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c295_assign1_2008_sol

# c295_assign1_2008_sol - Commerce 295 Sections 101-106 FRE...

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1 Commerce 295: Sections 101-106 FRE 295: Sections 001 and 002 Fall 2008 Solution to Assignment 1 Assigned: Sept. 22/Sept. 23 Due: Oct. 1/2 (See comment 2 below.) 1. Suppose that the monthly demand function for apples in Canada is given by Q D = 100 – 2P a + 0.5P o + 0.01Y where P a is the price of apples, P o is the price of oranges and Y is monthly average income. Suppose that the monthly supply function is given by Q S = 50 + P a – 2P f where P f is the price of fertilizer mix. a) Initially, P o = 20, Y = 4000, and P f = 10. Derive algebraic expressions for the demand curve and the supply curve by substituting these values into the equations for the demand function and the supply function. (3 pts). Q D = 100 – 2P a + 0.5P o + .001Y = 100 – 2P a + 0.5(20) + .01(4000) = 100 – 2P a + 10 + 40 = 150 – 2P a (2 pts) Q S = 50 + P a – 2P f = 50 + P a – 2(10) = 30 + P a (1 pt) b) Illustrate the curves derived in part a) on a diagram, and show and calculate the equilibrium price and quantity. (Also show the intercepts.) (3 pts) Should show intercepts and equilibrium quantities. (1 pt) To find the equilibrium price we can equate quantity supplied to quantity demanded. Q D = Q S => 150 – 2P a = 30 + P a (1 pt) Therefore 3P a = 120 so P a = 40. D S

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2 To obtain the associated quantity we substitute this price into either the demand curve or the supply curve. Using the supply curve we get Q = 150 – 2P a = 150 – 2(40) = 150 – 80 = 70. = 150 – 2P a c) Suppose now that the price of oranges rises to 32. Derive the new equilibrium price and quantity. Illustrate the solution on a diagram, showing the old demand curve and the new one. Explain in words why an increase in the price of oranges would affect the price of apples in this way. (3 pts) 1 pt for diagram Show the intercepts on both demand curves Q D = 100 – 2P a + 0.5P o + .001Y = 100 – 2P a + 0.5(32) + .01(4000) = 100 – 2P a + 16 + 40 = 156 – 2P a (1 pt) Q D = Q S => 156 – 2P a = 30 + P a so P a = 126/3 = 42. Using the demand curve, Q = 156 – 84 = 72. (1 pt) d) You work for a small agri-business company that specializes in producing applesauce. You know that oranges are substitutes for apples, but not for applesauce. Applesauce is produced using apples. How would you expect the quantity of applesauce sold to be affected by the increase in the price of oranges described in part c? Explain, using words and diagrams. (3 pts) The quantity of applesauce sold will fall. (1 pt). As shown in part c, an increase in the price of oranges will cause the demand curve for apples to shift out as apples and oranges are substitutes. The price of apples will rise, as shown in part c. (1 pt for this full answer, including a comment about substitutes.) Apples are an input to applesauce. As the price of this input rises, the supply curve for applesauce will shift in, as shown in the following diagram. D S D’
3 As we can see on the diagram, the equilibrium quantity of applesauce will fall. (1 pt) It should be clear that the diagram is of the applesauce market and the new and old quantity should be shown.

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c295_assign1_2008_sol - Commerce 295 Sections 101-106 FRE...

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