K Use the price-demand equation x = f(p)=√552-8p to find the values of p for which demand is elastic and the values for which demand is inelastic. Assume that price and demand are both positive.

Why is the demand curve with constant unitary elasticity concave?

The Stopdecay Company sells an electric toothbrush for $25. Its sales have averaged 8,000 units per month over the past year. Recently, its closest competitor, Decayfigh ter, reduced the price of its electric toothbrush from $35 to $30. As a result, Stopde cays sales declined by 1,500 units per month. What is the arc cross elasticity of demand between Stopdecays toothbrush and Decayfighters toothbrush? What does this indicate about the relationship between the two products? If Stopdecay knows that the arc price elasticity of demand for its toothbrush is 1.5, what price would Stopdecay have to charge to sell the same number of units as it did before the Decayfighter price cut? Assume that Decayfighter holds the price of its toothbrush constant at $30. What is Stopdecays average monthly total revenue from the sale of electric toothbrushes before and after the price change determined in part (b)? Is the result in part (c) necessarily desirable? What other factors would have to be taken into consideration?

What does a price elasticity of demand of 0.39 mean?

(Calculating Price Elasticity of Demand) Suppose that 50 units of a good are demanded at a price of Si per unit. A reduction in price to $0.20 results in an increase in quantity demanded to 70 units. Using the midpoint formula, show that these data yield a price elasticity of 0.25. By what percentage would a 10 percent rise in the price reduce the quantity demanded, assuming price elasticity remains constant along the demand curve?

If supply is elastic, will shifts in demand have a larger effect on equilibrium quantity or on price?

If the price of a good or service increases and the total revenue received by the seller declines, is the demand for this good over this segment of the demand curve elastic or inelastic? Explain.

Explain why using the midpoint formula for calculating the elasticity of demand gives the same result whether price increases or decreases, but using the initial price and quantity instead of the average does not.

Prove that price elasticity of demand is not the same as the slope of a demand curve.

Using the following equation for the demand for a good or service, calculate the price elasticity of demand (using the point form), cross-price elasticity with good x and income elasticity. Q=82P+0.10I+Px Q is quantity demanded, P is the product price. P1 is the price of a related good, and I is income. Assume that P= $10, I = 100, and Px = 20.