E303

Davis, Spring 2006

Problem Set #11

1.  Characterizing Cost Functions Analytically. Consider the Cost function

TC = 100 +10Q + Q2

  1. What are the fixed costs for this relationship? What are Variable Costs?

Fixed Costs: ____100______

Variable Costs: _10Q + Q2 ______

  1. What is the marginal cost function?

Marginal Cost: ___10+2Q______

  1. Identify Expressions for Average Variable and Average Total Cost

Average Variable Costs: __ 10+Q______

Average Total Costs: ____ 100/Q + 10 + Q______

  1. Finally, identify the output levels where AVC and ATC are minimized.

AVC min: ___0______

100/Q + 10 + Q = 10 + 2Q

100/Q = Q

ATC min: _Q = 10______

2. Sunk Cost vs. Fixed Cost: Radio broadcaster CoolPlay Inc., paid $50,000 for an operating license last year, and the company is not meeting its advertising revenue expectations. Currently, they company is taking in $6,000 per month in revenues and has $5,000 per month in variable expenses. What difference does it make to CoolPlay if the license is transferable (e.g., resalable) or not? Under which condition would CoolPlay remain in the market longer (resalable or not resalable?)

Difference ___If the license is nontransferable, it is a sunk costs.

Condition Under Which CoolPlay will remain in the market longer?

Saleable/ Not Resalable (Circle one)
3. Long Run Costs for the Firm. Consider the following long run cost curve.

a. On the figure to the left, identify the range of the LRAC where the firm enjoys economics of scale What factors might allow a firm to enjoy economies of scale?

Reasons for scale economies: __Gains from specialization. Physical relationships

b. Identify the range of the LRAC where the firm suffers diseconomies of scale. What factors would result in diseconomies of scale

Reasons for diseconomies of scale: Transportation Costs, Managerial Inefficiency (‘Crowding’)

c. What is MES on the above figure? Suppose that at an average cost of $10 per unit demand is such that the industry could sell 40 units. What is the maximum number of firms that are sustainable in this market? Why?

Maximum number of sustainable firms: __If MES is 4, the industry could suppose 10 firms (students might see MES at 3 units as well.) Firms must operate at MES to efficiently survive.

4. Returns to Scale. Jake’s Free Runoff Bottled Water Company Produces with the Long Run Production Function

Q = (KL)2/3

Currently K = 4 and L = 4. If Jake’s doubles inputs to K=8 and L=8, will it realize increasing, constant or decreasing returns to scale (circle one)?

As a result, does Jake’s enjoy economies of scale, diseconomies of scale, or does Jake’s appear t be operating at Efficient Scale? (circle one)