Question

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

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.

Key concepts

Long-Run Average Cost Curve

A long-run average cost (LRAC) curve helps to understand how costs change as a firm's scale of operation grows. It's a U-shaped line on a graph, representing how the average cost per unit tends to decrease, reach a low point, and then increase again with larger production volumes.

Initially, as the production scale increases, average costs go down due to better resource management. This part of the curve shows economies of scale, where bigger operations help save on costs. However, beyond a certain point, the cost benefits start to disappear.

• At the lowest point of the curve, the firm achieves the "minimum efficient scale," where it efficiently balances cost and production.
• Once past this point, increasing production actually increases costs, a phenomenon known as diseconomies of scale.

The LRAC curve is therefore crucial for firms, including investment funds, to determine their optimal size for cost efficiency.

Minimum Efficient Scale

Minimum efficient scale (MES) is the sweet spot on the cost curve where a company operates most efficiently. It occurs at the lowest point of the long-run average cost curve, where firm costs per unit are minimized and production is most cost-effective.

Reaching the MES means using all resources optimally. Firms aim to achieve this scale to ensure their competitiveness while keeping costs down. At this scale:

• Firms fully utilize their production capabilities.
• Costs per unit are at their lowest.
• Firms can safely grow, knowing they won't incur additional unnecessary costs.

For an investment fund, hitting the MES allows it to maximize returns for investors by minimizing overhead and maximizing efficiency. It's a delicate balance where expansion continues to pay off without overburdening costs.

Diseconomies of Scale

Diseconomies of scale occur when a firm's costs increase with further production beyond a certain point. It's the opposite of economies of scale and causes the long-run average cost curve to rise after reaching the minimum efficient scale.

As firms grow excessively, they become less efficient due to factors such as:

• Complex management structures leading to communication breakdowns.
• Increased operational complexity, causing inefficiencies.
• Duplication of roles or mismanagement of resources.

For investment funds, diseconomies of scale mean that expanding beyond the optimal size results in lower returns for investors. The goal is to stay within a size that allows them to manage funds effectively, ensuring returns are maximized without unnecessary cost increases.

Constant Returns to Scale

Constant returns to scale occur when an increase in inputs results in a proportional increase in output. This concept is key to understanding how some investment funds can grow effectively without changes in efficiency.

In practice, this means:

• Doubling inputs such as time, labor, or capital results in a doubling of output.
• Maintaining the balance of production efficiency through consistent resource management.
• Investment funds can expand as long as their operational efficiency remains constant, ensuring costs and returns scale in step.

This period of constant returns to scale appears on the long-run average cost curve as a horizontal stretch. It indicates that the firm is operating efficiently, and increases in production or fund size will not adversely impact its profitability.