- The decisions to vs. or vs. are closely related: ‘buy rent’ ‘use lease’ i.e. substitute ways of doing the same thing: this links prices and rental rates. Renting or Leasing Capital: - Say that the business firm rents or leases all of its capital (Kt). It also hires labour (Lt) and output is then determined by a production function F(Kt,Lt) with diminishing returns. - Assume competitive markets for inputs and output: the firm is a price taker i.e. the firm treats wages (wt), the rental price of capital (rKt) and the output price (pt) as exogenous (determined in the market). - Profit at time t (t) is then: = pt F(Kt,Lt) rKtKt - wtLt t – - problem is not dynamic in this case: each period the firm chooses Kt The firm’s and Lt to maximize profits. f.o.c. K: pt FK rKt=0 – (FK ≡∂F/∂K) L: pt FL wt=0 – (FL ≡∂F/∂L) these conditions can be solved for capital demand and labour demand. Then the output supply function can be found using the production function. Capital demand takes the form: K = K(wt,rKt,pt, production function parameters) - What is rK? rental or lease price of K: price charged by the owner of the capital to allow the firm to use it for one period.
- The decisions to ‘buy vs. rent’ or ‘use vs. lease’ are closely related: i.e. substitute ways of doing the same thing: this links prices and rental rates. Renting or Leasing Capital: - Say that the business firm rents or leases all of its capital (Kt). It also hires labour (Lt) and output is then determined by a production function F(Kt,Lt) with diminishing returns. - Assume competitive markets for inputs and output: the firm is a price taker i.e. the firm treats wages (wt), the rental price of capital (rKt) and the output price (pt) as exogenous (determined in the market). - Profit at time t (t) is then: t = pt F(Kt,Lt) – rKtKt - wtLt - The firm’s problem is not dynamic in this case: each period the firm chooses Kt and Lt to maximize profits. f.o.c. K: pt FK – rKt=0 (FK ≡∂F/∂K) L: pt FL – wt=0 (FL ≡∂F/∂L) these conditions can be solved for capital demand and labour demand. Then the output supply function can be found using the production function. Capital demand takes the form: K = K(wt,rKt,pt, production function parameters) - What is rK? rental or lease price of K: price charged by the owner of the capital to allow the firm to use it for one period.