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)

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7. The demand equation for a certain product is q= 500 - D. Find the point elasticity of demand when p = 400. Is the demand elastic, inelastic or does it have unit elasticity? A = -0.5, inelastic B n= -2, elastic © n =-1, unit elasticity D2=-2, inelastic None of these

5. (a) Assume p = f(q) = (q + 3)e-9 is a demand function where q> 0 is quantity. Find all values of such that the (point) elasticity of demand is elastic. [9 points) (b) In this question assume all money is in units of $1,000's. An initial investment of 47 in a small business is guaranteed to produce the following cash flows: 5 at the end of Year 1; 14 at the end of Year 2; F at the end of Year 4. Interest is 4% APR compounding quarterly. The letter F represents the cash flow pay- ment amount that makes the business "neutral" (i.e. the business has no loss and no profit). Solve for F. [5 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)

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