Chapter 6 Production Production function---utility function Isoquants---indifference curve Short-run and long-run in production MRTS Returns to scale

6.1.1 The technology of production In neoclassical economics,firms are considered as black boxes,which means it only care about the input and output relations and say nothing about the inner stimulation problem or the structure of firm.In another word, production in neoclassical economics is a pure technological problem. So it leaves out the space for neo-institutional economics to develop which emphasize on the relationship between economic behaviors. Production function---functions showing that the highest output that a firm can produce for every specific combination of inputs with given technology. Y=f(X 1, X 2 ) or Q=F(K,L).

6.1.2 Some special production function Perfect substitution technology: Two inputs can substitute each other conveniently. For example,Q=X 1 +2X 2, X 1 stands for the number of inexperienced typists and X 2 stands for the number of competent typists. Perfect complement technology: Two inputs can ’ t substitute each other at all. For example, Q=min(K,L/2),such function is also called Leontif technological function. K--- the quantity of buses, and L --- the number of employees. A kind of production function symbolize a kind of technology. (utility function and preference)

6.1.3 Technology efficiency and economical efficiency Technology efficiency---the firm uses each combination of inputs as effectively as possible.It ’ s just a technology problem. Economical efficiency---besides the consideration of technology efficiency, the firm chooses the most economic technology (which will produce the most cheaply) from alternative technologies. An example: Chinese mail departing system.Chinese mail departing system.

6.3.1 Short-run and long-run in production Short-run: Period of time in which at least the input amount of one factor can ’ t be changed. Long-run: Period of time needed to make all inputs variable. Short-run and long-run problem in economics is distinguished according to specific technology in contrast to accounting. (grocery and chemical plant) Variable input and fixed input: the former will change with the level of output while the latter don ’ t. In short-run,at least one input ’ s amount is fixed and in long-run,all the input are variable.

6.3.2 Production with one variable input TP(L)=Q=F(K,L),K is usually considered as fixed input (like machines and buildings), whose input amount can ’ t be changed and L is considered as variable input( like labors, non- endurable materials), whose input amount can be varied in short run. TP means total products. With the increase of labor input and fixed capital,we get two new concepts----average products (AP) and marginal products (MP). AP(L)=Q/L MP(L)=dQ/dL. Calculate AP and MP for Q=KL 2,K=10

Figure 6.1 Total, Average and Marginal Product Curves Point of diminishing average returns AP MP Average product [AP] and marginal product [MP] Quantity of Labor [i] Total Product[ii] Average and Marginal Product Point of diminishing marginal returns Quantity of labor Total product [T/P] TP 0 B C D convex concave E F

6.3.3 Relationship between TP,AP and MP Total production curve----pay attention to three special points B,C and D. Average production curve. Its highest point and its slope.(first positive then negative) Marginal production curve. Its highest point and its slope.(first positive then negative) TP and AP,AP and MP (they will intersect at the highest point of AP).the mathematic proof.MP (they

Summary Production function Q=F(K,L) Technology efficiency and economic efficiency Production in the short run and in the long run The definition for TP AP and MP and the relationship between the curves. Isoquants: the input bundle that can at most produce the same output level.

6.2 Isoquants Isoquant----Curve showing all possible combination of inputs that yields the same output.(the association of indifference curve) Isoquant map---a map of different isoquants which is used to describe a kind of technology. Input flexibility----The downward slope of isoquant shows the input flexibility---Different kinds of inputs can be substituted each other,just like diligence can compensate the slow-understanding ability in study.Managers always try to choose input combination that minimize cost and maximize profit.

The characters of isoquant Downward sloping.( With more inputs, the firm can produce higher output level) Convex.( Balanced inputs bundle can produce higher output level than extreme bundles ) Higher isoquants stand for higher output level. Different isoquants never intersect.

6.3.4 The law of diminishing marginal returns(product) Law of diminishing marginal returns----principle that as the use of one factor increases while other inputs fixed,the resulting increase of output will eventually decrease. Example: additional waiters in a restaurant. The conditions of law of diminishing marginal returns:given technology, short-run (there is at least one kind of fixed variable). Technology progress often seems to break the law of diminishing marginal returns. Malthus ’ s population theory.Malthus ’ s population theory. Marginal returns doesn ’ t decrease because the quality of labor decreases when labor input is increased. In fact the additional labor input are of the same quality.It exist because variable input has an appropriate ratio compared to the fixed input.

6.4 Production with two variable inputs Marginal return is diminishing respectively for K and L. Pg.192.Figure6.6. Marginal rate of technical substitution-(MRTS)---To keep the output level unchanged, the amount of K that should be increased when we reduce one unit of input L.Or the amount of K that can be reduced when we increase one unit of L. It measures the efficiency of using factor labor to substitute factor K. The higher is MRTS LK, the contribution of labor in production is higher. MRTS LK =-dK/dL=Q L /Q K (How to prove it ?) Diminishing MRTS: the amount of capital that one unit of labor can substitute is decreasing with the increase of labor input. Pg.193. Figure6.7

What does MRTS diminishing law mean? The isoquant is convex. MRTS=-slope of isoquant at inputs bundel(L,K). MRTS is diminishing so the slope of isoquant is increasing, then the curve is convex. It shows that production (just like consumption) welcomes a balanced inputs bundle for extreme factor bundles is relatively low-productive. 1 Give out the production function for the technology that MRTS don ’ t diminish when we move down along an isoquant.2 The production function for the technology that MRTS decrease from infinitely large to zero when we move along an isoquant.

6.5 Returns to scale Returns to scale:if inputs are increased proportionately,how will the total product increase? Increasing returns to scale: t>1 Increasing returns to scale Constant returns to scale: Decreasing returns to scale: An example: The increasing returns to scale and diminishing marginal returns. For Q=K a L b (Cobb-Douglas production function) a+b>1, 0<a<1,0<b<1,a=b=2/3

Summary Curves for AP.MP and TP. Marginal rate of technical substitute(MRTS) =-k isoguant, in order to keep the output level unchanged, the efficiency of using factor L to substitute factor K. The law of MRTS decreasing and the law of marginal return (product) decreasing. Returns to scale:the relation of t · f(k,L) and f(t · K,t · L),t>1.