1 / 17

Production Function Multiple Variable Input

Production Function Multiple Variable Input. The 3D production function can be compressed into a set of isoquants plotted in a 2D (K,L) space. An isoquant shows all the input mixes of (L,K) that produce the same amount of Q. One isoquant for each level of Q

nyssa-casey
Download Presentation

Production Function Multiple Variable Input

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Production Function Multiple Variable Input • The 3D production function can be compressed into a set of isoquants plotted in a 2D (K,L) space. • An isoquant shows all the input mixes of (L,K) that produce the same amount of Q. • One isoquant for each level of Q • Isoquants have negative slope: more output from one input can offset less output from the other input

  2. Isoquant • The shape of the isoquant reveals the degree of substitution between the inputs. • If the technology allows for perfect substitution between labor and capital, the isoquants are straight lines. • The inputs can substitute each other at the same rate to produce the same output. e.g. each unit of K can always be replaced by 2 units of L.

  3. Isoquant • In reality, inputs are imperfect substitutes and the isoquants are convex to the origin. • Check: as you move up an isoquant in Fig 7.4, you need to use more and more capital to replace each unit of labor in order to stay on the same isoquant. • The magnitude of the slope of the isoquant is greater as you move “up” an isoquant.

  4. Isoquant • Slope of an isoquantdK/dL is called the marginal rate of technical substitution. • MRTS is the amount of capital input (dK) needed to replace an amount of labor input (dL) to keep the same level of output: it measures the degree of substitution. • Q = Q(K, L). • As you move “up” along an isoquant, the total differential of Q is zero

  5. Isoquant • dQ = (∂Q/∂L) (dL) + (∂Q/∂K) (dK) = 0 (MPL) (dL) + (MPK) (dK) = 0 (dK)/dL = - MPL/MPK < 0 • MRTS at different points on the isoquant is different since MPL and MPK are changing. • As you move “up” an isoquant, MRTS becomes larger “in magnitude” (more negative).

  6. Isoquant • This is the result of the law of diminishing marginal productivity (LDMP). • LDMP states that “as you increase the amount of one input while keeping other inputs fixed, the marginal product of this input declines with output. • LDMP is a physical constraint – we can’t escape from it.

  7. Isoquant • If LDMP is true, so is a weaker version of it: “as you increase the amount of one input while reducing other inputs, the marginal product of this input declines with output. • As we use less labor and more capital inputs along an isoquant, MPK, MPL  • MRTS = (dK)/dL = - MPL/MPK • “magnitude” of MRTS (more negative)

  8. Optimal level of Input Mix to EmployMultiple variable input • For a profit max output Q, there are now many input mixes of L and K (along the isoquant for this output Q) that can be used to produce Q • Which input mix is cheapest? You need to take into account inputs prices

  9. Isocost line • The amount of input you can employed depends on (1) their prices and (2) budget. • Define: an isocost line consists of all the input mixes (L, K) that can be employed with an expenditure budget M and a set of inputs prices of PL and PK.

  10. Isocost line • Isocost line are all the (L, K) such that • PLL + PKK = M • K= M/PK – (PL/PK)L • Plot this eqt in the K-L space • Slope of isocost line = – (PL/PK) • X-axis intercept = M/PL • Y-axis intercept = M/PK

  11. Isocost line • If M double, the line shifts out parallelly and the intercepts doubled (same effect if inputs prices are halved) • If both M and input prices are doubled, the isocost line is unchanged • If the price of labor inputs , the isocost line rotate: steeper and the x-axis intercept decreases.

  12. Optimal level of Input (Mix) to EmployMultiple variable input • Suppose we know the profit max output Q. • Plot the isoquant of Q • Given input prices PL and PK, plot several isocost lines, each corresponds to a different expenditure budget M • The optimal input mix is one such that the isocost line just “touch” the isoquant of Q

More Related