Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Eco 300 Intermediate Micro Instructor: Amalia Jerison Office Hours: T 12:00-1:00, Th 12:00-1:00, and by appointment BA 127A, [email protected] A. Jerison (BA 127A) Eco 300 Spring 2010 1 / 11 1. The necessary condition for a firm with different plants to be maximizing its profit is that marginal costs are equal in all the plants that produce. This does not mean that average costs have to be the same. The two plants could have different cost functions which lead to different average costs, even though their marginal costs are the same. For instance, suppose that plant A has the cost function CA (qA ) = 27 + 2qA for all qA ≥ 0. Let plant B have the cost function CB (qB ) = 10 + qB2 for all qB ≥ 0. Then M CA (qA ) = 2, M CB (qB ) = 2qB , ACA (qA ) = 27/qA + 2 and ACB (qB ) = 10/qB + qB . A. Jerison (BA 127A) Eco 300 Spring 2010 2 / 11 Setting M CA (qA ) equal to M CB (qB ), we get qB = 1. Then setting ACA (qA ) equal to 3 × ACB (qB ), we get 27/qA + 2 = 10/qB + qB = 10 + 1 = 11, so 27/qA = 9, and qA = 3. This shows that it is possible to have the average costs of plant A be 3 times the average costs of plant B, yet the marginal costs of the two plants are equal. So the firm owning these two plants can be profit maximizing. A. Jerison (BA 127A) Eco 300 Spring 2010 3 / 11 2. a. q = 3L + 2K. When we multiply L and K by a positive constant c, we get q = 3cL + 2cK = c(3L + 2K), which is c times the original q. So this function has constant returns to scale. The marginal product of labor is 3, so the marginal product of labor doesn’t change as L is changed. Similarly, the marginal product of capital is 2, so the marginal product of capital doesn’t change as K is changed. A. Jerison (BA 127A) Eco 300 Spring 2010 4 / 11 b. q = (2L + 2K)1/2 . Given a positive constant c > 1, q(cL, cK) = (2cL + 2cK)1/2 = c1/2 (2L + 2K)1/2 < c(2L + 2K)1/2 . So this function has decreasing returns to scale. The marginal product of labor is (1/2)(2)(2L + 2K)−1/2 = (2L + 2K)−1/2 , which is decreasing as L increases. Similarly the marginal product of capital is (2L + 2K)−1/2 , which is decreasing as K increases. A. Jerison (BA 127A) Eco 300 Spring 2010 5 / 11 c. q = 3LK 2 . q(cL, cK) = 3cL(cK)2 = c3 (3LK 2 ) > c(3LK 2 ) for c > 1. So the function has increasing returns to scale. The marginal product of labor is 3K 2 which does not change with L. The marginal product of capital is 6LK, which increases with K. A. Jerison (BA 127A) Eco 300 Spring 2010 6 / 11 d. q = L1/2 K 1/2 . q(2L, 2K) = 21/2 L1/2 21/2 K 1/2 = 2L1/2 K 1/2 . So this function has constant returns to scale. The marginal product of labor is (1/2)L−1/2 K 1/2 , which decreases with L. Similarly, the marginal product of capital decreases with K. A. Jerison (BA 127A) Eco 300 Spring 2010 7 / 11 e. q = 4L1/2 + 4K. q(2L, 2K) = 4(21/2 )L1/2 + 8K < 8L1/2 + 8K. So this function has decreasing returns to scale. The marginal product of labor is 2L−1/2 , which decreases with L. The marginal product of capital is 4, which is constant in K. A. Jerison (BA 127A) Eco 300 Spring 2010 8 / 11 3. The equation of the isoquant corresponding to an output of 1 chair is L + K = 4. The equation of an isocost line is 30L + 15K = C. So the slope of the isoquant is −1 and the slope of an isocost line is −2. Because of these different slopes everywhere, the solution to the cost-minimization problem must be a corner solution. We have to find the lowest-cost isocost line that touches the isoquant. The lowest-cost point of intersection of the two lines is where L = 0, K = 4. This makes sense because labor and capital are equally productive, but capital costs less than labor. So the firm should use only capital in its production. The graphical illustration of the current production and optimal production is below. A. Jerison (BA 127A) Eco 300 Spring 2010 9 / 11 K(hours) Optimal Current production L (hours) A. Jerison (BA 127A) Eco 300 Spring 2010 10 / 11 4. Explain why the short run supply curve in a competitive market might slope upward while the graph of the long run supply in the same market is horizontal. In the long run, firms can enter and exit the market, which they cannot do in the short run (once a firm has decided to exit a market, it takes quite a long time to do so, and once a potential firm has decided to enter, it also takes some time to get set up). When there is a positive demand shock, the short run market response leads to an increase in price. However, in the long run, this price increase is counteracted by an increase in short run supply due to the entrance of more firms. This causes the long run supply curve to be horizontal in a constant cost industry, as nothing can cause an increase (or decrease) in price in the long run. A. Jerison (BA 127A) Eco 300 Spring 2010 11 / 11