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Exercise n° 6

Exercise n° 6. Chapter: 18 – The Markets for the Factors of Production. Practice Exercise n.1. Firm “A” manufactures good “X”.

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Exercise n° 6

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  1. Exercise n° 6 Chapter: 18 – The Markets for the Factors of Production Istituzioni di economia 2002/2003 corso C

  2. Practice Exercise n.1 Firm “A” manufactures good “X”. The following table shows for firm “A” the quantity of labor employed (hours) and the corresponding quantities of good “X” manufactured. The firm sells good “X” in a perfectly competitive market at the price of 10€; the labor market is perfectly competitive too and the hourly wage is equal to 11€ Istituzioni di economia 2002/2003 corso C

  3. A) Compute the marginal product of labor, the value of the marginal product and the marginal profit MPL: the marginal product of labor is the increase of the quantity manufactured due to an increase of a unit of labor employed ( N.B. MPL is decreasing) MPL=Q/ L VMPL=PxMPL VMPL: the value of the marginal product is the marginal product of a factor multiplied by the price of the product (N.B. VMPL is decreasing). It represents the marginal contribution to revenues due to the increase of one unit of labor.  : the marginal profit is the change in profits due to the last unity of labor employed, and is obtained as the difference between the marginal revenue (VMPL value of the marginal product), and the marginal cost (W wage). =VMPL - W Istituzioni di economia 2002/2003 corso C

  4. Istituzioni di economia 2002/2003 corso C

  5. B) Show graphically the production function, the marginal product, the value of the marginal product, and the marginal profit. Production Function: the relationship between the quantity of the factor employed and the quantity manufactured of a good Istituzioni di economia 2002/2003 corso C

  6. The marginal product of labor is decreasing, i.e. it decreases with the increase of the quantity of labor MPL:“the increase of the quantity of product due to a unit increase of the labor” Istituzioni di economia 2002/2003 corso C

  7. VMPL:“the marginal product of labor (in units of the good) multiplied by the price of the good” Istituzioni di economia 2002/2003 corso C

  8. Marginal Profit:“ change of profit due to a unit increase of labor employed” Istituzioni di economia 2002/2003 corso C

  9. W = 11€ C) How much labor will be employed? The firm in order to select the optimal quantity of labor compares the marginal revnue due to the last unit of labor (value of the marginal product) with the marginal cost of the same unit (wage). It keeps to employ new workers as long as the marginal profit is positive. Optimal choice VMPL = W Istituzioni di economia 2002/2003 corso C

  10. >0 <0 Optimal Qty labor MR > MC VMPL > W  >0 If the marginal profit is positive, profits are increasing, and viceversa. The firm maximizes its profits by employing 5 hours of labor. Istituzioni di economia 2002/2003 corso C

  11. D) If the fixed cost is equal to 100€ and there is only one variable input (labor), what is the total profit of the firm? The optimal choice of 5 units of labor at a wage of 11€, the output will therefore be 19 units of good at a price of 10€ each. TR = qty manufactured x price = 19 x 10 = 190 TC = FC + VC = FC +(qty labor x wage) = 100 + (5x11) = 155 Profit = TR – TC = 190 – 155 = 35€ Istituzioni di economia 2002/2003 corso C

  12. E) How does the optimal choice of the firm change if the price of the product raises up to 12€? The firm should now employ a further unit of work as compared to the previous situation Istituzioni di economia 2002/2003 corso C

  13. F) What happens if the wage increase up to 15€, while the price of the good is 12€? Istituzioni di economia 2002/2003 corso C

  14. New cost of labor is 15 €, while the price of the good is 12 €. Since the wage has increased, the employment of the sixth unit of work is not convenient anymore: the profit maximising firm will use 5 units of work. Istituzioni di economia 2002/2003 corso C

  15. Problem n. 3 pag. 335 • Discuss the effect of each of the following events on the labor market of the computer industry: • The Ministry of Education buys a Personal Computer for each graduate student. • An increasing quantity of students graduates in engineering and in information sciences. • The firms manufacturing computers build new productive plants. Istituzioni di economia 2002/2003 corso C

  16. PC Market Labor Market price wage S S W1 P1 W P D1 D1 D D quantity L L1 VMPL = P x MPL n.workers VMPL = P1 x MPL a) If the Ministry of Education buys a PC for each student, the demand of PC increases, the price increases as well as the value of the marginal product of the workers that manufacture computers. Therefore, the labor demand on the market of PCs increases, and it will result in an increase in the wages and in the number of employed workers. Istituzioni di economia 2002/2003 corso C

  17. Wage S S1 W W1 D L1 L n° workers b) If a greater number of students graduates in engineering and information sciences, the number of workers that would like to work for firms manufacturing computers increases. The labor supply increases, therefore the wage decreases and the number of employed workers increases. Istituzioni di economia 2002/2003 corso C

  18. Wage S W1 W D1 D L1 L n° workers c) The building of new plants in this industry causes an increase in the marginal product of labor and in the value of the marginal product of labor, for all levels of labor employed. The labor demand will increase, and both the number of workers and the wage level will increase. Istituzioni di economia 2002/2003 corso C

  19. Problem n. 6 pag. 396 Sara is awake for 100 hours a week. Show in a graph the budget line for Sara if she earns 6, 8 or 10 € per hour. Draw the indifference curve for Sara in a way in which her labor supply curve is positively sloped if the wage is between 6 and 8 € and negatively sloped if it is between 8 and 10 €. Istituzioni di economia 2002/2003 corso C

  20. Consumption(€) 1000 800 600 100 Leisure time (hours) Sara’s budget line when she earns 10€ per hour, maximum consumption 1000€, maximum n° of hours of leisure time 100 Sara’s budget line when she earns 8€ per hour, maximum consumption 800€, maximum n° of hours of leisure time 100 Sara’s budget line when she earns 6€ per hour, maximum consumption 600€, maximum n° of hours of leisure time 100 Istituzioni di economia 2002/2003 corso C

  21. Between 6€ and 8€ of hourly wage. Indifference curves that result in a positively sloped labor supply curve (labor supply increases with the wage) must exhibit an increase in the worked hours, and therefore a reduction of leisure, after an increase in the wage. Leisure is relatively more expensive, as the wage increases, and the substitution effect implies a reduction of leisure. The income effect determines an increase in the consumption of all goods, included leisure. In such case the substitution effect must prevail, with a net reduction of leisure, and a labor supply curve which is positively sloped. Istituzioni di economia 2002/2003 corso C

  22. Between 8€ and 10 € of hourly wage. Indifference curves that result in a negatively sloped labor supply curve (labor supply decreases as the wage increases) must exhibit a reduction in worked hours, therefore an increase of leisure, as the wage increases. Leisure is relatively more expensive, if the wage increases, and the substitution effect has the effect of reducing the hours of leisure and increasing the quantity of consumed goods. The income effect determines an increase in the consumption of all goods, included leisure. In such a case the income effect must prevail, with a net increase of leisure, that brings to a negatively sloped labor supply curve. Istituzioni di economia 2002/2003 corso C

  23. consump (€) 1000 800 600 C3 C2 C1 L1 L2 L3 100 Leisure time (hours) For a wage between 6€ and 8€ leisure time reduces from L1 to L2. For a wage between 8€ and 10€ leisure time increases from L2 a L3 The consumption of goods different from leisure always increases as the wage increases Istituzioni di economia 2002/2003 corso C

  24. Practice Exercise In the labor market, when wages increase, the substitution effect determines an increase of the quantity of labor, while the income effect brings a reduction of the quantity of labor. (True/False) Describe with a graph. True Initial situation: point A Hourly wage 50 €, 20 hours available for labor and leisure time Choice of the worker, given his preferences: 6 hours of leisure and 14 hours of work at 50 € that allow a consumption of 700 € After the wage increase: point B Hourly wage 75 €, 20 hours available for labor and leisure time, the maximum availability of leisure does not change, but the maximum amount of consumption changes. For each hour devoted to leisure one abandons the possibility to consume a greater quantity of goods. Worker’s choice, given his preferences: 5 hours of leisure and thus 15 hours of work that allow to consume goods for 1125 € Istituzioni di economia 2002/2003 corso C

  25. consump B 1125 € I3 C I2 A 700 € I1 6 hours 5 hours Leisure time Istituzioni di economia 2002/2003 corso C

  26. Substitution Effect: from A to C The wage increase renders leisure more expensive in terms of consumption, therefore one increases consumption and reduces leisure, i.e. the worked hours increase Income Effect: from C to B The wage increase determines an income effect similar to an increase in the income, so both leisure and consumption of other goods increase, i.e. the worked hours decrease Istituzioni di economia 2002/2003 corso C

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