Suppose a production function is q = K^1/2L^1/3 and in the short run capital (K)is fixed at 100. If the wage is $10 and the rental rate on capital is $20,the short run average cost is A) $\frac { 2,000 } { q } + \frac { q ^ { 2 } } { 100 }$ B) $\frac { 200 } { q } + 10 q ^ { 2 }$ C) $\frac { 2,000 } { q }$ D) $q ^ { 2 }$

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The short-run average cost (SAC) in production economics includes both fixed costs and variable costs. Fixed costs are those that do not change with the level of output, such as the rental rate on capital when the capital is fixed. Variable costs change with the level of output, such as costs associated with labor if labor is the variable input. The SAC can be represented as the sum of average fixed costs (AFC) and average variable costs (AVC). Given that capital (K) is fixed at 100 and the rental rate on capital is $20, the total fixed cost (TFC) is 100 * $20 = $2,000. The AFC is TFC divided by quantity (q), which is $2,000 / q. Without specific information on the variable costs or the functional form relating output to labor input, we cannot directly calculate the AVC or the part of the SAC that varies with q. However, the given option A, $\frac { 2,000 } { q } + \frac { q ^ { 2 } } { 100 }$, correctly represents a structure where there's a component that decreases with increasing q (representing the spreading out of fixed costs over more units) and a component that increases with q, possibly representing increasing variable costs with output. This structure is consistent with typical short-run average cost curves in economics.

Suppose a Production Function Is Q = K1/2L1/3 and in the Short

Suppose a Production Function Is Q = K^1/2L^1/3 and in the Short