Microeconomics 2 John Hey

Supply: the firm Firms have to decide (at least) two things: (1) How to produce and (2) How much to produce. (If a monopolist or an oligopolist also the price – chapters 28 and 31). How to produce: Chapter 11 - Cost minimisation and the demand for factors. Chapter 12: Cost curves (preliminary to chapter 13) How much to produce: Chapter 13 – Supply. Note that there is some ‘homework’ at the end of this presentation.

Rating the lectures Lecture 10 (technology): no stars Lecture 11 (how to produce): * Lecture 12 (cost curves): ** Lecture 13 (supply): *** Lecture 14 (ppfs): **** Lecture 15 (prod n & exchange): ***** Lecture 16 (empirics): ****** but tough

Chapter 11 In Chapter 10 we introduced the idea of an isoquant – the locus of the points (in the space (q 1,q 2 ) of the quantities of the inputs) for which the output is constant. Also the production function: y = f (q 1,q 2 ) where y denotes the output. An isoquant is given by: y = f (q 1,q 2 ) = constant.

Particular cases of technology Perfect substitutes 1 to a: isoquants are straight lines with slope a. Perfect complements 1 with a: isoquants are L-shaped and the line joining the corners has slope a. Cobb-Douglas with parameter a: isoquants are smoothly convex everywhere. CES with parameters c 1, c 2, ρ and s: isoquants are smoothly convex everywhere.

Two dimensions The shape of the isoquants: depends on the substitution between the two inputs. (We call the magnitude of the slope of an isoquant the marginal rate of substitution between the inputs). The way in which the output changes from one isoquant to another – depends on the returns to scale.

Returns to scale with Cobb- Douglas technology : examples Case 1: f(q 1,q 2 ) = q q Constant returns to scale. Case 2: f(q 1,q 2 ) = q q Decreasing returns to scale. Case 3: f(q 1,q 2 ) = q q Increasing returns to scale. Note: the ratio of the exponents is the same – hence the shape of the isoquants is the same – but they have different returns to scale.

Chapters 11, 12 and 13 We assume that a firm wants to maximise its profits. We start with a small firm that has to take the price of its output and those of its inputs as given and fixed. Given these prices, the firm must choose the optimal quantity of its output and the optimum quantities of its inputs.

Chapters 11, 12 and 13 We do the analysis in stages… …in Chapter 11 we find the optimal quantities of the inputs – given a level of output. …in Chapter 12 we develop the idea of a cost function, which enables us......in Chapter 13 to find the optimal quantity of output. (Recall that we are assuming that all prices are given.)

Chapter 11 So today we are finding the cheapest way of producing a given level of output at given factor (input) prices. This implies demands for the two factors which are obviously dependent on the ‘givens’ – namely the level of output and the factor prices. If we vary these ‘givens’ we are doing comparative static exercises. The way that input demands vary depends upon the technology.

Notation We use the following notation: y for the level of the output. p for the price of the output. w 1 and w 2 for the prices of the inputs. q 1 and q 2 for the quantities of the inputs. We define an isocost by w 1 q 1 + w 2 q 2 = constant …this is a line with slope –w 1 /w 2 Let’s go to Maple…

How to produce The optimal combination of the inputs is given by the condition: The slope of the isoquant at the optimal point must be equal to to the relative prices of the two inputs. (MRS=w 1 /w 2 ) This assumes that the isoquants are strictly convex. Rather obviously, the output must be equal to the desired output.

Conclusions The demand curve for an input is a function of the prices of the inputs and the desired output. The shape of the demand function depends upon the technology. From the demand functions we can infer the technology of the firm. Before you go, some homework...

Homework CES technology with parameters c 1 =0.4, c 2 =0.5, ρ=0.9 and s=1.0. The production function: y = ((0.4q )+(0.5q )) -1/0.9 In the next slide I have inserted the isoquant for output = 40 (and also that for output=60). I have inserted the lowest isocost at the prices w 1 = 1 and w 2 = 1 for the inputs. The optimal combination: q 1 = q 2 = and the cost = =

What you should do Find the optimal combination (either graphically or otherwise) and the (minimum) cost to produce the output for the following: w 1 = 2 w 2 = 1 y=40 w 1 = 3 w 2 = 1 y=40 w 1 = 1 w 2 = 1 y=60 w 1 = 2 w 2 = 1 y=60 w 1 = 3 w 2 = 1 y=60 Put the results in a table.

Chapter 11 Goodbye!