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3. In all of this question let p= 4,900 - 2 be a demand function where 0 sq < 70. (a) Show that the point) elasticity of demand satisfies the equation n+ 2 oil? - = 0. [5 points] (b) Is the (point) elasticity of demand elastic or inelastic when q = 42 ? (3 points) (c) Find the value (or values) of q for which the (point) elasticity of demand is unit. (4 points)
4. In all of this question let q> 0 represent quantity (i.e. number of units) of some product and 2250 let p > 0 represent unit price in $ per unit). Assume a demand function p= 400 – 50q+ __800 In(q +5) and an average cost function i= (a) State the profit function. [4 points] (b) Find the quantity that maximizes profit and calculate the maximum profit. Sufficiently justify your answer. (11 points)
3. In all of this question let q> 0 represent quantity (i.e. number of units) and p > 0 represent unit price (i.e. price per unit). Assume a demand function p = and an average cost 1 100 function cq) = + (a) Given that "profit = revenue - cost" find the profit function, F(q). [4 points) (b) Find the value of q that maximizes total profit and state the maximum profit. Sufficiently justify that your value actually maximizes the total profit function. [9 points) (c) Verify that "marginal revenue" = "marginal cost" at the value of q that maximizes total profit. [3 points)