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# empirical cost function

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Palm Products Company has collected data on its average variable costs of production for the past 12 months. The costs have been adjusted for inflation by deflating with an appropriate price index. The AVC and associated output data are presented below:

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

a. Run the appropriate regression (below) to estimate the parameters for the empirical cost function:
AVC = a + bQ + cQ2

b. Using a 10 percent significance level test for the statistical significance of the parameters obtained in a, then discuss the suitability (considering their algebraic signs) of the parameter estimates.

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

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

e. (i) Compute AVC and SMC when Palm Products produces 20 units of output:
(ii) Is AVC rising or falling when Palm produces 20 units? Explain.

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