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homothetic production function and the corresponding minimum cost function
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# homothetic production function and the corresponding minimum cost function an illustration. by Finn R. FГёrsund

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Published in Oslo .
Written in English

### Subjects:

• Production functions (Economic theory)

## Book details:

Edition Notes

Bibliography: leaf 7.

Classifications The Physical Object Statement By Finn R[agnar] Førsund. Series Memorandum from Institute of Economics, University of Oslo, Memorandum fra Sosialøkonomisk institutt, Universitetet i Oslo. LC Classifications HB241 .F59 Pagination 7 l. Open Library OL5331294M LC Control Number 72184414

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A cost function corresponding to a homothetic production function can be wrist^n in the form C (w, Q)=h(w 1 - T (Q). (1) where tv is the input price vector, Q is the scale of production in terms of real output, C is total cost in value terms as a function of input prices and output, and T is a function which specifies the output expansion, by: The homotheticity properties of production technologies were first stated by Shephard (). Input and output homotheticity have been widely studied in economic literature Hanoch (), Knox. 1. The Process Production Function.- 2. Heuristic Principle of Minimum Costs.- 3. The Producer's Minimum Cost Function.- 4. Dual Determination of Production Function From Cost Function.- 5. Geometric Interpretation of the Duality Between Cost and Production Function.- 6. Constraints on the Factors of Production.- 7. Homothetic Production. I know that homothetic production function implies that cost function is multiplicatively separable in input prices and output, and it can be written as C(w,y)=h(y)C(w,1). Can some one help me derive the functional form of profit function in case of homothetic production functions?

Theory of Cost and Production Functions on JSTOR Production Functions and Cost of Production Outline 1. Chap 6: Returns to Scale 2. Chap 6: Production Function Derivation 3. Chap 7: Cost of Production 1 Returns to Scale Increasing Returns to Scale (Lecture 11) Constant Returns to Scale • Doubling the inputs leads to double the output.   Production/Cost Function. The production function of a firm is how the firm transforms the inputs into output. Suppose if the firm produces only one good y, then the production function for y is y=f(x1,x2 an), or y=f(x), if x is the vector of all different factors it takes to produce cost function for producing y, is then c(y*)=w1x1+ wnxn, or WX*, if W and X are both vectors. production is homothetic Suppose the production function satis es Assumption and the associated cost function is twice continuously di erentiable. Then: When the production function is homothetic, the cost function is multiplicatively separable in input prices and output and can be written c(w,y) = h(y)c(w,1), where h0. The minimum cost c wx to problem () depends on the levels of input prices wand output y, and of course on the production function y Df.x/. By solving () using different value of.w;y/we can in principle trace out the relation between minimum cost cand parameters.w;y/, conditional on the ﬁrm’s particular production function yDf.x/.

The duality between cost function and production function is developed by introducing a cost correspondence, showing that these two functions are given in terms of each other by dual minimum problems. The special class of production structures called Homothetic is given more general definition and extended to technologies with multiple outputs. (b) If F(x) is a homogeneous production function of degree, then i. the MRTS is constant along rays extending from the origin, ii. the corresponding cost function derived is homogeneous of degree 1. 4. Euler’s Theorem can likewise be derived. The theorem says that for a homogeneous function f(x) of degree, then for all x x 1 @f(x) @x 1. Homogeneous and homothetic production functions. There are two special classes of production functions that are often analyzed. The production function Q = f(X 1,X 2) is said to be homogeneous of degree n, if given any positive constant k, f(kX 1,kX 2) = k n f(X 1,X 2). The Producer’s Minimum Cost Function. Pages Shephard, Ronald W. Preview Buy Chap95 € Dual Determination of Production Function from Cost Function. Pages Dynamics of Monopoly Under Homothetic Production Function. Pages Shephard, Ronald W.