Zeta Inc has estimated its short-run cost function with the following regression, where total cost is the dependent variable, and quantity and quantity squared are the independent variables:

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.9599844
R Square	0.94157005
Adjusted R Square	0.9291615
Standard Error	38.8941172
Observations	200
ANOVA
		SS	MS	F
Regression		124426.3335	62213.17	41.12581
Residual		10589.26649	1512.752
Total		135015.6
	Coefficients	Standard Error	t Stat	P-value
Intercept	175.856917	36.56482377	4.8099667	0.002512
q	-10.753767	2.21933182	-4.85827	0.003159
q2	1.4530907	0.377353691	3.854424	0.005742

1. What is the cost function for the firm?
2. What are the MC and AC functions? Draw a general graph of these.
3. At what quantity does AC reach a minimum (MES quantity)? What is the AC at that MES? If Zeta is currently producing 20 units, what is the index of scale economies? What would you recommend for Zeta to reduce AC?
4. New regulations require Zeta to use a more environmentally friendly input, raising total costs by $5 per unit. What is the percentage increase in AC at MES as a result?