Queen s University Department of Economics ECON 111*S

Transcription

1 Queen s University Department of Economics ECON 111*S Suggested Solutions to Take-Home Midterm Examination May 25, 2006 Instructor: Sharif F. Khan Page 1 of 9 Pages

2 PART A TRUE/FALSE/UNCERTAIN QUESTIONS 20 Marks Explain why each of the following statements is TRUE, FALSE, or Uncertain according to economic principles. Use diagrams where appropriate. Unsupported answers will receive no marks. It is the explanation that is important. A-1. A frost that kills half of the Colombian coffee bean crop will increase the equilibrium price and quantity in the market for tea. TRUE A frost that kills half of the Columbian coffee bean crop will decrease the supply of coffee. This decrease in coffee supply is shown as a leftward shift in the coffee supply curve from S1 to S2 in Figure 1. Consequently, the equilibrium price will increase from P1 to P2 and the equilibrium quantity will decrease from Q1 to Q2 in the coffee market, which is illustrated in Figure 1. Since tea and coffee are substitute goods, the increase in the price of coffee will cause people to substitute coffee for tea. In other words, the demand for tea will increase. This increase in tea demand is shown as a rightward shift in tea demand curve from D1 to D2 in Figure 2. Consequently, the equilibrium price will increase from P1 to P2 and the equilibrium quantity will increase from Q1 to Q2 in the coffee market, which is shown in Figure 2. PPp Figure 1: Coffee Market Figure 2: Tea Market Page 2 of 9 Pages

3 A-2. Price floors lead to excess supply. UNCERTAIN A price floor, which is the minimum permissible price that can be charged for a particular good or service, does not always lead to excess supply. Only if the price floor level is set above the free-market equilibrium price, it will cause a surplus. Figure 3 shows the case of an effective price floor where price floor is set at P 1, which is higher than the freemarket equilibrium price P 0. At P 1, there is an excess supply of good, which puts downward pressure on price. But due the legal restriction, price cannot fall below P 1. Consequently, the market price will remain at P 1 with a surplus as shown in Figure 3. Figure 3: An Effective Price Floor However, if a price floor level is set at or below the equilibrium price, the policy will not be effective because the free-market equilibrium remains attainable. In this case, the price will be equal to the market-clearing price and there will not be any surplus or shortage. Figure 4 shows the case where the price floor is set below the free-market equilibrium price. At this price floor there is an excess demand, which puts upward pressure on price. Eventually price will move to the free-market equilibrium price P 0 at which Q 0 amount of quantities will be sold in the market with no excess supply or shortage. Page 3 of 9 Pages

4 Figure 4: An Ineffective Price Floor A-3. A household will save more when the interest rate increases. UNCERTAIN Whether a household will save more depends on the actual magnitude of the substitution and income effect of an increase in the interest rate (assuming that both present consumption and future consumption are normal goods). If the substitution effect is weaker than the income effect, a household will choose to save less. However, if the substitution effect is stronger than the income effect, a household will choose to save more. See page Part III-46 and Figure S2-3 of the Course Notes for a detailed graphical explanation. Page 4 of 9 Pages

5 A-4. The following table shows how many units of bread or steel can be produced with a unit of resources in Canada and U.S. We can conclude that Canada will export steel and U.S. will export bread, if both countries trade based on the principle of comparative advantage. Units of Bread or Steel Produced Per Unit of Resources Bread Steel Canada 4 loaves 2 tons U.S. 5 loaves 10 tons False The following table shows the opportunity costs of bread and steel in Canada and the U.S.: Bread Steel Canada ½ tons of steel 2 loaves of bread U.S. 2 tons of steel ½ loaves of bread Canada has a comparative advantage in bread because it has lower opportunity costs of bread (1/2 tons of steel) than the U.S. (2 tons of steel). On the other hand, the U.S. has a comparative advantage in Steel because it can produce steel with lower opportunity costs (1/2 loaves of bread) compared to Canada (2 tons of steel). Therefore, based on the principle of comparative advantage, Canada should export bread and the U.S. should export steel in a mutually beneficial trade. Page 5 of 9 Pages

6 PART B Problem Solving Question 20 Marks Read each part of the question very carefully. Answer all parts of the question and show all steps of your calculations to get full marks. Use diagrams where required. B-1. Consider the following demand and supply relationships in the market for a product: Demand: Supply: Q d = 500 5P Q s = 15P a) Calculate the equilibrium price and quantity in this market. Illustrate your results using a diagram. Clearly identify the vertical and horizontal intercepts of the demand and supply curve, and the market equilibrium values on the diagram. [ 5 marks] To find the vertical intercept (P-intercept) of the supply curve, set Q s = 0 in the supply function, 0=15P or, P=0 To find the horizontal intercept (Q-intercept) of the supply curve, set P = 0 in the supply function, Q s =15*0 or, Q s =0 To find the vertical intercept (P-intercept) of the demand curve, set Q d = 0 in the demand function, 0=500-5P or, 5P=500 or, P = 100 To find the horizontal intercept (Q-intercept) of the demand curve, set P = 0 in the demand function, Q d =500-5*0 or, Q d =500 The equilibrium price must satisfy the following condition: Q d = Q s or, 500 5P= 15P or, 500 = 20P or, P = 25 So, the equilibrium price is 25. Page 6 of 9 Pages

7 To solve for the equilibrium quantity, set = 25 into the demand or supply function, Q d = 500-5*25 = 375 Q s = 15(25) = 375 So, the equilibrium quantity is 375. Figure 5 illustrates the market equilibrium. Figure 5: The Market Equilibrium b) At the market equilibrium, calculate the price elasticities of both demand and supply. [ 5 marks] Using the arc elasticity method, the price elasticity of demand or supply can be calculated by the following formula: Q1 Qo ( Po + P1 ) / 2 η = x P1 Po ( Qo + Q1 ) / 2 where Q o, Q 1, P o, and P 1 are quantities and prices around the equilibrium quantity and price. Page 7 of 9 Pages

8 For the price elasticity of demand, choose P 0 = 24 and P 1 = 26 so that the average of the P 0 and P 1 is equal to the equilibrium price of 25. Substitute these values of P into the demand function to obtain Q 0 and Q 1 : Q 0 = 500 5(24) = 380 Q 1 = 500 5(26) = 370 η D ( ) / 2 10 = x = x ( ) / = 0.33 So, at the equilibrium the price elasticity of demand is To calculate the price elasticity of supply, substitute P 0 = 24 and P 1 = 26 into the supply function in order to first find Q 0 and Q 1. Q 0 = 15(24) = 360 Q 1 = 15(26) = 390 η S ( ) / 2 30 = x = x ( ) / = 1 So, at the equilibrium the price elasticity of supply is 1. c) Now suppose that the demand curve for the same product is given by Qd = Pand the market supply curve remains unchanged from part (a). What are the new equilibrium price and quantity in this market? Illustrate your results on the diagram drawn for part (a). Clearly identify the vertical and horizontal intercepts of the new demand curve, and the new market equilibrium values on the diagram. [ 5 marks] To find the vertical intercept (P-intercept) of the new demand curve, set Q d = 0 in the new demand function, 0=1000-5P or, 5P=1000 or, P = 200 To find the horizontal intercept (Q-intercept) of the new demand curve, set P = 0 in the new demand function, Q d =1000-5*0 or, Q d =1000 Page 8 of 9 Pages

9 To solve for the new equilibrium price, set the new Q d equal to the initial Q s : P = 15P or, 1000 = 20P or, 50 = P So, the new equilibrium price is 25. To solve for the new equilibrium quantity, set = 25 into the new demand or initial supply function, Q d = *50 = 750 Q s = 15(50) = 750 So, the new equilibrium quantity is 750. Figure 5 illustrates the new market equilibrium. d) Which of the following events are consistent with the changes in the market mentioned in part (c)? Explain why those events are consistent. [5 marks] i) An increase in consumer income. ii) An increase in input prices. iii) A decrease in the price of a complementary good. iv) A decrease in the price of substitute good. v) A decrease in technology. The new demand curve in part (c) shows that there is an increase in market demand. Events (i) and (iii) are consistent with this change in market. i) An increase in consumer income. Assuming that the price of the product is constant, an increase in consumer income leads to an increase in consumer real income or purchasing power. Assuming that the product is a normal good, the consumers will buy more of that product to maximize their utilities. As a result, the market demand of that product will increase which will, in turn, cause a rightward shift in the market demand curve. iii) A decrease in the price of a complementary good. A decrease in the price of a complementary good (for example, coffee mate) of the product in question (for example, coffee) will increase the quantity demanded of the complementary good (coffee mate). To consume higher amount of coffee mate consumers will need to also buy higher amount of coffee. So, each consumer s demand for coffee will increase. As a result, the market demand for coffee will increase, which will, in effect, cause a rightward shift in the market demand curve of the product (coffee). Page 9 of 9 Pages