HE5091 Tutorial 1 Solution

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1 Nanyang Technological University HE5091 Principles of Economics First Semester 2023 Tutorial 1 Question 1 You are taking two courses this semester: Economics and Mathematics. You have two examinations coming up in both classes. The table below shows your grade on each examination for different numbers of hours spent studying for each: Hours of Study Economics Mathematics 0 70 60 1 77 68 2 82 74 3 85 78 Your goal is to maximize your average grade on the two quizzes. Use the idea of optimization in differences to decide how much time you would spend studying for each quiz if you had three hours in total to prepare for the two exams. Note: you can only choose to study in increments of one hour. Guide to Question 1 The key idea of this question is to compare grade points gained from each additional hour of study. Note that maximize average grade is equivalent to maximize total grade. If you had just one hour, you should study Mathematics since you would raise your Mathematics grade by 68 – 60 = 8 points; if instead you studied Economics, you would raise your Economics grade by just 77 – 70 = 7. If you had a second hour, you should study Economics since you would raise your Economics grade by 77 – 70 = 7; if instead you studied Mathematics for a second hour you would raise your Mathematics grade by just 74 – 68 = 6. If you had a third hour, you should study Mathematics since you would raise your Mathematics grade by 74 – 68 = 6; if instead you studied Economics, you would raise your Economics grade by just 82 – 77 = 5. So, you should spend 2 hours in Mathematics and 1 hour in Economics. Hours of Study Economics Mathematics Grade Increase due to 1 more hour of study Grade Increase due to 1 more hour of study 0 70 - 60 - 1 77 7 68 8 2 82 5 74 6 3 85 3 78 4

2 Alternatively, there are 4 potential options to fully spend 3 hours studying for the exams: A. 3 hours in Economics B. 2 hours in Economics & 1 hour in Mathematics C. 1 hour in Economics & 2 hours in Mathematics D. 3 hours in Mathematics We can calculate the total points gained from each option. Option Economics Mathematics Total gain Grade Gain Grade Gain A 85 15 60 0 14 B 82 12 68 8 20 C 77 7 74 14 21 D 70 0 78 18 18 Option C has the largest increase in total grade.

3 Question 2 Explain how shifts in demand and/or supply curves could explain the equilibrium price of houses increases but the equilibrium quantity remains unchanged. You should consider three different situations and support your answers with three suitable diagrams. Guide to Question 2 To maintain a fixed equilibrium quantity, we must either keep the quantity supplied or the quantity demanded constant or create a situation where shifts in both demand and supply impact the price but not the quantity. Accordingly, the three potential situations are: 1. Demand increases with perfectly inelastic supply curve 2. Supply decreases with perfectly inelastic demand curve 3. Simultaneous shift of demand increases and supply decreases of equal magnitude. In the first scenario, the supply is perfect inelasticity, implying that the supplied quantity is fixed regardless of price. Graphically, this is depicted as a vertical supply curve. To induce a price increase, we can achieve this by shifting the demand curve upwards (to the right), indicating an increase in demand. Intuitively, when there is a surge in demand, but the supply remains fixed, buyers become more willing to pay a higher price for the goods. P S P 2 P 1 D 2 D 1 Qe Q This situation is the most probable in reality. Given that construction of buildings takes time, in the short term, the housing supply is considered relatively stable. When there is a surge in housing demand, it leads to an increase in prices. (This is for your information only, not required in solution).

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4 P Q P 2 P 1 Qe D S 1 S 2 P Q P 2 P 1 Qe D 1 D 2 S 2 S 1 In the second scenario, the demand is perfect inelasticity, implying that the demanded quantity is fixed regardless of price. Graphically, this is depicted as a vertical demand curve. To induce a price increase, we can achieve this by shifting the demand curve upwards (to the left), indicating a decrease in demand. Intuitively, when the demand is fixed, but the supply is reduced, sellers can set a higher selling price for the goods. In the third scenario, both demand and supply are not perfectly inelastic. The demand curve slopes downward while the supply curve slopes upward. An increase in demand shifts the demand curve upward (rightward), increases both equilibrium price and quantity. A decrease in supply shifts the demand curve upward (leftward), increases equilibrium price but decreases equilibrium quantity. For a shift of equal magnitude, the increase in equilibrium quantity due to demand surge is countered by the decrease from supply reduction. Thus, the equilibrium price increases but the equilibrium quantity remains unchanged.

5 Question 3 Consider the market for online education. Due to the improvement in education technology, it is easier for education institution to offer courses online. At the same time, due to Covid-19 which results in movement restrictions, there are more people wish to purse studies online. Analyse the effects of these two incidents on the online education market with the help of suitable market diagrams. Guide to Question 3 When an external factor that is not directly related to price and quantity affect either demand or supply, there will be a shift in the demand or supply curve. By an increase in demand/supply, it means that for the same price level, the demanded/supplied quantity is higher. For demand: • An increase in demand shifts the demand curve to right (upward). Both equilibrium price and quantity are higher. • A decrease in demand shifts the demand curve to left (downward). Both equilibrium price and quantity are lower. For supply: • An increase in supply shifts the demand curve to right (downward). Equilibrium price is lower while equilibrium is higher. • A decrease in demand shifts the demand curve to left (upward). Equilibrium price is higher while equilibrium is lower. In this question, the improvement in education technology is an external factor that improves supply while the Covid-19 restriction is an external factor that causes a surge in demand for online education. • An increase in supply reduces price while increases quantity. • An increase in demand increases both supply and demand. Combine the 2 effects, equilibrium quantity is increased while the impact on equilibrium price is unclear. The actual change in price will depend on how the curves are shifted relatively. There are 3 possible outcomes, namely demand shifts more than supply (price increases, quantity increases), supply shifts more than demand (price decreases, quantity increases), and supply and demand shift by the same magnitude (price remains unchanged, quantity increases). Refer to the 3 figures in next page.

6 Demand shifts more than supply: Price S 1 S 2 P 2 P 1 D 2 D 1 Q 1 Q 2 Quantity Supply shifts more than demand: Price S 1 S 2 P 1 P 2 D 2 D 1 Q 1 Q 2 Quantity Both demand and supply are shifted by the same magnitude: Price S 1 S 2 P 1 D 2 D 1 Q 1 Q 2 Quantity

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7 Question 4 The market for rice in a small country has the following demand and supply functions: Demand function: P = 6 – 0.5Q D Supply function: P = 2 + 0.5Q S Where Q D is the quantity demanded, Q S is the quantity supplied and P is the unit price of rice. (a) Determine the equilibrium price and quantity in the rice market. Support your answers with a suitable market diagram. (b) Since rice is the staple good in the country, the government decides to impose a price ceiling of rice at $2.50 per unit to help consumers. At this price, determine the quantity of rice consumed and produced. What is the maximum price that consumers are willing to pay in this situation? (c) To increase the income of rice farmers, the government implement a price floor policy (legal minimum price) of rice at $5.50 per unit. Determine the quantity of rice consumed and produced. Will this policy increase the earning of the famers? Guide to Question 4 (a) At equilibrium, supplied quantity is met by demanded quantity, Q S = Q D . Solving the two simultaneous equations: P = 6 – 0.5Q = 2 + 0.5Q → 6 – 2 = 0.5Q + 0.5Q → Q = 4 → P = 6 – 0.5×4 = 4 The equilibrium quantity is 4 units, and the equilibrium price is $4. (b) Because the legal maximum (ceiling) price at $2.50 is smaller than the equilibrium price at $4, there is a shortage. Quantity demanded at $2.50: 2.5 = 6 – 0.5Q D → Q D = (6 – 2.5) × 2 = 7 Quantity supplied at $2.50: 2.5 = 2 + 0.5Q S → Q S = (2.5 – 2) × 2 = 1 Although the quantity demanded is 7 units, the quantity supplied is 1 unit. There is an excess demand (shortage of supply) of 6 units. Hence the effective quantity traded in the market is also 1 unit. From the demand curve, if only 1 unit of rice is available, consumers are willing to pay the price of $5.50 for rice: P = 6 – 0.5×1 → P = 5.5

8 Supply > Demand (surplus) Demand > Supply (shortage) (c) Because the lowest minimum (floor) price at $5.50 is larger than the equilibrium price at $4, there is a surplus in the rice market. Quantity demanded at $5.50: 5.5 = 6 – 0.5Q D → Q D = (6 – 5.5) × 2 = 1 Quantity supplied at $2.50: 5.5 = 2 + 0.5Q S → Q S = (5.5 – 2) × 2 = 7 Although the quantity supplied is 7 units, the quantity demanded is 1 only unit. There is an excess supply of 6 units. Hence the effective quantity traded in the market is also 1 unit. At equilibrium price of $4: Revenue = P×Q = $4×4 = $16 At floor price of $5.50: Revenue = P×Q = $5.5×1 = $5.5 The rice farmers actually earn a lower revenue unless the government absorbs the rice from the farmers (the government buy the 6 units of excess rice produced by the farmers). Price 6 Supply curve 5.50 4 2.50 2 Demand curve 1 4 7 Quantity

HE5091 Tutorial 1 Solution

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