Chapter 19: Technology

Econ 301 W2026 Chapter 19 Technology Section H, MW, 4:15 p.m. - 5:30 p.m. Section K, F, 8:45 a.m.-11:30 a.m. Carol Lau A Producer's Problem In our remaining Chapters 19-22, we turn our focus to the supply side. We assume that the firm has only one goal-maximizing its profits. Other goals could include maximizing sales or exposure and incur a loss, at least temporarily, if it has a new product to launch. Similarities between the consumer optimization and the firm optimization: Consumer - Consumer is household Household has utility function - Household consumes x, and x₂ - Result = maximized utility; demands Firm - Consumer is the firm Firm has production function - Result = maximized profit; supplies Supply LR - Firm "consumes" workers and machinery (inputs) (2) Cost-minX ASR Differences: - Optimization for a firm can be solved in one step or in two steps. A results depend on market sheotype Haster, less insightful Supply LR - One:step: Profit-max, changes based on market structure (such as monopoly) - Chapter 20. -Two-step: Cost-min and then profit-max... this approach gives us cost functions/curves. Cost functions are independent of market structure-more insightful-Chapters 21 and 22. - Time frame -short run versus long run - a firm is likely to behave differently. Goose equations do not Change due to market Stricture Same results Inputs (≈ X1, X2 for households) We focus on two types of inputs, labour and capital. Two other general types of inputs are managerial abilities and natural resources. Type #1: Labour (L) X from previous ths -L refers to workers, which can be measured in hours of work, or units. - In subsequent chapters, we will see that the firm pays L the wage rate (w). P Type #2: Capital (K) X - K refers to physical capital, such as machinery, furniture, etc., which can be measured in units. - In subsequent chapters, we will see that the firm pays K owners the rental rate rate (r). (r). P 301 focus From the perspective of the firm, w and rare production costs; Cost=wL+rK.→00sts for forms From the perspective of Land K owners, w and rare income. m=WL+rk Income for Landk These two sides of the same coin will eventually enable us to take a more complete picture of the economy-the intro courses' circular diagram, or, in Econ 302, general equilibrium analysis. Technology (≈ preferences of households) In this chapter, we assume that the firm can hire as many Land K as it desires at the given w and r, respectively. Pip fixed wir fixed Similar to our consumer problem - the consumer can demand x, and x2 at the given constant p, and p₂. A consumer demanding more or less of x, (x2) cannot affect p₁ (p2). what are fired?) → Eg. F=10 our focus →(2) x= Loiskas However, the firm faces a constraint, especially in the short run. This constraint is the technological know-how. Therefore, the firm faces a production method constraint (such as internet speed, online security, skills of L, etc.) This is similar to the consumer's budget or income constraint; however, this constraint affects the production function of the firm. Production Function (≈ utility function of households) We can represent our verbal discussion by an equation - a production function. A production function shows the maximum output a firm can produce by hiring L and K, given current technological level. Technology determines the functional form of the production function (such as linear, quadratic, Cobb-Douglas, etc.) - similar to U function. Utility function: For a given utility level, different x, and x2 combinations. Example: U(x,, X2) = X, 0.8X20.2 Production function: For a given output level, different L and K combinations. Example: x₁(L, K) = L0.8K0.2 Isoquant (≈ indifference curve of households) In the consumer problem, we saw that an indifference curve (IC) traces out the different combinations of x, and x₂ that yield a given level of utility. Eg. 4-12 For a firm, we have an isoquant that traces out the different combinations of L and K that yield a given level of output. 7 combinations of Land KE X+12 X23 etc. Similar to utility functions, we also assume that production functions have the well-behaved properties of monotonicity (adding inputs yields more output) and convexity (weighted average of inputs yields more output)... let's skip them! Examples of Technology Case #1: Perfect substitutes -x₁(L,K)=L+KIC→ Eg. X=10 - Linear isoquant, firm hires the cheaper input, or hires both inputs if w = r_{c} K overline x approx overline x_{1} = 10 Case #2: Perfect complements - x_{1} * (L, K) = min\{L, K\} = TC - 74g*X_{1} = 10 K L - Kinked isoquant, firm has to hire a fixed number of L with a fixed number of K, cannot substitute. x_{4} = 10 Case #3: Cobb-Douglas - x_{1} * (L, K) = L ^ 0 * K ^ 0.2 >1c-7 epsilon g.x 1 =10 K L - Firm can substitute across Land K. overline X_{10} = 10 L_{2} Marginal Product (≈ MU of households) Similar to MU in the consumer problem, we can also derive the marginal product (MP) in the producer problem. For the producer, the hiring of an extra L gives rise to M*P_{L} units of additional output, holding K constant. 大 L 1,X i or partial x_{1} partial t >0 partial U partial x 1 = M*u_{1} partial x y partial L = M*P_{L} = (Delta*x_{y})/(Delta*L) "Law of diminishing MP"-each additional L gives us a bit smaller additional output. M*P_{L} falls as L rises. The second derivative is < 0 but M*P_{L} is still positive. partial^ 2 x 1 partial L^ 2 = partial MPL partial L <0 G → LT, XIT but xit shrinks as LT L