True or False? 1. When total profit is maximized, marginal profit is equal to zero. Similarly, when total revenue is maximized, marginal revenue is equal to zero. 2. In general, consumer surplus increases as the price of a good decreases. 3. At the output level where total revenue is maximized, price elasticity of demand is equal to zero. 4. At quantities corresponding to the elastic portion of the inverse demand curve, the total revenue curve slopes up.
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- (Categories of Price Elasticity of Demand) For each of the following absolute values of price elasticity of demand, indicate whether demand is elastic, inelastic, perfectly elastic, perfectly inelastic, or unit elastic. In addition, determine what would happen to total revenue if a firm raised its price in each elasticity range identified. Absolut Value Elasticity Effect of Price Increase a b c d1. Suppose that the demand curve for a good is given by D(P) = 100/P, what price will maximize revenue? 2. If D(P)=12 -2P, what price will maximize revenue? 3. If the market demand curve is D(p) = 100 - 0.5P, what is the inverse demand curve? 4. Show that when the elasticity of demand is equal to one, the marginal revenue of producing an extra unit of a good is zero.An end-of-aisle price promotion changes the price elasticity of a good from −4 to −5. Suppose the normal price is $48, which equates marginal revenue with marginal cost at the initial elasticity of –4. What should the promotional price be when the elasticity changes to –5? (Hint: In other words, what price will equate marginal revenue and marginal cost?) a. $27.00 b. $45.00 c. $36.00 d. $31.50
- Can you assist with questions 2 and 3 please. (2) The price p (in dollars) and the quantity q sold of a certain product obey the demand equation q=800-20 and 0 ≤ p ≤ 40 (i) Express the revenue R as a function of q. (ii) What is the revenue if 20 units are sold? (iii) What quantity q maximizes revenue? What is the maximum revenue? (iv) What price should the company charge to maximize revenue? (v) What price should the company charge to earn at least $3500 in revenue? (3) You are an accountant for a manufacturer of radios. The demand function for the tablets is 2 p x = 40-4x2 where x is the number of tablets produced in millions. It costs the company $15 to make a tablet. (i). Write an equation for the manufacturer’s profit as a function of the number of tablets produced. (ii). The company currently produces 1 million 2tablets and makes a profit of $21,000,000, but you would like to scale up production a bit. What greater number of tablets could the company produce to…A firm produces a steel bar. When the price of the steel bar is $ 30,000, the quantity demanded is 8 metric tons, a 100% change in the price would change the quantity demanded by 25%. 1. What is the price function of demand of the firm? 2. What is the total revenue function of the firm? 3. At what production output should the firm produce to maximize its total revenue?The market supply and demand for a product are shown in the diagram below. Is the price elasticity of supply less than one, equal to one, or greater than one? Explain. Calculate consumer surplus at the equilibrium price. Show your work. Now suppose the government imposes a per-unit tax of $1 on producers. What happens to total revenue received by producers after they pay the tax to the government? Explain. Will producer surplus increase, decrease, or stay the same? Will total surplus increase, decrease, or stay the same? Explain.
- Suppose the following data represent the market demand for catfish: Price (per unit) $20 19 18 17 16 15 14 13 12 11Quantity demanded (units per day) 12 13 14 15 16 17 18 19 20 21Total revenue — — — — — — — — — —Marginal revenue — — — — — — — — — —Compute total and marginal revenue to complete the table above. At what rate of output is total revenue maximized? At what rate of output is MR less than price? At what rate of output does MR first become negative? Graph the demand and MR curves.Economics 1 If the elasticity of demand for a product is -0.2, the demand curve is relatively ________ and an increase in price will _______ total revenue. Group of answer choices steep; increase flat; increase 2 If the elasticity of demand for a product is -2, the demand curve is relatively ________ and an increase in price will _______ total revenue. Group of answer choices steep; increase flat; decrease steep; decrease flat; increase flat; decrease steep; decreaseA firm sells two goods (X and Y) that are related in consumption. The estimated demand and cost conditions are: PX = 20 − 0.1QX− 0.05QY PY = 70−0.3QY−0.1QX MCX = 1 + 0.1QX MCY = 2 + 0.25QY MRX = 20 − 0.2QX− 0.05QY MRY = 70 −0.6QY− 0.1QX What are the profit-maximizing levels of output for the two goods? a. QX = 51, QY = 74 b. QX = 41, QY = 24 c. QX = 20, QY = 10 d. None of the choices are correct e. independent
- The demand curve for product a is given as Q = 2000 - 20P. a. How many units will be sold at $10? b. At what price would 2,000 units be sold? 0 units? 1,500? c. Write equations for total revenue and marginal revenue (in terms of Q). d. What will be the total revenue at a price of $70? What will be the marginal revenue? e. What is the point elasticity at a price of $70? f. If price were to decrease to $60, what would total revenue, marginal revenue, and point elasticity be now? g. At what price would elasticity be unitary?Suppose there are three types of Apples A, B, and C being sold and consumed. The demand and supply equations for each type are: DA = 20-2PA+4PB+PC SA = 4PA-5 DB = 10+3PA-5PB+2PC SB = 3PB-7 DC = 70+4PA+2PB-5PC SC = 5PC-16 Determine equilibrium prices and quantities using Cramer's rule. Calculate the elasticity of demand for B with respect to prices of variety A, B, and C and interpret the economic meaning of the results.(Price Elasticity and Total Revenue) Fill in the blanks for each price-quantity combination listed in the following table. What relationship have you depicted? Price P Q Elasticity Total Revenue $9 1 $8 2 ________ ___________ $7 3 ________ ___________ $6 4 ________ ___________ $5 5 ________ ___________ $4 6 ________ ___________ $3 7 ________ ___________ $2 8 ________ ___________
