# MICROECONOMICS EV Prof. Davide Vannoni. Exercise session 2 Chapters 6-7 1.Production and Marginal Product 2.Costs of Production, efficiency scale and.

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MICROECONOMICS EV Prof. Davide Vannoni

Exercise session 2 Chapters 6-7 1.Production and Marginal Product 2.Costs of Production, efficiency scale and scale economies 3.Personal computers of DISK and FLOPPY 4.From production functions to cost curves Exercises

D. Vannoni e M. Piacenza Microeconomia C, A.A. 2007-2008 Esercitazione 2 3 Exercise n. 1 Consider the following Production Function: N. Workers 012345678910 Total quantity produced 010254050596162 60 Marginal product Draw the production function. Compute the marginal product When does marginal product start to decline? When is marginal product becoming negative?

D. Vannoni e M. Piacenza Microeconomia C, A.A. 2007-2008 Esercitazione 2 4 59 9 = product increase due to a further worker, moving from 4 to 5 15 = increase in product due to a further worker, moving from 1 to 2

D. Vannoni e M. Piacenza Microeconomia C, A.A. 2007-2008 Esercitazione 2 5 N. workers 012345678910 Total quantity produced 010254050596162 60 Marginal Product 01015 1092100-2 By employing the 10 th worker, the marginal product becomes negative, and also the total quantity will reduce. (marginal productivity both decreasing and negative) The marginal product starts to decrease with the 4° worker. When the marginal product starts to decrease, the total quantity still increases but at reducing path (marginal productivity reducing but still positive)

D. Vannoni e M. Piacenza Microeconomia C, A.A. 2007-2008 Esercitazione 2 6 crescentedecrescente

D. Vannoni e M. Piacenza Microeconomia C, A.A. 2007-2008 Esercitazione 2 7 Exercise n. 2 Firm WWW shows the following costs. QuantityFixed costsVariable costs 046 €0 € 146 €30 € 246 €50 € 346 €58 € 446 €64 € 546 €84 € 646 €114 € 746 €150 € 846 €190 € 946 €240 € Compute: 1)TC 2)MC 3)AVC 4)AFC 5)AC Draw the average and marginal cost curves

D. Vannoni e M. Piacenza Microeconomia C, A.A. 2007-2008 Esercitazione 2 8 QtyFCVCTCMCAVCAFCAC 0460 0000 1 307630 4676 246509620252348 34658104819,315,334,7 4466411061611,527,5 546841302016,89,226 64611416030197,726,7 7461501963621,46,628 8461902364023,85,829,5 9462402865026,75,131,8

D. Vannoni e M. Piacenza Microeconomia C, A.A. 2007-2008 Esercitazione 2 9 MC AC AVC AFC

D. Vannoni e M. Piacenza Microeconomia C, A.A. 2007-2008 Esercitazione 2 10 From which point is the marginal product decreasing?. Marginal Product: the increase in quantity due to an increase in the use of inputs The marginal product start to decrease when the marginal cost reduces. Indeed, it is the reduction of the marginal product that causes the reduction of marginal costs.

D. Vannoni e M. Piacenza Microeconomia C, A.A. 2007-2008 Esercitazione 2 11 Which is the relationship between: Average Total Costs and Marginal Costs and between: Average Variable Costs and Marginal Costs? The marginal cost curve crosses both the ATC and the AVC at their mimimum points. In both cases the average values of both TC and VC are influenced by value of the marginal cost: If MC > ATC AVC Se MC > AVC Se MC < ATC Se MC < AVC AC AVC

D. Vannoni e M. Piacenza Microeconomia C, A.A. 2007-2008 Esercitazione 2 12 Which is the efficient dimension for the firm? The efficient dimension corresponds to a quantity at which average total costs are at their minimum level. By looking at both the table and the graphs, it is straightforward to see that such a quantity is equal to “5”. For quantities higher or lower than 5, average total costs are larger. What about returns to scale? When average costs are decreasing (increasing, constant) scale economies are increasing (decreasing, constant). In such a case, there are scale economies up to Q=5 and scale diseconomies for Q>5

D. Vannoni e M. Piacenza Microeconomia C, A.A. 2007-2008 Esercitazione 2 13 The production function for personal computers of firm DISK is Q = 10 K 0.5 L 0.5, where Q is the number of computers manufactured each day, K is the number of hours-machines and L of hours-work. The firm FLOPPY, which is competing with DISK, has the following production function Q = 10 K 0.6 L 0.4. a)If both firms are using the same units of capital and labour, which firm will produce more pcs? Exercise n. 3

D. Vannoni e M. Piacenza Microeconomia C, A.A. 2007-2008 Esercitazione 2 14 Let us define: Q = number of computers manufactured each day by DISK Q 2 = number of computers manufactured each day by FLOPPY X = number of hours-machines for DISK = number of hours- machines for FLOPPY = number of hours-work for DISK = number of hours-work for FLOPPY The two firms manufacture respectively: Q = 10X 0.5 X 0.5 = 10X (0.5+0.5) = 10X Q 2 = 10X 0.6 X 0.4 = 10X (0.6+0.4) = 10X Q = Q 2 The same number of pcs per day

D. Vannoni e M. Piacenza Microeconomia C, A.A. 2007-2008 Esercitazione 2 15 Notice that if the two firms use the same number of hours-machines and the same number of hours-work but with the two numbers which differ between them, the number of pcs produced would not be the same. In particular, if K > L Q 2 > Q a)Suppose that the capital is now fixed at 9 hours-machines, while work is not constrained. In which of the two firms will the marginal product of labour be higher? Explain.

D. Vannoni e M. Piacenza Microeconomia C, A.A. 2007-2008 Esercitazione 2 16 If the capital is fixed at 9 hours-machines, the production functions of the two firms become: Q = 30L 0.5 Q 2 = 37.37L 0.4 To understand which of the two firms has a higher marginal product of labour, look at the following table:

D. Vannoni e M. Piacenza Microeconomia C, A.A. 2007-2008 Esercitazione 2 17 LQ MP L DISK Q2 MP L FLOPPY 00-0- 130 37.37 242.4312.4349.3111.94 351.969.53588.69 4608.0465.077.07 For all units of works > 1, the MP L of DISK is higher than the MP L of FLOPPY

D. Vannoni e M. Piacenza Microeconomia C, A.A. 2007-2008 Esercitazione 2 18 Exercise n. 4 : From the production function to the cost function A firm is using two variable inputs (S and L) to manufacture a good (Y), according to the following production function: Y = S 1/5 L 3/10 The prices are: P S = 2 and P L = 3; apart from variable costs, there fixed costs equal to 20. 1) Find the firm's cost function

D. Vannoni e M. Piacenza Microeconomia C, A.A. 2007-2008 Esercitazione 2 19 The marginal rate of technical substitution (equal to the ratio of the marginal productivities of the inputs) must be equal to the ratio of input prices (optimal condition for the firm):

D. Vannoni e M. Piacenza Microeconomia C, A.A. 2007-2008 Esercitazione 2 20 We can therefore substitute L to S in the equation that defines the variable cost (isocost): VC = P S *S + P L *L = 2S + 3L = 5L By making the same substitution on the production function we can obtain L as a function of Y: Y = L 1/5 L 3/10 = L 1/2 L = Y 2

D. Vannoni e M. Piacenza Microeconomia C, A.A. 2007-2008 Esercitazione 2 21 Substituting L in VC we get: VC = 5Y 2 By adding fixed costs we get the total cost function for the firm: CT = 5Y 2 + 20

D. Vannoni e M. Piacenza Microeconomia C, A.A. 2007-2008 Esercitazione 2 22 2) Show in a graph the shape of the average total cost, the average fixed cost, the average variable cost and the marginal cost

D. Vannoni e M. Piacenza Microeconomia C, A.A. 2007-2008 Esercitazione 2 23 ATC AVC MC AFC

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