COMM 295 Assignment 1 SOLUTIONS

Quantity demanded is 1000 50 d q p and quantity

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be the net price received by firms. Quantity demanded is 1000 50 d Q P = and quantity supplied is 80 40( ) S Q P t = − + . Market equilibrium requires that quantity demand equal quantity supplied: 1000 50 80 40( ) P P t = − + . Solve this equation to obtain the equilibrium price for consumers: * 12 (4/9) P t = + . This confirms that pass through for consumers is less than 50 percent. Q tax = 5 S D

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3 f) Suppose the government plans to raise the tax. Draw a diagram and use it to explain why the tax revenue for government will initially increase but will eventually decrease if the government continues to raise the tax. (4 pts) One possible diagram is as follows. Tax after increase \$ \$ The basic logic is that when the tax is 0 revenue is zero and must increase when the tax rate rises. As the tax rate continues to rise the amount sold will fall. Ultimately a sufficiently high tax would reduce sales to 0 and tax revenue would fall to zero. At some intermediate point tax revenues would reach their maximum and would fall after that. The left-hand diagram above shows the tax box getting larger with a small increase in t (this is the “small” t case). Conversely, the right-hand diagram above shows the tax box getting smaller with a small increase in t (this is the “large” t case). Thus, when starting from a small value, a continuous increase in t implies that tax revenue will initially increase but will eventually decrease. The more elastic the demand schedule, the more quickly the system switches from the situation depicted in the left-hand graph to that depicted in the right-hand graph. Students might not use this diagram. They might have a diagram with the tax rate on the horizontal axis and total tax revenue on the vertical axis. That would be okay if the explanation is correct.
4 Question 2: Demand Analysis A well-known producer of pizzas decided to analyze the demand for thin crust pizzas. The regular price for pizza was \$7.00 per pizza but this price was varied using temporary in- store discounts that varied by supermarket. Thus, for example, in one supermarket a temporary in-store discount of \$1.00 was available, making the net price \$6.00 per pizza. The producer was able to track the number of pizzas purchased per 1000 customers who shop at each supermarket, yielding the following data. Quantity Price 21.0 \$7.00 22.5 \$6.50 27.0 \$6.00 28.5 \$5.50 24.0 \$5.00 28.5 \$4.50 33.0 \$4.00 34.5 \$3.50 a) Copy this data in a spreadsheet (preferably Excel 2007 or Excel 2010). Put quantity in column A and price in column B. Create a scatterplot chart showing these points and generate a linear trendline through these points. (If you do not know how to create a scatterplot and make a trendline using Excel, read the instructions posted on the course website.) Using Excel, label the axes and put the title “Pizza Demand” on the chart. Print out the chart as an “embedded chart” so that it appears on the same page as the data. (4 pts) Quantity Price 21 \$7.00 22.5 \$6.50 27 \$6.00 28.5 \$5.50 24 \$5.00 28.5 \$4.50 33 \$4.00 34.5 \$3.50 Students do not need to print out the numbers again or the full spreadsheet. All they need is the graph .

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