notes_on_investment - Notes on Investment These notes are...

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Page 1 of 6 Notes on Investment These notes are meant for you to better understand the relationship between interest rates (r) and investment decisions (I). A few things before we begin : 1) Remember, investment in this class refers to the purchasing of plant, tools, machines, and equipment by firms. These resources are used as an input into production. * I is a flow variable (measured over time). * K is a stock variable (measured at a point in time). K is the capital stock in our production function. Formally, K is the sum of all past investment decisions (less any depreciation). 2) The capital stock next period is a function of how much we invest this period. If we invest more today, the capital stock tomorrow will be higher. As an identity (we will see this formula again in the Solow model, please try to understand it well): K(t+1) = (1- δ ) K (t) + I(t), where K(t+1) is the capital stock next period (in period t + 1), K(t) is the capital stock today (in period t), and δ is the depreciation rate on existing capital and I(t) is investment today (in period t). The equation above say that investing today raises the capital stock tomorrow. In other words, if you plan to buy a new machine today, it will be productive for you tomorrow (the delay is due to the fact that it takes time to build a new plant or install a new machine or train your workers to use the machine, etc.). How much capital should a firm have? In this class, we assume firms optimize. They are going to set the benefit of purchasing capital to the cost of purchasing capital. What is the benefit of purchasing capital? The extra benefit associated with one more unit of capital is the MPK. Recall that in last handout one example of MPK was: MPK = 0.3 A (L/K) 0.7
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Page 2 of 6 As K increases, MPK falls (law of diminishing marginal product of capital). The more machines you have – holding A and L fixed – the less additional production you can get from an additional unit of capital. If you buy another computer and you do not have a worker to use the computer, the computer has little effect on your firm’s productivity! Holding K constant, what increases the MPK? Technology (A) and workers (L). So, increasing A, increases the benefits of capital. All else equal, firms will want to invest more! What is the cost associated with purchasing capital? Basically, we are going to focus only on interest rates in this class (we will ignore the other parts of the user cost of capital – i.e., the depreciation rate and the maintenance costs). As interest rates increase, it is more expensive for firms to invest. Firms can get the funds to invest from two main resources: a) Loans b) Retained earnings. If the real interest rate increases, borrowing is more expensive.
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This note was uploaded on 06/07/2011 for the course ECON 1 taught by Professor Staff during the Spring '08 term at UPenn.

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notes_on_investment - Notes on Investment These notes are...

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