(a) Let the demand function for a good be   

                             q = A p^α y^β

where q =  the quatity demanded, p = the price per unit and y = the income. What do the parameters α  and β imply and what is the sum of α and β ? Interpret your result. 

(b) Consider the utility function u = log x₁ + x₂  which is to be maximized subject to the budget constraint m = p₁x₁ + p₂x₂ , where p₁ and p₂ are the prices per unit of the goods x₁ and x₂ respectively, and m is the income of the consumer. Derive the demand for x₁ and x₂ and interpret your results.

(c) Given the demand function and total cost function of a perfectly competitive firm as p = 32 - X, c = X² + 8X + 4, p being price, c being cost and X = output.

Find out the output, price, profit and total revenue corresponding to maximization of total profit.

(300 words) (8+10+7=25 Marks)