FEEDBACK TUTORIAL LETTER. 1st SEMESTER 2018 ASSIGNMENT 2 INTERMEDIATE MICRO ECONOMICS IMI611S

Transcription

1 FEEDBACK TUTORIAL LETTER 1st SEMESTER 2018 ASSIGNMENT 2 INTERMEDIATE MICRO ECONOMICS IMI611S 1

2 Course Name: Course Code: Department: INTERMEDIATE MICROECONOMICS IMI611S ACCOUNTING, ECONOMICS AND FINANCE Course Duration: ONE SEMESTER NQF Level and Credit: LEVEL6; 13 CREDITS Moodle Enrollment Key: Marker-tutor Details Tel.: kalila.mackenzie@gmail.com ASSIGNMENT 2 FEEDBACK TUTORIAL LETTER Solutions and explanations to the questions are provided in italics QUESTION 1 [30 marks] You are given the production function: Q(K,L) = K 0.5 L 0.5 a) What is the average product of labour, holding capital fixed at K? Simplify fully [6 marks] Average product of labour (APL) is quantity divided by labour. Quantity is equal to K 0.5 L 0.5. APL = Q/L (2 marks) APL = K 0.5 L 0.5 / L (2 marks) To divide by L, subtract the denominator power from the numerator power APL = K 0.5 L = K 0.5 L -0.5 Terms with a negative power move to the denominator APL = K 0.5 /L 0.5 or APL =(K/L) 0.5 (2 marks) b) What is the marginal product of labour? Simplify fully [6 marks] Marginal product of labour (MPL) is the partial derivative of the quantity function (Q) in terms of labour (L), holding capital (K) constant. MPL = U / L or MPL = Q / L (2 marks) MPL = 0.5 K 0.5 L = 0.5K 0.5 L -0.5 Terms with a negative power move to the denominator MPL = 0.5K 0.5 / L 0.5 MPL = 0.5 (K/L) 0.5 (4 marks) c) What is the marginal product of capital? Simplify fully [6 marks] 2

3 Marginal product of capital (MPK) is the partial derivative of the quantity function (Q) in terms of capital (K), holding labour (L) constant. MPK = U / K or MPK = Q / K (2 marks) MPK= 0.5 K L 0.5 = 0.5K -0.5 L 0.5 Terms with a negative power move to the denominator MPK = 0.5L 0.5 / K 0. 5 MPK = 0.5(L/K) 0.5 (4 marks) d) What is the marginal rate of technical substitution (MRTS)? Simplify fully [6 marks] The marginal rate of technical substitution (MRTS) is the negative ratio of MPL and MPK MRTS = - MPL / MPK (2 marks) MRTS = - (0.5K 0.5 / L 0.5 ) / (0.5L 0.5 / K 0.5 ) 0.5 in the numerator and in the denominator cancel out MRTS = - (K 0.5 / L 0.5 ) / (L 0.5 / K 0.5 ) You multiply by the inverse MRTS = - (K 0.5 / L 0.5 ) (K 0.5 / L 0.5 ) 0.5 plus 0.5 adds up to 1 MRTS = - K / L (4 marks) Don t forget the negative e) Does the above function exhibit increasing, decreasing or constant returns to scale? Illustrate why and explain what this means [6 marks] Constant returns to scale ( 2marks) Since the exponents of the factors of production in the production function sum to = 1 (2 marks) Constant Returns to Scale means that that output increases by the same proportional change as all inputs to the production function (2 marks). QUESTION 2 [30 marks] Given a production function where MRTS = - K / L, the following cost function applies: w (wage rate) = N$10, r (cost of capital) = N$ 20 and C (total cost) = N$ a) Derive the isocost equation and draw the isocost curve with labour on the horizontal axis and capital on the vertical axis, showing the L and K intercepts [8 marks] Iscocost equation: wl + rk = total cost (C) 10L + 20K = (2 marks) You needed to state the isocost equation as above to get the marks. K intercept is where L =0 K = / 20 = 500 (2 marks) L intercept is where K =0 L= / 10 = 1000 (2 marks) (2 marks) for fully labeled graph you needed to label the axes and the intercepts as illustrated in the graph below. 3

4 b) What is the slope of the isocost curve? Simplify fully [4 marks] Slope = - w/r (2 marks) = - 10/ 20 = or ½ ( 2marks) Don t forget the negative c) What is the optimal resource allocation? [8 marks] Optimal resource allocation is where MRTS = - w/r (2 marks) So where - K / L = The negatives cancels out K / L = 0.5 Multiply through by L So, K = 0.5L Plug into the isocost equation: 10L + 20K = L + 20(0.5L) = (2 marks) 10L + 10L = L = L = 500 (2 marks) K = 0.5(500) = 250 ( 2marks). d) Illustrate the optimal resource allocation graphically, with labour on the horizontal axis. Fully label your graph [ 5 marks] 1 mark each for labelling axes, 1 mark each for showing the optimal labour & capital, 1 mark for showing tangency of curves. You needed to label your graph fully to get the marks. 4

5 e) Explain the law of diminishing marginal returns. When might a firm overcome diminishing marginal returns? [5 marks] The law of diminishing marginal returns states that as the use of an input increases, with the other inputs held fixed, a point will eventually be reached where adding additional units of the input results in a decrease in total output (2 marks). A firm will usually overcome diminishing marginal returns in the long-run, when all factors of production are variable (3 marks). Note that if you responded about the diminishing marginal utility of consumers you would not have received marks. QUESTION 3 [20 marks] Explain each of the following market structures and provide an example of each in the Namibian economy. Explain your example. a) Monopoly [5 marks] A monopoly is a market with a single supplier of a good or service. Monopolies are price makers (3 marks). An example of a monopoly in Namibia is Nampower as it is the only supplier of electricity in Namibia, or any other relevant example (2 marks). Note that it was important to explain your example. b) Oligopoly [5 marks] An oligopoly is a market with limited competition, in which a market is shared by a small number of producers or sellers (3 marks). An example of an oligopoly in Namibia is retail banking, which only has 4 main players, or any other relevant example (2 marks). Note that it was important to explain your example. c) Perfect competition [5 marks] 5

6 A perfectly competitive market is a market with numerous buyers & sellers selling a homogenous good (3 marks). An example of a perfectly competitive market in Namibia is the market for apples, as it is a homogenous product and both buyers and sellers are price takers, or any other relevant example (2 marks). Note that it was important to explain your example. d) Monopolistic competition [5 marks] A monopolistic competitive market is a market in which firms compete by selling differentiated products that are highly substitutable for one another but not perfect substitutes, and where firms compete on product differentiation rather than price (3 marks). An example of a monopolistic competitive market in Namibia is the market for fuel, where firms compete on brand differentiation rather than price, or any other relevant example (2 marks). Note that it was important to explain your example. QUESTION 4 [20 marks] The demand function for labour is D L = 100-2w and the supply function for labour is S L = 40 +8w, where w is the wage rate prevailing in the labour market. a) Find the wage rate and quantity of labour that will enable equilibrium in the labour market [5 marks] Equilibrium is where D L = S L, so where 100-2w = 40 +8w (1 mark) = 8w + 2w Take all constant terms to the left-hand side and all terms with w to the right-hand side 60 = 10 w Divide through by 10 w = N$ 6 ( 2 marks) and Q L = 100-2(6) = 88 (2 marks) Check with the supply function: S L = 40 +8w = (6) = 88 So at equilibrium, w = N$ 6 and Q L = 88. b) Illustrate the equilibrium in the labour market graphically, based on the demand and supply functions of labour stated in (a) [5 marks] 1 mark each for labelling axes, 1 mark each for showing the equilibrium wage rate and quantity of labour, 1 mark for showing upward / downward sloping supply / demand curve. You needed to label your graph fully to get the marks. 6

7 c) Explain what the effect of trade unions on the labour market equilibrium wage rate and quantity of labour will be, according to bargaining theory? Illustrate this graphically [10 marks] The effect of trade unions, according to bargaining theory, is that trade unions can use their bargaining power to force wages higher than they would be without trade unions (2 marks). This is shown graphically where wage rate with trade unions, wt is at a higher level than equilibrium wage rate, we, and quantity of labour employed with trade unions, Qt is at a lower level than equilibrium quantity, Qe (3 marks). (5 marks) for the graph, 1 mark each for labelling each axes, 1 mark for showing higher wage rate, 1 mark for showing lower quantity of labour, 1 mark for labeling SL and DL curves. You needed to label your graphs fully to get the marks. 7

8 [END OF ASSIGNMENT 2] 8