The firms in this economy own productive capital and hire labour to produce

The firms in this economy own productive capital and

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ultimately focus on the choices of a single, representative firm. The firms in this economy own productive capital and hire labour to produce consumption goods. We can describe the production technology available to each firm by a production function. This will describe the technological possibilities for converting factor inputs into outputs. The production function can be expressed as: Y = zF(K, N d ), where z is total factor productivity, Y is output of consumption goods, K is the quantity of capital input in the production process, N d is the quantity of labour input measured as total hours worked by employees of the firm, and F is a function. Because this is a static model, we treat K as being a fixed input to production, and N d as a variable factor of production. In the short run, firms cannot vary the quantity of plants and equipment ( K ) they have, but they have flexibility in hiring and laying off workers ( N d ). Total Factor productivity, z , captures the degree of sophistication of the production process. An increase in z makes both factors of production, K and N d , more productive, in that, given factor inputs; higher z implies that more output can be produced. The marginal product of a factor of production is the additional output that can be produced with one additional unit of that factor input, holding constant the quantities of the other factor inputs. Five key properties of the production function: 1. Constant returns to scale 2. Output increases with increases in either labour input or capital input 3. The marginal product of labour decreases as the labour input increases 4. The marginal product of capital decreases as the capital input increases 5. The marginal product of labour increases as the quantity of the capital input increases Production Function, Fixing Quantity of Capital and varying Quantity of Labour
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The marginal product of labour is the slope of the production function at a given point. The marginal product of labour declines with the quantity of labour. If all factor inputs are changed by a factor x , then output changes by the same factor x . For example, if all factor inputs double, then output doubles. The alternatives to constant returns to scale in production are increasing returns to scale and decreasing returns to scale. Increasing returns to scale implies that larger firms are more efficient than smaller firms as they produce larger quantities of output. Decreasing returns to scale thus implies that smaller firms are more efficient. Given a constant returns to scale production function, the economy behaves in exactly the same way if there were many small firms producing consumption goods as it would if there were a few larger firms, provided that all firm behave competitively. Production Function, Fixing Quantity of Labour and Varying Quantity of Capital The slop of the production function is the marginal product of capital, and the marginal product of capital declines with the quantity of capital. Thus the production function has the property that output increases when either the capital input or the labour input increases. In other words, the marginal
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