FEEDBACK TUTORIAL LETTER. 1st SEMESTER 2018 ASSIGNMENT 1 INTERMEDIATE MICRO ECONOMICS IMI611S

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1 FEEDBACK TUTORIAL LETTER 1st SEMESTER 2018 ASSIGNMENT 1 INTERMEDIATE MICRO ECONOMICS IMI611S 1

2 Course Name: Course Code: Department: Course Duration: INTERMEDIATE MICROECONOMICS IMI611S ACCOUNTING, ECONOMICS AND FINANCE ONE SEMESTER NQF Level and Credit: LEVEL6; 13 CREDITS Moodle Enrollment Key: Marker tutor Details Tel.: E mail: kalila.mackenzie@gmail.com ASSIGNMENT 1 FEEDBACK TUTORIAL LETTER Solutions and explanations to the questions are provided in italics QUESTION 1 [30marks] The below questions look at the demand and supply of bread. Consumers determine how much bread to purchase based on the price of bread, consumers income, the price of margarine and the price of maize meal. The demand function of bread is given as: Qd = 50 4P + 5Pm 2Pg + Y Where: Qd = demand for bread P = price of bread Pm = price of maize meal Pg = price of margarine Y = consumers income Producers of bread determine how much bread to supply based on the price of bread, the price of flour and the wage rate of labour. The supply function of bread is given as: Qs = P 2W 2Pf Where: Qs = supply of bread P = price of bread W = wage rate of labour Pf = price of flour 2

3 a) If Pm = 4, Pg = 6 and Y = 20, state the demand function and draw the demand curve, illustrating the price (vertical) and quantity (horizontal) intercepts [6 marks] You are given the demand function stated above as: Qd = 50 4P + 5Pm 2Pg + Y Now what you needed to do is plug in the values for Pm, Pg and Y: Qd = 50 4P + 5(4) 2(6) +20 Then you needed to simply the equation: Qd = 78 4P (3 marks) So now you have the demand function (Qd) of bread in terms of P (price of bread). For the graph, you were asked to illustrate the price (vertical) and quantity (horizontal) intercepts. The price (vertical) intercept is where Q = 0, so 78 4P = 0 P = 78 / 4 = 19.5 Point on the graph: (0; 19.5) The quantity (horizontal) intercept is where P = 0, so Q = 78 Point on the graph: (78; 0) The demand curve is downward sloping as there is a negative relationship between price and quantity demanded (as price increases, quantity demanded decreases and vice versa). 3 marks for the graph 1 mark for each intercept, 1 mark for downward sloping demand curve You needed to show the intercepts graphically as illustrated below. b) Are bread and maize meal substitutes or complements? Explain your choice [6 marks] Bread and maize meal are substitutes (2 marks), as there is a positive relationship between quantity demanded of bread and the price of maize meal. This illustrates that when the price of maize meal increases, consumers will substitute maize meal for the relatively cheaper bread, and thus the quantity demanded of bread increases (or vice versa). (4 marks). Note that if you just stated what substitutes are or that consumers can substitute between bread and maize meal, you would not have received all the marks. You needed to show that you 3

4 understand the nature of the relationship of substitutes a positive relationship between the price of one good and the quantity demanded of the other good. c) If W = 10 and Pf = 5, state the supply function and draw the supply curve, illustrating the quantity (horizontal) intercept [6 marks] You are given the supply function stated above as: Qs = P 2W 2Pf Now what you needed to do is plug in the values for W and Pf: Qs = P 2(10) 2(5) Then you needed to simply the equation: Qs = P ( 3 marks) So now you have the supply function (Qs) of bread in terms of P (price of bread). For the graph, you were asked to illustrate the quantity (horizontal) intercept. The quantity (horizontal) intercept is where P = 0, so Q = 24 Point on the graph: (24; 0) The supply curve is upward sloping as there is a positive relationship between price and quantity supplied (as price increases, quantity supplied increases and vice versa). 3 marks for the graph 1 mark for the intercept, 2 marks for the upward sloping supply curve d) Why is there a negative relationship between supply of bread and the price of flour? Explain in full [6 marks] Flour is a factor of production / input to the production of bread (2 marks), so an increase in the price of flour will reduce the quantity supplied of bread (and vice versa), hence there is a negative relationship (4 marks). Note some students stated that there is a negative relationship because flour and bread are complements. This is incorrect, as complements means that the goods are consumed together (i.e. consumers buy flour and bread at the same time), which is not the case. Further, 4

5 complements are a consumer phenomenon which affect the quantity demanded, not the quantity supplied. e) Find the equilibrium quantity and price of bread, and illustrate this graphically [6 marks] Equilibrium is where demand = supply, so the first step is to equate the functions from (a) and (c): Qd = 78 4P = Qs = P Now take all the P terms to the right hand side and all the constant terms to the left hand side: = 54 = 8P + 4P = 12P (remember when you take terms across the sign changes) Divide through by 12 to solve for P: Pe = 54/12 = 4.5 (2 marks) Equilibrium price Substitute the P term into one of the functions to solve for equilibrium quantity: Qe = 78 4(4.5) = 60 (2 marks) Note you can always check your answer by seeing if the equations for Qd and Qs now equate: So Qs = P = (4.5) = 60 This is the same as the Qd func on above, so we know that the Pe value is correct as it equates the Qd and the Qs functions. The equilibrium point of the graph is (60; 4.5). You needed to show this graphically where the demand and the supply curves intersect. Don t forget to label you axes and curves! (2 marks) for the graph 1 mark for showing Ye and 1 mark for showing Pe QUESTION 2 [20marks] a) Explain how information on prices of goods in the market will affect market demand for a good? Provide an example [5 marks] If consumers have information of the prices of all goods in the market, they are aware of the prices of substitutes and of complements. This would affect their demand for a singular good (3 5

6 marks). For example, if consumers are aware that the price of a Samsung Galaxy is less than an iphone 8 (substitute goods), they would demand more of the Samsung Galaxies (2 marks for any relevant example). OR: If consumers have information on the price of goods, they will be aware when the price increases / decreases, and this will affect their demand of the good. For example, if consumers receive information that there is a 50% sale at Edgars, the market demand for Edgars goods will increase. Note that to answer the question, you needed to explain how information on prices impacted market demand. If you answered in terms of the effect of price on market demand or the impact on information of the quality / uses of the good, you would not have received all the marks. The point of the question is that consumer awareness on prices in the market (of the good and of substitutes and complements) will affect market demand of that good. b) Explain how sales tax on the price of a good affects the market demand for a good? Provide an example [5 marks] Sales tax on a good increases the prices that customers face and thus decreases the market demand (3 marks). For example, sin tax is applied to reduce the consumption of undesirable goods (2 marks for any relevant example). Note that the question asked how sales taxes affect market demand. If you answered how sales tax affects market supply, you would not have received any marks. Additionally if you did not provide a real life example, you would have only received part marks. c) Explain how expectations of the future price of a good affects the market supply of a good? Provide an example [5 marks] If there is an expectation that the price of a good will increase in the future, then suppliers will hoard stock now to sell at a later higher price. Likewise, if there is an expectation that the price will fall in the future, suppliers will sell more now at the higher price (3 marks). For example, suppliers of oil will adjust supply of oil depending on the expectation of future prices (2 marks for any relevant example). Note that the question asked how expectations of future prices affects market supply. If you answered how expectations affect market demand, you would not have received any marks. Additionally if you did not provide a real life example, you would have only received part marks. d) Explain how an import quota on a good will affect domestic supply of a good? Provide an example [5 marks] If there is an import quota, then there is a restriction on the foreign supply. Thus, domestic suppliers will increase market supply to meet market demand (3 marks). For example, Namibia has put an import quota on dairy products that has increased domestic dairy supply (2 marks for any relevant example). Note that the question asked how an import quota affects domestic supply. If you answered how import quotas affect total supply or foreign supply, you would not have received any marks. Additionally if you did not provide a real life example, you would have only received part marks. 6

7 For all of the above questions, the affect on market demand / market supply could have been illustrated graphically. Please take note that the demand and supply model, including the numerical determination of equilibrium price and quantity in Question 1 and the factors that affect demand and supply in Question 2 are fundamental concepts in Microeconomics. It is therefore very important for students to master these types of questions in preparation for the exam. QUESTION 3 [40 MARKS] Consider a consumer that consumes two goods, pizza (Z) and coca cola (C), with prices Pz = N$ 40 and Pc = N$ 10. Her utility function is represented by U (Z,C) = Z 2 C 2. Her income is N$ 2,000. a) Show the equation of the budget line and graph the budget line with Z on the vertical axis and C on the horizontal axis, indicating the intercepts and the slope [8 marks] The budget line is the price of each good multiplied by the quantity of each good, where summed up the terms must equal the consumer s income. Budget line: Pz.Z + Pc.C = Y Now plug in the values for the price of pizza (Pz = N$ 40) the price of coca cola (Pc = N$ 10) and the consumer s income (Y = N$ 2,000): 40Z + 10 C = 2000 (2 marks) The question also asked for the intercepts: Z intercept is where C = 0, so 40Z = 2000 Z intercept = 2000/40 =50 (1 mark) C intercept is where Z = 0, so 10C = 2000 C intercept = 2000/10 = 200 (1 mark) Slope of the budget line = Pc / Pz = 10/40 = 1/4 (2 marks) Many students did not solve for the slope of the budget line, and thus lost marks. You must ensure that you read the question carefully to determine what is required. (2 marks) for fully labeled graph 7

8 b) What does the budget line illustrate? [2 marks] The budget line illustrates the quantity of pizzas and coca colas the consumer can buy, given the income available and the market prices of pizza and coca cola (2 marks) c) Determine the marginal utility of good Z and the marginal utility of good C [10 marks] The consumer s utility function is: U (Z,C) = Z 2 C 2 The marginal utility of good Z is the differential of the utility function in terms of Z, treating the C term as a constant: MUz = U / Z= (2. Z 2 1 )( C 2 ) = 2Z C 2 (5marks) The marginal utility of good C is the differential of the utility function in terms of C, treating the Z term as a constant: MUc= U / C= (Z 2 )( 2C 2 1 ) = 2Z 2 C (5 marks) Note to solve these partial differential equations in terms of one variable, you treat the other variable as a constant. In general, with a function f in terms of A and B), f(a;b) = A x B y then: f / A= xa x 1 B y (the B y term is treated as a constant and thus does not change), and f / B= ya x B y 1 (the A x term is treated as a constant and thus does not change). Note that for Intermediate Microeconomics you are expected to understand how to solve for partial differentials as above. If you do not understand, you can watch this video called Finding Partial Derviatives: Or speak to your tutor. d) What is the consumer s marginal rate of substitution? Simplify fully [5 marks] The marginal rate of substitution is the negative ratio of the marginal utility of the horizontal variable over the vertical variable. So: MRS = MUc / MUz 8

9 Using the marginal utilities solved for in (c): MRS = 2Z 2 C / 2ZC 2 (2 marks) Now cancel out the like terms in the numerator and denominator: MRS = Z / C (3 marks) Don t forget the negative sign. e) Determine the consumer s optimal bundle. Represent this graphically [15 marks] Consumer s optimal bundle is where MRS = Pc / Pz So where Z / C = ¼ ( 2 marks) Multiply through by C: Z = ¼ C Plug into the budget line: 40Z + 10 C = (1/4C) + 10 C = C + 10C = 20 C = 2000 C = 2000 / 20 C = 100 (4 marks) Plug the C value in to find Z: Z = ¼ (100) = 25 (4 marks) So the optimal bundle is (100; 25) (5 marks) for the graph: 1 mark for budget line, 2 marks for indifference curve and 2 marks for showing the optimal amounts of Z and C (point e) QUESTION 4 [10 MARKS] Given the below graph of economic incidence: 9

10 a) Which of the following shapes indicates the tax burden on the consumer? [3 marks] i. ADGB ii. ADEB iii. BEFC ii. ADEB (3 marks) This is the area that represents the amount paid by the consumers at the higher price A (price after tax). b) Which of the following shapes indicates the tax burden on the producer? [3 marks] i. BEFC ii. ADFC iii. BEGC i. BEFC (3 marks) This is the area that represents the difference between the new price A (price after tax) and the cost of production at quantity F. c) Explain how the price elasticity of demand impacts the consumer s tax burden [4 marks] If the consumer s price elasticity is relatively inelastic, then consumers will not change consumption quantity greatly in response to a change in price, and thus the consumer s tax burden will be higher (2 marks). If the consumer s price elasticity is relatively elastic, then consumers will change consumption quantity greatly in response to a change in price and thus the consumer s tax burden will be lower (2 marks). 10

11 [END OF ASSIGNMENT 1] 11

FEEDBACK TUTORIAL LETTER ASSIGNMENT 1 INTERMEDIATE MICRO-ECONOMICS IMI611S

FEEDBACK TUTORIAL LETTER ASSIGNMENT 1 INTERMEDIATE MICRO-ECONOMICS IMI611S FEEDBACK TUTORIAL LETTER 1 st SEMESTER 2017 ASSIGNMENT 1 INTERMEDIATE MICRO-ECONOMICS IMI611S 1 Solutions and explanations to the questions are provided in italics Question One [30 marks] The current world