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3. Consider the following regression log(c)=0+1log(q)+2log(q)2+u Where c is cost of a firm, and q is the output of the firm. The regression result is log(c)=0.06+0.54log(q)0.03log(q)2(0.13)(0.20) The sample includes observations from 100 firms. (a) Calculate cost elasticity. (Hint: cost elasticity is percentage change in cost corresponding to one percent change in output). Write your answer in terms of q. (b) Is the relationship between log (c) and log(q)U-shaped, linear, or reverse U-shaped? Explain. (Hint: discuss the significance of 1 and 2. (c) Suppose q=10.5. Calculate mean and standard error of cost elasticity (you can use your answer in (a)). Is cost elasticity larger than 1 or smaller than 1? Explain. (d) (Extra credit) Show that the minimum average cost occurs at the outout level q^=exp[(1^1)/2^2] and calculate its 95% confidence interval. You can derive it analytically or generate it by simulation