Chapter 11: Problem 6

In describing the optimal size of an investment fund, a writer for the Wall Street Journal observed: … at first, bigger is better for both investors and managers…. Managing money is expensive. Small funds have many fixed costs…. If a fund is small, it can’t generate enough fees to cover costs…. The result is that in terms of performance, funds should want to get big to cover costs and maximize returns, but not so big that diseconomies of scale erode returns. Draw a graph of a long-run average cost curve for a typical firm in the investment fund industry. In your graph, draw and label the following. a. A short-run average total cost curve for an investment fund that has not reached minimum efficient scale b. A short-run average total cost curve for an investment fund that has reached minimum efficient scale c. A short-run average total cost curve for an investment fund that experiences diseconomies of scale d. A range of output within which investment funds experience constant returns to scale

Short Answer

Expert verified

The exercise solution involves drawing a U-shaped LRAC curve and three SRATC curves. SRATC1, sitting entirely above LRAC, represents an investment fund not yet reaching MES. SRATC2, tangentially touching the LRAC at its minimum point, represents a fund at MES. SRATC3, initially intersecting LRAC from below and then remaining above, shows diseconomies of scale. A horizontal line from the lowest point of LRAC to the right indicates the output range for constant returns to scale.

Step by step solution

Define the terms

First, let's define the relevant terms:\n\n1. Minimum Efficient Scale (MES) is the point on the cost curve where the company has fully exploited all its production capacity to achieve the lowest possible cost per unit.\n\n2. Diseconomies of scale occur when a firm's costs per unit increase as it produces more.\n\n3. Constant returns to scale occur when the increase in output is proportionate to the increase in inputs.

Draw and Label the Long-Run Average Cost Curve

Start by drawing a U-shaped Long-Run Average Cost (LRAC) curve, representing a typical firm in the investment fund industry. Label this graph as LRAC. The U shape indicates that the cost per unit decreases at first due to operations efficiency (economies of scale), reaches a minimum point (minimum efficient scale) and then increases because of diseconomies of scale.

Draw the Short-Run Average Total Cost Curve for Unreached Minimum Efficient Scale

Draw a Short-Run Average Total Cost (SRATC) curve that sits entirely above the LRAC curve, except at the point where it tangentially touches the LRAC curve. This curve depicts a fund that has not yet achieved its MES. Label this curve as SRATC1.

Draw the Short-Run Average Total Cost Curve for Reached Minimum Efficient Scale

Next, draw another SRATC curve that tangentially touches the LRAC curve at its minimum point, indicating that the firm has achieved its MES. Label this curve as SRATC2.

Draw the Short-Run Average Total Cost Curve for Diseconomies of Scale

To show diseconomies of scale, draw another SRATC curve that intersects the LRAC curve from below and then remains above the curve. Label this SRATC3.

Indicate the range for constant returns to scale

Finally, to depict the range of output within which investment funds experience constant returns to scale, draw a straight horizontal line starting from the minimum point on the LRAC curve and extending to the right.