Term 1 Week 8: Producer Theory Flashcards
What does producer theory look at (2,1)
-What choices firms make (what inputs)
-What constraints they face (Technological or what combinations)
-The main thing a producer does is produce G/S, with the ultimate incentive to maximise profit
How do we model a production function (2)
-The production function tells us the maximum amount of a good a firm can produce, using various combinations of inputs
-Q = f(K, L), where we assume Q is concave and monotonic
What is the producers choice set (3)
-The producers choice set is the set of production plans that are technologically feasible (inputs are sufficient to produce the output), and the production function tells us the set of production plans with no input waste
-On a production function diagram (labour hours x axis, good X y axis), under the line is input wastage, on the line is efficient, over the line is technologically infeasible
-Diminishing returns hit at the point of inflection
What is the marginal and average product of labour (3,1)
-The Marginal product of labour is the additional output produced by one more worker
-MPL = Change in total product/Change in Ql = partially differentiate Q with respect to L
-Linear production functions have a constant MPL, but we usually assume diminishing marginal productivity, where partially differentiating MPL with respect to L < 0
-The Average product of labour = total product/number of workers
How to show the MPL and APL on a production function (2,2)
-The slope of the production function at any point gives the MPL
-The chord of the production function from the origin at any point gives the APL (y/x)
-The MPL cuts the axis at the production functions max point
-The MPL’s max point is the PF’s point of inflection (where diminishing marginal returns kick in)
What is an Isoquant (2)
-An Isoquant is all the combinations of the 2 inputs which can be used to produce a particular level of output (f(K, L) = Q0)
-With Labour hours on the x axis, and machine hours on the y axis, Isoquants slope down, as more labour means less capital (similar shape to indifference curve)
What is the Marginal Rate of Technical Substitution (3)
-The Marginal Rate of Technical Substitution of Labour for Capital is the slope of the isoquant
-This represents how much K must be given up to use 1 more L, keeping output constant (gradient)
-MRTS decreases as you move down the isoquant
How do you work out the MRTS (3,1)
-Take the total differential of the production function (dq = df/dL x dL + df/dK x dK)
-Since dq = 0 along an isoquant, (MPL)dL = -(MPK)dK
-MRTS (L for K) = dK/dL = -MPL/MPK
-The shape of the isoquant determines the rate of technical substitution
What are the main differences between indifference curves and isoquants (3)
-The main difference is Utility is not measurable, so there was no objective to the numbers, whereas output is measurable, so changing the labelling has real economic meaning
-Utility is ordinal only, but output is ordinal and cardinal
-Doubling all values on an indifference map provides the same tastes as before, but doubling all values with isoquants alters the production technology, with twice as much output
What does it mean to have convex/concave production function (1,3,1)
-With consumer theory, convexity just meant averages > extremes
-A production function has 3 axis, with Labour and Kapital the 2 on the floor, and Output going up
-A concave production function means as L and K increases, the rate at which output rises falls (both horizontal and vertical slices are convex)
-A Quasi-concave production function means as L and K rise, the rate at which output rises rises (only horizontal slices are convex)
(The horizontal slices = isoquant, the vertical slices = what happens to output as you move up isoquant)
How do you work out returns to scale (2,3,3)
-Returns to scale measure how much total output rises if if all inputs increase simultaneously (assuming MPL and MPK > 0)
-Returns to scale = %change of output/%change of input
Consider a homogeneous production function, such that f(tK, tL) = t^kf(K, L) = tQ
-k>1 = IRS
-K = 1 = CRS
-K < 1 = DRS
For a Cobb-Douglas production function f(K, L) = AL^aK^b
-a + b > 1 = IRS
-a + b = 1 = CRS
-a + b < 1 = DRS
How to show the different returns to scale on the vertical slice of the production function (2)
-Have both inputs on the x axis (K = L), and output on the y axis
-For CRS, the slice will be a linear upwards sloping line, IRS = increasing slope, DRS = decreasing slope
How can we use the exponents of production functions to tell us about returns to scale (2)
-Summing the exponents tells us about the long run returns to scale
-Looking at them individually (second order partial derivative) tells us about the short run and returns to that particular factor
What are different types of production functions ()
-
