COMM 220 Practice Problems 1

Transcription

1 COMM 220 RCTIC ROLMS 1. (a) Statistics Canada calculates the Consumer rice Index (CI) using a similar basket of goods for all cities in Canada. The CI is in Vancouver, in Toronto, and in Montreal. 1,250 sq. ft. apartment unit located in the downtown area is selling for $300,000 in Vancouver, $290,000 in Toronto, and $280,000 in Montreal. Which city has the highest real price of an apartment unit and which city has the lowest? (5 marks) Use the CI of Vancouver as the base: rice in Vancouver = $300,000 rice in Toronto = $290,000*(143.2 / 135.8) = $305, rice in Montreal = $280,000*(143.2 / 126.5) = $316, Or, use the CI of Toronto as the base: rice in Vancouver = $300,000*(135.8 / 143.2) = $284, rice in Toronto = $290,000 rice in Montreal = $280,000*(135.8 / 126.5) = $300, Or, use the CI of Montreal as the base: rice in Vancouver = $300,000*(126.5 / 143.2) = $265, rice in Toronto = $290,000*(126.5 / 135.8) = $270, rice in Montreal = $280,000 Or, use 100 as the common base for all cities: rice in Vancouver = $300,000*(100 / 143.2) = $209, rice in Toronto = $290,000*(100 / 135.8) = $213, rice in Montreal = $280,000*(100 / 126.5) = $221, Montreal has the highest real price of apartment unit while Vancouver has the lowest. (b) The price of long-distance telephone service fell from 25 cents per minute in 2000 to 10 cents per minute in The Consumer rice Index increased by 15-percent over this period. What is the percentage change in the real price of long-distance telephone service from 2000 to 2006? (5 marks) Let the CI for 2000 equals 100 and the CI for 2006 equals 115, which reflects a 15% increase in the overall price level. To find the real price of long-distance telephone service in each period, divide the nominal price by the CI for that year. For 2000, we have 25/100 or 25 cents, and for 2006, we have 10/115 or cents. The real price therefore fell from 25 cents to cents. % change in the real price of long-distance telephone service from 2000 to 2006 = ( ) / 25 = % 2. The Canadian government is interested in analyzing the domestic market for wheat. The staff economists estimate the following equations for the domestic supply and demand curve: Q D = Q S = Quantities are measured in millions of bushels and prices are measured in Canadian dollars per bushel. (a) Calculate the equilibrium price and quantity that will prevail in a completely free market, that is, a purely competitive market. (2 marks) Set Q D = Q S to find the equilibrium price and quantity: = = ( ) / ( ) = $4 per bushel Substitute = $4 into Q D to find Q: Q = (4) = 600 million bushels COMM 220 ractice roblems 1

2 Or, substitute = $4 into Q S to find Q: Q S = (4) = 600 million bushels (b) Calculate the price elasticities of supply and demand at the equilibrium price and quantity. (2 marks) S The price elasticity of supply, Q 4 = = (90) = 0.60 Q 600 D The price elasticity of demand, Q 4 = = (-70) = Q 600 (c) The government currently has a $5.00 per bushel support price in place. What impact will this support price have on the market? Will the government be forced to purchase wheat under the program that requires them to buy any surpluses? If so, how many bushels? nd how much? (4 marks) t = $5.00, Q S = (5) = 690 million bushels Q D = (5) = 530 million bushels Surplus = Q S Q D = = 160 million bushels Yes, the government will be forced to purchase 160 million bushels of wheat. The government will have to pay $800 millions ($5.00 x 160). (d) Illustrate part (a) and (c) on a graph. e sure to label your graph clearly. (2 marks) D Surplus S Q 3. Northern nergy Company is interested in obtaining quick estimate of the weekly supply and demand curves for coal. The firm s research department informs you that the price elasticity of supply is approximately 0.8, the price elasticity of demand is approximately 0.64, and the current price and quantity are $40 and 1280, respectively. rice is measured in C$ per ton and quantity is measured in tons per week. (a) stimate the weekly supply and demand curves at the current price and quantity. (5 marks) Given = $40 and Q = 1280, S Q 40 = = d = 0.8 d = 25.6 Q 1280 Substitute = 40, Q = 1280, and d = 25.6 into Q S = c + d, c = Q d = (40) = 256 So, Q S = Given = $40 and Q = 1280, D Q 40 = = b = -.64 b = Q 1280 Substitute = 40, Q = 1280, and b = into Q D = a b, a = Q + b = (40) = So, Q D = COMM 220 ractice roblems 2

3 (b) What impact would a 20% increase in weekly demand and a 10% decrease in weekly supply have on the equilibrium price and quantity? (5 marks) To find the new demand curve with a 20% increase, Q D = 1.2Q D = (1.2)*( ) = To find the new supply curve with a 10% decrease, Q S = 0.9Q S = (0.9)*( ) = quate Q D with Q S to find the new equilibrium price and quantity, = = ( ) / ( ) = $ per ton Substitute = into Q S to find Q, Q = ( ) = tons Or, substitute = $ into Q D to find Q: Q = ( ) = tons (c) What is the percentage change in the equilibrium price and quantity caused by the 20% increase in demand and 10% decrease in supply? (2 marks) ercentage change in price = ( ) / 40 = 20.16% ercentage change in quantity = ( ) / 1280 = 4.516% (d) Illustrate the supply and demand curves in part (a) and (b), and their equilibrium prices and quantities on the same graph. e sure to label your graph clearly. (3 marks) S S D D Q Suppose that the current price of a product is $30 per unit. t this price, 18,000 units will be sold. If the price is lowered to $24, sales will increase to 20,000 units. (a) What is the price elasticity of demand at $30 and at $24? (2 marks) D Q = = = = Q D Q = = = 0.4 Q (b) What is the arc elasticity of demand over the price range of $24 and $30? (2 marks) D Q (24+ 30)/ = = = Q ( )/2 6 COMM 220 ractice roblems 3

4 (c) Derive the equation for a linear demand curve. (2 marks) Q D = a + b a = Q D b = 18,000 ( 2,000 / 6)(30) = 28,000 Or, a = 20,000 ( 2,000 / 6)(24) = 28,000 Q D = 28,000 (2000/6) = 28, (d) What would happen to revenue if the price were to increase by 20% from $30? (3 marks) Revenue (=30) = 30 18,000 = $540,000 t = $36, Q D = 28, (36) = 16,000 Revenue (=36) = 36 x 16,000 = $576,000 Revenue goes up by $36,000 (i.e., +6.67%) when price is increased by 20% (e) What conclusion can you draw from the result of part (d)? (1 mark) When demand is price inelastic, increase in price will increase total revenue. 5. (a) Draw a representative indifference curve for each of the following individual s preference for beef (on the y-axis) and broccoli (on the x-axis): (4 marks) i. is a vegetarian who does not eat meat. ii. has a strong preference for broccoli. iii. C always consumes exactly one beef for every three broccolis. iv. D always gets four times as much satisfaction from one broccoli as he does from one beef. (i) (ii) eef eef roccoli roccoli (iii) (iv) eef eef roccoli roccoli (b) Discuss the shape of each indifference curve and relate it to the MRS of each individual. (6 marks) is a vegetarian. He only eats broccoli and does not care for beef, which means no amount of beef can compensate for the loss of a broccoli. The price of broccoli in terms of beef is infinite. s indifference curve is a vertical line. Hence, the MRS T =. COMM 220 ractice roblems 4

5 has a strong preference for broccoli, which means that is willing to give up many beef for one broccoli. The price of broccoli in terms of beef is large. s indifference curve is steep. Hence, the MRS T is large. C likes exactly one beef for every three broccolis, which means C likes the two goods in a specific combination. roccoli and beef are perfect complements. C s indifference curve is shaped as right angle. Hence, the MRS T = whenever there are more beef than broccoli, and the MRS T = 0 whenever there are more broccoli than beef. D always gets four times as much satisfaction from one broccoli as he does from one beef, which means the satisfaction obtained from an extra broccoli always equals to the satisfaction obtained from four extra beef. roccoli and beef are perfect substitutes. D s indifference curve is a straight line with a slope of 4. Hence, the MRS T = Mia spends her weekly income of $600 on two goods, and. Her utility function for consumption is given 2 3 by the expression of U (, ) =. The current prices of and are $3 and $5, respectively. (a) Write the expression for Mia s budget constraint. Graph the budget constraint and determine its slope. (3 marks) I I = + = - = = = Slope = 0.6 slope = -0.6 (80, 72) 200 (b) Determine the quantities of and that maximize Mia s utility given her budget constraint. Graph your answer. (6 marks) U(,) = MU = 2 and MU = 3 Utility maximization occurs when MUX MRS = = = = = or = 2 2 MU Y Substitute =10/9 into the budget equation 600 = to find the optimal and, = = 72 and = (72) = lternatively, we can find the optimal quantities of and as follows: First, find the demand curves of and in terms of their prices, = = or = Substitute =2 /3 into the budget equation 600 = + to find the demand curve of in terms of and substitute =3 /2 into the budget equation to find the demand curve of in terms of. COMM 220 ractice roblems 5

6 = = = = + = = 2 2 Then, plug the prices in the equations to find the optimal quantities: = 3, = 240/3 = 80 = 5, = 360/5 = 72 (c) Calculate the impact on Mia s optimum basket of a decrease in the price of to $2 and an increase in the price of to $6. What would happen to her utility as a result of these price changes? (6 marks) Decrease in price of to $2 and increase in price of to $6, change Mia s budget constraint: = 2+ 6 = 100 slope= 3 3 Utility maximization occurs when MU 2 2 MRS = = = = 2 MU 6 3 Sub =2 into the budget equation 600 = to find the new optimal and, 600= 2(2) + 6 = 60 and = 2( 60) = 120 Or, plug = 2 into = 240/ to find the optimal quantity of = 240/2 = 120, and = 6 into = 360/ to find the optimal quantity of = 360/6 = 60 t (80, 72), Mia s utility = (80) 2 (72) 3 = 2,388,787,200 t (120, 60), Mia s utility = (120) 2 (60) 3 = 3,110,400,000 Changes in prices of and ; increase Mia s utility to 3,110,400,000 from 2,388,787,200 (Note: Don t express the change in % because of ordinal ranking) 7. Jason is entirely indifferent between having two cups of coffee (C) or three cups of tea (T). (a) What can you say about Jason s marginal rate of substitution of tea for coffee? (2 marks) Jason s MRS TC can be defined as the number of cups of coffee he would be willing to give up in exchange for one cup of tea. Since he is always willing to trade two for three, his MRS TC = 2/3. (b) Draw a set of indifference curves for Jason. (3 marks) Coffee Since Jason is always willing to trade two cups of coffee for three cups of tea, his indifference curves are linear with a slope of 2/ Tea (c) Draw budget lines with different slopes and illustrate the satisfaction-maximizing choice. What conclusion can you draw? (5 marks) Jason s indifference curves are linear with a slope of 2/3. Jason s budget line is also linear, and will have a slope that reflects the ratio of the two prices. If the price of coffee is exactly 1-1/2 of the price of tea, the budget line will coincide with the indifference curve and Jason will be indifferent between any points on the budget line. If the price of coffee is more than 1-1/2 of the price of tea, or the price of tea is more than 2/3 of the price of coffee, Jason will always choose to consume only the relatively cheaper good, which results in a corner solution. COMM 220 ractice roblems 6

7 Coffee tea If coffee is relatively cheaper than tea, Jason will choose to consume If coffee costs exactly 1-1/2 as much as tea, the budget line will coincide with the indifference curve and Jason will be indifferent between any points on the budget line If tea is relatively cheaper than coffee, Jason will choose to consume COMM 220 ractice roblems 7