associated average variable cost (AVC) data

1. Consider you own a small restaurant business. You collected data on the average variable costs of your business for the past 12 months. You have been adjusted the cost data for inflation by deflating with an appropriate price index. Your output (Q) and the associated average variable cost (AVC) data are presented below:

Obs Q AVC
1 22 $208
2 31 202
3 31 206
4 25 214
5 41 174
6 41 203
7 45 172
8 45 158
9 45 173
10 62 170
11 62 152
12 70 175

a. Use the data to run the appropriate regression to estimate the parameters for the empirical cost function:

AVC a + bQ + cQ2

(Paste your computer printout here)

b. Using a 10 percent significance level, discuss suitability of the parameter estimates obtained in part a. Consider both the algebraic signs and statistical significance of the parameter estimates.

c. Present the estimated average variable cost, total variable cost, and short-run marginal cost functions.

d. At what level of output does AVC reach its minimum value? What is the minimum value of AVC at its minimum?

e. (i) Compute AVC and SMC when you produce 20 units of output.

(ii) Is AVC rising or falling when you produce 20 units? Explain.

f. At what level of output does SMC equal AVC? How did you get this answer?

2. Gaton, Inc. is a firm operating in a competitive market. The manager of Gaton forecasts product price to be $28 in 2010. Gaton's average variable cost function in 2009 is estimated to be

AVC = 10 - 0.003Q + 0.0000005Q2

Gaton expects to face fixed costs of $12,000 in 2010.
a. At what level of output will Gaton's average variable cost reach its minimum value?

b. What is the minimum average variable cost?

c. What is the profit-maximizing (or loss-minimizing) output for Gaton?

d. How much profit (loss) does the company expect to earn?

3. The market demand for a monopoly firm is estimated to be:

Qd = 100,000 - 500P + 2M + 5000PR

Where Qd is quantity demanded, P is price, M is income, and PR is the price of a related good. The manager has forecasted the values of M and PR will be $50,000 and $20, respectively, in 2010. (Hint: You need to first derive several functional relationships to be able to answer the question). The firm's AVC function is estimated to be:

AVC = 520 - 0.03Q + 0.000001Q2

In addition, fixed cost is estimated to be $4 million.
a. If the firm wishes to maximize profit, how many units should it produce in 2010?
b. What price should the firm charge for its output in 2010?

c. How much profit does the company expect to make in 2010.