Label the section where the total demand is the same as one demand and where total demand is different from both individual demand curves.
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1 UVic Econ 103C with Peter Bell Technical Practice Exam #1 Markets Assigned: Monday May 12. Due: 5PM Friday May 23. Please submit a computer and/or handwritten response to each question. Please submit your work by or our dropbox by the Economics department office 3 rd floor BEC. Please list collaborators. Section 1: Aggregation Given demand curves for two individuals: Q D,1 =10-P, Q D,2 =50-P. (1) Solve the total demand curve. Q D = _ for P, Q D = _ for P. (2) Solve the inverse demand curve. P D = _ for Q, P D = _ for Q. (3) Show the following three curves together on one diagram: Q D,1, Q D,2, Q D. Label the section where the total demand is the same as one demand and where total demand is different from both individual demand curves. Repeat with algebraic formulas. Given: Q D,1 =a 1 b 1 P, Q D,2 = a 2 b 2 P; suppose that a 2 >a 1, b 2 >b 1, a 1 /b 1 >a 2 /b 2. (4) Solve the total demand curve. Q D = _ for P, Q D = _ for P. (5) Show the two individual demand curves together on one diagram: Q D,1, Q D,2. Label key points. (6) Show the following two curves together on one diagram: Q D,1, Q D. Label the breakpoints where the slope of the total demand curve changes and explain the shift. Given two supply curves: Q S,1 =ap, Q S,2 =bp + e. Suppose that a, b, e > 0. (7) Solve the total supply curve. Q S = _ for P, Q S = _ for P. (8) Solve the inverse total supply P S = _ for Q, P S = _ for Q. (9) What does e represent for a business? (10) Show the following three curves together on one diagram: Q S,1, Q S,2, Q S. Label some of the key points. Peter Bell, 2014 Page 1 of 5
2 Suppose there are two supply curves as follows. 0 for 0 P < 5 Q S,1 = { 1 for 5 P < 10 2 for 10 P 0 for 0 P < 3 and Q S,2 = { 1 for 3 P < 12 2 for 12 P (11) Solve the total supply curve in a table and graph. (12) Fill in the blanks for the table. P Q S,1 Q S,2 Q S 0 Section 2: Clearing Markets Suppose you are given demand and supply curves: Q D =100-P, Q S =5P. (13) Solve the equilibrium price and quantity. (14) Calculate the Consumer Surplus (CS) and Producer Surplus (PS) at equilibrium. (15) Fill in the blanks for the integrals for the CS and PS. CS = ( ) dp = ( ) dq PS = ( ) dp = ( ) dq Suppose you are given demand and supply curves: Q D =100 e -P, Q S =P 2. (16) Show the demand and supply on a graph (for P in [0,10] with step size equal to 0.01). (17) Solve the equilibrium price and quantity, such that quantity demand and supply are within 0.05 units of each other. Report the equilibrium price to two decimal points (nearest 0.01 units) and quantity to one decimal point (nearest 0.1 units). Suppose you are given demand and supply curves: Q D =a+bp, Q S =c+dp. (18) Solve the equilibrium price and quantity. (19) Under what conditions for (a,b,c,d) is this a reasonable model of a market? Show the demand and supply on a graph. (20) Fill in the blanks for the integrals for the CS and PS. CS = ( ) dp = ( ) dq PS = ( ) dp = ( ) dq Peter Bell, 2014 Page 2 of 5
3 Section 3: Basic Policies (21) Please show the following on a graph: continuous linear demand and supply curves, equilibrium price and quantity, CS and PS. This is the classic example of a microeconomic model. Suppose the quantity is forced to be below the equilibrium level: 0 < Q < Q. You can use Diagram A below as a template, but please create a separate diagram for each question for clarity. (22) Suppose the market clears this quantity at the demand curve. Create a diagram to show the clearing price (P ), CS, and PS under this assumption. (23) Denote the demand curve as Q D (P), inverse-supply curve as P S (Q), and price where demand equals zero as P 0 (Q D (P 0 )=0). Fill in the blanks for the specific integrals below when the market clears the demand curve. CS = ( ) dp, and PS = ( ) dq (24) Create a diagram to show what happens when the market clears this quantity at the supply curve. Label the price (P ), CS, and PS under this assumption. (25) Fill in the table below using the letters from Diagram A. Market clears at CS PS TS Demand curve Supply Curve (26) Discuss who receives economic rents in each case, based on the table above. Under what conditions would a black market develop? Suppose the price is forced to be below the equilibrium level: 0 < P < P. You can use Diagram B below as a template, but please create a separate diagram for each question for clarity. (27) Suppose the market clears the price at the demand curve. Create a diagram and label the quantity (Q ), CS, and PS under this assumption. (28) Suppose the market clears the price at the supply curve. Create a diagram and label the quantity (Q ), CS, and PS under this assumption. (29) Fill in the table below using the letters from Diagram B. Market clears at CS PS TS Demand curve Supply Curve (30) Discuss the distortions created in each case, based on the table. When would producers incur losses (negative PS)? (31) If the market faces the low price (P ) but the demand and supply curve are each able to do whatever is best for themselves, then what will happen? Will the market clear? Peter Bell, 2014 Page 3 of 5
4 Comment on Grading I will grade each question as 0, 1, or 2. I will assign 0 if you do not try the question or make incorrect statements. I will assign 1 if you try the question but make significant mistakes in content or formatting. I will assign 2 if you correctly address the question in a professional manner. There is a maximum of 62 points on the exam. However, I will calculate your score on the exam as follows. If your score is greater than 50 points, then you get 5% credit for this Practice Exam towards your final grade. If you get less than 50, then you get X/10 towards this portion of your final grade, where X is the number of points you get. Peter Bell, 2014 Page 4 of 5
5 Price A Supply B D C Demand Restricted Supply (Q ) Quantity Diagram A: Market outcomes with restricted supply. Price A B D F C E Restricted Price (P ) Quantity Diagram B: Market outcomes with restricted price. Peter Bell, 2014 Page 5 of 5
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