1101 Economics Michael Bar Problem Set II
University of Minnesota Spring 2005
Supply and demand In order to receive full credit, all diagrams in this section must be fully labeled. That is, you are required to give a title to each diagram and label the axis. 1. (35) Suppose that the demand curve for beer is given by: P = 20 - 0.1QD , where P is the price of beer and QD is the quantity demanded for beer (in six-packs). a. (5) Find the quantity demanded for beer at each of the following prices: P QD 20 0 15 50 10 100 5 150 1 190 First we need to solve for the quantity demanded as a function of price: P = 20 - 0.1QD QD = 200 - 10 P Then, we can plug the prices and the demand curve will tell us the quantity demanded at any price. b. (5) Using Excel, plot the graph of this demand curve. That is, plot the above points and choose the option that connects the points with straight lines. Remember that in Excel the left column is the horizontal axis (X) and the right column is the vertical axis (Y). So here the column for Q should be the left column.
25 20 15 P 10 5 0 0 50 100 Qd 150 200
Demand Curve
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c. (5) Suppose that the supply curve of beer is given by: P = 10 + 0.1QS , where P is the price of beer and the QS is the quantity supplied by the firms. (Important! Notice that the supply will be zero if the price is below 10). Find the quantity supplied of beer at each of the following prices: P QS 20 100 15 50 10 0 5 0 1 0 Notice that the quantity supplied cannot be negative. Negative numbers mean that the firm will not supply to the market at prices lower than 10, as you can see in the next graph. d. (5) Using Excel, plot the graph of this supply curve. That is, plot the above points and choose the option that connects the points with straight lines.
25 20 15 P 10 5 0 0 20 40 60 Qd 80 100 120
Supply Curve
e. (5) Based on the above tables, find the equilibrium in the market for beer and denote it by (Q*, P*). We see from the above tables that at the price of 15 the quantity demanded = quantity supplied = 50. Therefore, the equilibrium is (Q*, P*) = (50, 15). f. (5) Find the equilibrium in the market for goods algebraically, that is, solve the system of two equations (supply and demand) with the two unknowns (P, Q). Denote the solution by (Q*, P*). We just need to solve two equations with two unknowns (Q, P). Notice that in equilibrium, by definition we have Q = QD = QS. P = 20 - 0.1Q P = 10 + 0.1Q 20 - 0.1Q = 10 + 0.1Q
Q* = 50, P* = 15
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g. (5) (Bonus question) Using Excel, plot both the demand and the supply curves on the same diagram. Instructions: (1) create the following columns in Excel spreadsheet (filled with the correct quantities of course), QS P QD 20 0 100 15 50 50 10 100 0 5 150 0 1 190 0 (2) highlight the above columns, including the first row with the titles, (3) choose the "Chart Wizard", and choose the "XY (scatter)" option and the chart type that connects the points with straight lines, and click "Next", (4) in step 2 of the Chart Wizard click on "Series". And for each series choose the appropriate X Values and Y values. The X Values are the quantities and the Y values are the prices in this case. Don't forget to label the axis.
Market
25 20 15 P 10 5 0 0 50 100 Q 150 200
Demand Supply
2. (12) Suppose that the market for potatoes consists of Jennifer and Mark. Potatoes are normal good for Jennifer and inferior good for Mark. a. (4) Suppose that Mark's income goes up and Jennifer's income goes down. Show the effects of these changes on the individual demand curves of Jennifer and Mark. Mark's demand for potatoes P
D1
D2
Q 3
Jennifer's demand for potatoes P
D2
D1
Q
Important! It is a mistake to plot the supply curve on the above graphs. If you draw the supply curve on the above diagrams you are implying that the market price is determined at the intersection of the Aggregate supply with Mark's demand or with Jennifer's deamand, which is obviously wrong. The market price is determined by Aggregate Supply and Aggregate Demand.
b. (4) Show the effects of the changes in income on the market for potatoes and state what happens to the equilibrium price and quantity. The market for potatoes P S P1 P2 D2 Q2 Q1 D1
Q
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c. Suppose instead that the income of both Jennifer and Mark goes up. Show the effect of this increase in incomes on the market for potatoes and state what happens to the equilibrium price and quantity. The market for potatoes P S
?
D Q Notice that since one buyer increased the demand and the other decreased the demand for potatoes, we cannot determine what will happen to the aggregate demand. It could remain unchanged, shift or to the left, or shift to the right. It is a mistake to say that the demand curve will remain unchanged. 3. (5) Show the effect of a decrease in the price of movie tickets on the market for popcorn and determine what happens to the equilibrium price and quantity traded of popcorn. How are the two goods related to each other? The market for popcorn P S P2 P1 D1 Q1 Q2 D2
Q
Movie tickets and popcorn are complements. When the price of movie tickets the demand for popcorn , and the equilibrium price and quantity traded of popcorn .
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4. (5) Show the effect of an increase in the price of "Hungry Jack" pancake mix on the equilibrium price and quantity of "Aunt Jemima" pancake mix. Explain what your assumption is about the relationship between the two goods in question. The market for Aunt Jemima pancakes P S P2 P1 D1 Q2 Q2 D2
Q
Assumption: the two brands of pancakes are substitutes. When "Hungry Jack" becomes more expensive, the demand for "Aunt Jemima" and the equilibrium price and quantity. 5. (10) a. (5) Suppose that a study published in the "Science" journal claims that cacao (an ingredient in chocolate) slows the aging of the skin. That is, chocolate facemask is very effective in maintaining young looks. Show the effect of this publication on the market for chocolate and determine what happens to the equilibrium price and quantity traded of chocolate. The market for Chocolate P S P2 P1 D1 Q1 Q2 D2
Q
Equilibrium price and quantity traded of chocolate .
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b. (5) Suppose that in addition, a hurricane destroyed many cacao plantations in Mexico and Brazil. Show both effects (the new publication in section a + the hurricane) on the market for chocolate and determine what happens to the equilibrium price and quantity traded of chocolate. The market for Chocolate P S2 P2 S1
P1 D1 Q1 Q2 D2
Q
The effects of the shifts in supply and demand are summarized in the following table P P Q ?
D S Total effect
Thus, the equilibrium price will go up but the impact on the equilibrium quantity traded is ambiguous. 6. (8) Scientists developed a new kind of chicken that is featherless and bigger than the usual chicken. The new chicken has the same meat taste as the old one. a. (4) Show the effect of the new development on the market for chicken and determine what happens to the equilibrium price and quantity. The market for chicken P S1 S2
P1 P2 D Q1 Q2 Q
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The new brand of chicken economizes on the cost of production and therefore the supply of chicken increases. As a result, the equilibrium price of chicken and the quantity traded . b. (4) Show the effect of the new development on the market for beef and determine what happens to the equilibrium price and quantity. How are the two goods relate...