1. Fill in the missing blanks (“XXXXXXXXXXX” means that there is nothing to fill in this spot): Quantity Total utility Marginal utility 0 0 XXXXXXXXXXX XXXXXXXXXXX XXXXXXXXXXX 200 – 0 = 200 1 200 XXXXXXXXXXX XXXXXXXXXXX XXXXXXXXXXX 150 2 200 + 150 = 350 XXXXXXXXXXX XXXXXXXXXXX XXXXXXXXXXX 125 3 350 + 125 = 475 XXXXXXXXXXX XXXXXXXXXXX XXXXXXXXXXX 575 – 475 = 100 4 575 XXXXXXXXXXX XXXXXXXXXXX XXXXXXXXXXX 665 – 575 = 90 5 665 XXXXXXXXXXX XXXXXXXXXXX XXXXXXXXXXX 735 – 665 = 70 6 735 XXXXXXXXXXX XXXXXXXXXXX XXXXXXXXXXX 50 7 735 + 50 = 785 XXXXXXXXXXX XXXXXXXXXXX XXXXXXXXXXX 40 8 785 + 40 = 825 XXXXXXXXXXX XXXXXXXXXXX XXXXXXXXXXX 800 – 825 = –25 9 800 XXXXXXXXXXX 2. Your willingness to pay for oranges is $5 per pound for the first pound, and decreases by $1 for each additional pound (i.e. $4 for the second pound). If you can purchase as many pounds of oranges you want at $1 per pound, what is your consumer surplus? CS1 = $5 – $1 = $4 CS2 = $4 – $1 = $3 CS3 = $3 – $1 = $2 CS4 = $2 – $1 = $1 CS5 = $1 – $1 = $0 Total CS is the sum of the five pounds purchased, or $10. 3. In a given country, if supply is represented by the equation P = 2Q, and demand is represented by the equation P = 12 – Q, what are the equilibrium price and quantity? Determine the new price and quantity equilibrium when a $1 tax is imposed on sellers. Without tax: Set 2Q = 12 – Q Î Q = 4 Î P = 8 With tax: New supply is P = 2Q + 1. Set 2Q + 1 = 12 – Q Î Q = 11/3 Î P = 25/34. Suppose that you plan on growing peas this summer in your back yard to supplement your income. Assume that you have already paid $20 to get the garden ready, that peas sell for $2 per pound, and that you can add fertilizer at a cost of $5 per pound. Based on the yield table below, how much fertilizer should you add to maximize your summer profit? Pounds of fertilizer Pounds of peas 0 20 1 30 2 35 3 38 4 39 5 39.5 6 39.75 To maximize, produce as long as MB ≥ MC. (Note that the $20 sunk cost is irrelevant here.) MB of 1st pound of fertilizer is 10 pounds of peas, or $20; 2nd pound, $10 (from 5 add’l pounds); 3rd pound, $6 (from 3 add’l pounds); 4th pound, $2 (from 1 add’l pounds); 5th and 6th pounds, < $2. MC = $5 per pound of fertilizer. Thus, add 3 pounds of fertilizer to maximize profits. You will see that profits are positive, and so you will not need to check the shutdown condition here. 5. From the information in the previous problem, what are your total summer profits? Total benefit, 38 pounds of peas, or $76 Total cost, $20 + 3 μ $5 = $35 Total profit, $76 – $35 = $41 6. If supply shifts to the left and demand shifts to the right, what can you conclude about the new equilibrium price and quantity, relative to the old equilibrium? Shift to the left in supply (keeping demand the same) increases P and reduces Q. Shift to the right in demand (keeping supply the same) increases both P and Q. Thus, P will definitely increase, but we cannot say anything conclusively about Q. 7. When the price of tennis balls increases, what would you expect to happen to the supply and demand of tennis rackets? In this case, we can probably assume that tennis balls and tennis rackets are complements. Thus, when the price of tennis balls increases, the cost of playing tennis increases, and so the demand for tennis rackets will shift to the left. There is no indication about anything that changes the supply of tennis rackets, and so the supply does not change.8. From the information in Problem 3, what would be the excess supply if a price floor is set at $10? What happens if the price floor is set at $4? In each case, compare consumer and producer surplus to equilibrium without price floors. (Assume no taxes.) In Problem 3, Q = 4 and P = $8. In this case, PS is a triangle that is 4 units long and 8 units high, leading to PS of $16. CS is a triangle that is 4 units long and 4 units high, leading to a CS of $8. A price floor is a minimum price that has to be received. So when the price floor is $4, the market still clears, since equilibrium is above the price floor. When the price floor is $10, quantity supplied is 5, and quantity demanded is 2. So there is an excess supply of 3 units. In this case, PS is a trapezoid that is 2 units “high” and has bases of “length” 10 and 6.1 Since the area of a trapezoid is the height times the average of the bases, PS is $16 (at most, since there is no guarantee that low-cost suppliers will supply). CS is a triangle that is 2 units long and 2 units high, leading to a CS of $2. 9. If price elasticity of demand for peanuts is 4 (in absolute value) and an increase in percentage change in quantity demanded is 5 percent, how much does price change? Elasticity = %DQ / %DP Î 4 = 0.05 / %DP Î Price change is 1.25%. Since quantity demanded goes up and slope is negative, the price drops 1.25%. 10. Assume that there is a linear demand curve with vertical intercept at price $10 and horizontal intercept at quantity 20. What are the price elasticities of demand when price is $8, $6, $4, and $2? Recall that elasticity can be expressed as P / (Q μ slope). Based on the two intercepts, there is a rise of 10 and a run of 20, leading to a slope of 0.5. Thus, demand can be represented by P = 10 – 0.5 μ Q. P = $8 Î Q = 4 Î elasticity is 4 P = $6 Î Q = 8 Î elasticity is 1.5 P = $4 Î Q = 12 Î elasticity is 2/3, or about 0.67 P = $2 Î Q = 16 Î elasticity is 0.25 11. From the information in the previous question, at what price and quantity will total expenditures be maximized? The midpoint between the intercepts is the point of elasticity equal to 1. This occurs when P is $5 and Q is 10. 12. If two individuals have demand curves represented by P = 10 – Q and P = 20 – 2Q, what is the total demand? (Notes: Assume that quantity demanded is never negative. Graphing the total demand may be easier than representing it algebraically.) To represent the demand algebraically, note that when P > 10, only the second individual has a positive demand. When P < 10, we add the quantities demanded. So P ≥ 10 Î …