 6 Eve 11 Oliver 8 Flora 10 Pete 10 Gordon 9 Quinn 12 Harry 8 Ray 14 Ibrahim 7 Sue 16 Jordan 6 Tory 18 a) What is the equilibrium quantity of sweatshirts bought/ sold? At what equilibrium price? Which individuals are indifferent between trading and not-trading? b) At the equilibrium price and quantity, what is the amount of producer surplus? What is consumer surplus? What is social surplus? c) Is the equilibrium outcome pareto efficient? Explain why or why not. Does it maximize social surplus? Explain why or why not. d) Suppose the equilibrium price in the market is $10, but the market is constrained so only 2 sweatshirts are allowed to be sold. What is social surplus in this scenario? Is this pareto efficient? Why or why not? e) Suppose a price floor of $12 is imposed on this market, which does not allow the price of sweatshirts to drop below $12. How many sweatshirts will be sold and what is the new social surplus? Is this pareto efficient? Why or why not? 7) Lupita and Nazim live in a small town. The figure on the left below shows the demand for fuel by Lupita and Nazim during ordinary times. Assume that Lupita and Nazim are the only consumers. In the figure on the right, D0 is the market demand, and S0 is the supply in ordinary times in the town. Problem Set #2 – UN 1105 – Noor – Fall 2019 5 a) How is the market demand function (D0) generated? b) A hurricane hits the town. The acute need for fuel to operate electric generators pushes the demand for fuel to D1. Meanwhile, the supply plummets to S1 because some of the fuel storage tanks owned by the town seller have been damaged by the storm. This occurrence pushes the price up to $5 per liter where only Lupita can afford some fuel. Is this a pareto efficient equilibrium? Why or why not? Is this an equitable outcome? Why or why not? c) Nazim complains to the town council of price gouging by the fuel sellers. In response, an anti- price-gouging law is immediately passed that puts the price ceiling at $1.75 per liter. What will likely happen next? d) Suppose that fuel sellers outside the affected area have a cost of production such that MC = ATC at $2.50 per liter, which includes the cost of transporting the fuel under hazardous conditions. Suppose that the price-gouging law was never enacted, and the price was $5 per liter. What will the presence of outside fuel sellers do to the price? Why? Is this equilibrium pareto efficient? Is it equitable? 8) Assume that the market demand for slices of chocolate cake is given by QD = 650 − 25P and the market supply of chocolate cake is given by QS = 200 + 20P. a) What is the market equilibrium price for slices of chocolate cake? b) Marcello wants to sell chocolate cake. He has a marginal cost curve of MC(q) = 2 + ½ q where q is the number of slices of chocolate cake produced by Marcello. What is his marginal revenue for each slice of cake? How many slices of chocolate cake will Marcello make given the equilibrium price? c) Marcello’s Fixed Cost in order to set up the business is $40. His variable costs are VC(q)= 2q+ ¼ q2. Draw out