Question

a. How much would the firm’s revenue change if it lowered price from $12 to $10? Is demand elastic or inelastic in this range? Revenue change: $ -3.66 -3.66 Incorrect Demand is elastic Correct in this range b. How much would the firm’s revenue change if it lowered price from $4 to $2? Is demand elastic or inelastic in this range? Revenue change: $ 20 20 Incorrect Demand is inelastic Correct in this range c. What price maximizes the firm’s total revenues? What is the elasticity of demand at this point on the demand curve? Price that maximizes total revenues: $ 7 7 Correct Demand is unitary elastic Correct at this point

Answer 1

Solution -

a. When P = $12, R = ($12)(1) = $12. When P = $10, R = ($10)(2) = $20. Thus,the price decrease results in an $8 increase in total revenue, so demand iselastic over this range of prices.

b. When P = $4, R = ($4)(5) = $20. When P = $2, R = ($2)(6) = $12. Thus, theprice decrease results in an $8 decrease in total revenue, so demand is inelasticover this range of prices.

c. Recall that total revenue is maximized at the point where demand is unitaryelastic (meaning elasticity is -1). We also know that marginal revenue is zero atthis point. For a linear demand curve, marginal revenue lies halfway between thedemand curve and the vertical axis. In this case, marginal revenue is a line starting at a price of $14 and intersecting the quantity axis at a value of Q = 3.5.Thus, marginal revenue is 0 at 3.5 units, which corresponds to a price of $7