CPR-no: 14th January 2013 Managerial Economics Mid-term

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1 Question 1: The market equilibrium can be found by setting demand = supply 20-0,00001Q D =5+0,000005Q S 15 =0,000015Q Q = P= 20-0,00001* = 10 Question 2: The price equilibrium at this point can be calculated with by help of the point-slope method for price elasticity of demand and plotting in the known values: E = (10/ )*(1/-0,00001) = -1 The elasticity at this point is unit-elastic meaning that a one percent decrease in price will lead to a one percent increase in quantity demanded and a one percent increase in price will lead to a one percent decrease in quantity demanded. The price elasticity of demand is -1 in the middle of the demand curve, and it is also here where Total Revenue is maximized, which is true when operating under perfect competition. Question 3: Since it is a perfectly competitive market suppliers are price-takers, and therefore must deliver a certain quantity at the market-price (which is P=10=MR=D). We know that the optimality condition is MR = MC under all forms of market structure, therefore, we simply set the market price P=MR=10 equal to BeefBrazz Marginal Cost function: 10 = 5 + 0,00001Q 2 Solving for Q we get two solutions: Q = -707,107 or Q= 707,107 Since they cannot produce a negative output they will produce an output of Q = 707,107 Page 1 of 14

2 Question 4: Average Variable Cost (AVC) = Total Variable Cost / Q Total Variable Cost (TVC) = integrate(mc) TVC = Integrate (MC) = AVC = TVC/Q = 0,000003Q 2 +5 We find the value at the optimum-price we found in question 3 (707,107) by inserting it into AVC: AVC = 0,000003*707,107^2+5 = 6,5 This is the average cost of producing each unit of Q since we don t have TC we cannot know whether there are any fixed costs. Assuming there are no fixed costs BeefBrazz will be making a profit since the cost of producing is lower than the selling price. Question 5: Page 2 of 14

3 Since it is a perfectly competitive market, entry barriers are low, and more suppliers will enter the market driving the profits down to zero in the long run. This means that in the long run ATC will be equal to the market-price, meaning that all the firms earn no profit in the long-run, as depicted in the graph below: Question 6: We can determine the demand function simply by using the formula for finding a straight with two points given: The two points are (0, 30) and (100, 25) To find the slope (a) of a linear function: a= (y2 y1)/(x2 x1 ) The intercept with the y-axis is given (b = 30) Inserting the values into the slope-formula we get a = -0,05 P = 30 0,05Q TR = P * Q = 30Q 0,05Q 2 MR = d(tr)/d(q) = 30 0,1Q Question 7: Given: P = *Q + 30 MR = -0.1 *Q + 30 Page 3 of 14

4 MC = 0.07 *Q + 7 MR = MC at optimum -0.1 *Q + 30 = 0.07 *Q + 7 Solving for Q = P = -0,05*135,29+30 = Find MR in optimum MR = TR (P*Q) = 3, TVC = TVC=0,035*135, *135,29 = 1, Profit (TR-TVC-TFC) = 1, FC Page 4 of 14

5 MC MR P Question 8: Point Income elasticity is defined as the percentage change in demand because of a 1 % increase in income. The effect of an income change on the demand for a good. Where price elasticity related to the demand curve, income elasticity relates to the engel curve. y Page 5 of 14

6 x y Normally food is considered a necessity good, with little changes in quantity demand when price is changed. However, since BeefBrazz produces beef it is likely that they produce various types of meat that experience different income elasticities according to the quality of the meat. For instance, ground meat has different fat percentages; in a hamburger the fat perce ntage is likely to be high, and since the consumer is likely to switch to a less fat variety of ground beef upon receiving a higher income, hamburgers are an inferior good, since consumption falls when income rises. On the other hand, ground beef with a lower fat percentage could be considered a normal good since consumption is likely to rise when income rises. Normally goods like food in general are said to be necessities, but since there are different classes of meat on a cow BeefBrazz can differentiate its prices in the Chilean market according to the various qualities of the different cuts of meat. Question 9: By separating the Chilean and South African markets with different demand functions, BeefBrazz is undertaking third-degree price discrimination, which will maximize profits by exploiting that different buyers are willing to pay different prices for the same products by separating geographical markets. In a perfectly competitive market, the firm cannot price discriminate as the firms are price-takers A monopolist, however, has market power to choose the profit-maximizing price of his product. Since the demand curves for the two markets BeefBrazz wishes to operate in are different, it is recommendable and in theory possible to differentiate prices in order to maximize profits. Question 10: Given: Joint cost: MC = 0,07 *Q + 7 Page 6 of 14

7 South Africa: Q MAX P = -0.1 *Q MR = -0.2 *Q Chile: P = *Q MR = -0.1 *Q First we find the quantity for MRSA at the MR-value where Chile enters the scenario. MR = 30 = -0.2 *Q + 40 Q = 50 The we perform a horizontal addition of the 2 MR's: MR QDK QS Q Total The we can find the 2 MR's for the intervals of a=y2-y1/x2-x1 and b=y1-a*x1 - MR = *Q <Q < 50 - MR = *Q <Q < 500 We can now draw it: Q MR MC Optimum Optimum Page 7 of 14

8 - 45,00 40,00 35,00 MR MC 30,00 25,00 20,00 15,00 10,00 5, We clearly see that the interception between MR and MC is in the second interval above Q = 50 MR = MC *Q = 0,07 *Q + 7 Qtotal = MRTotal = (the MR-value in optimum) MR optimum is the inserted into the 2 markets MR-functions: MRSA = = -0.2 *Q + 40 QSA = 98 PSA = MRC = = -0.1 *Q + 30 QC = 95 Page 8 of 14

9 PC = TC function: Q^2+ 7 Q Total Revenue, I (PSA*QSA): 2, Total Revenue (PC*QC), II: 2, Total Revenue, total (TRSA+TRC): Total Cost (TC*Qtotal), Total: 2,648 Profit (TRtotal-TCtotal): 2,704 Question 11: Q MC At 0<Q<300 MC is 2 Real pr. kg At Q = 300 we get an accumulated discount of 5% which gives us a MC at that output equal to -28 because 2-(300*2*0,05%) = -28 At 301<Q<500 the MC is equal to 2*0,95% = 1,9 Real with the 5% discount Page 9 of 14

10 At Q = 500 we get a non-accumulated discount of 10% meaning that the marginal cost will simply fall to 1.71 Brazilian Real pr. Kg. onwards since 1,9*0,9% = 1,71 Real MC & AVC Page 10 of 14

11 Question 12: 120 Relationship between Capital (y-axis) and Labor (x-axis) The relationship depicted above is the typical form of an isoquant which is input combinations that give the same output (in this case 500). Isoquants have negative slopes in the relevant area due to the more-isbetter assumption. The known values have simply been plotted into an x-y diagram in the above graph. MRTS is the ratio of the marginal products of the inputs (L and K) in which ratio, they can substitute each other. MRTS = - K/ L = MP L /MP K Question 13: The optimality condition for two variable inputs is found at the point of tangency between the isocost line (TC = L*w+K*r) and the isoquant. This is found at the place where the two slopes are equal to each other by setting MRTS = wage/rent MRTS can be calculated with the formula MRTS = - K/ L which has been done below for the given amounts of labour and capital. We know that the cost of labor (wage) = 400 Real, and the cost of capital (rent) = 50 Real. The price ratio of the isocost is therefore = 400/50= 8 Q Labor Capital MRTS Page 11 of 14

12 As we can observe from the graph above, there is no MRTS value that equals 8 exactly, therefore, we can conclude that the optimal use of labor and capital lies somewhere in between K = 48 and K = 42 and between L = 4 and L = 5.To minimize costs, BeefBrazz should therefore hire 4 workers and use 48 units of capital which gives them a Total Cost = 4*400+48*50 = 4000 at Q=500, assuming that units of labor are not divisible, since hiring 5 workers and using 42 units of capital would give them a total cost of 4100 (which is more). Question 14: A 10% decrease in the price of capital gives us: 50*0,9 = 45 Real. The new slope of the isocost function can now be given as 400/45 = 80/9 ~ 8,8889 If labor were continuously divisible it is likely that BeefBrazz would substitute away from labor and utilize more capital due to the lower price of capital. However, since we assumed above that labor is not continuously divisible the cost-minimizing input of capital and labor will continue to be L = 4 and K = 48 however with a lower Total Cost = 4*400+48*45 = 3760 to produce an output level equal to Q = 500 Page 12 of 14

13 Question 15: Since BeefBrazz production equipment is improved, and assuming that this leads to a more efficient production and that capital/wage costs do not change, BeefBrazz is experiencing process innovation. The isoquants will move/shift towards the origin since it is now possible to produce a higher amount of output with the same costs. The consequences for BeefBrazz of using this new equipment, assuming that costs are still the same, means that they are able to produce the same output with a lower Total Cost, meaning that this would improve their profits, under the assumption that they are the only supplier in the market. This new situation is illustrated below: Page 13 of 14

14 Question 16: Since BeefBrazz is cattle-farming firm, it is likely that there is a high degree of attention regarding animal welfare from the public. It is therefore likely that BeefBrazz should focus on proper treatment of the cattle and exert a high-degree of respect to animal welfare. Furthermore, cattle-breeding is known to have somewhat severe impact on the environment due to the vast amounts of resources used to breed cattle. In this respect BeefBrazz would do well in making sure that their production processes are efficient in such a way that they strain the environment as little as realistically possible. Other focus areas related to ethical business conduct could include: respect of human rights, child labour, fair pricing of products, working conditions and so on. Page 14 of 14