Calculate the price elasticity of demand for each island

Question

Homework 4-

1. Short-run average cost and long-run average cost:

This table illustrates four short-run average cost schedules (curves) for leather purses produced per month in China. The subscripts A, B, C, and D refer to four different size plants that can be built to produce leather purses. Plant size A can produce no more than 5000 leather purses, plant size B can produce no more than 6000 purses, plant size C can produce no more than 9000 purses, and plant size D can produce no more than 10,000 purses.

Q	SRACA	SRACB	SRACC	SRACD
1000	7.50	----	-----	-----
2000	5.40	6.00	-----	-----
3000	5.00	4.50	5.50	-----
4000	5.30	4.30	4.30	-----
5000	6.00	4.75	3.85	4.50
6000	-----	5.70	3.50	4.10
7000	-----	-----	4.00	3.80
8000	-----	-----	4.80	4.00
9000	-----	-----	6.00	4.75
10,000	-----	-----	-----	6.00

a. Use the above information in the table to graph all four short-run average cost curves in a single graph. Measure the quantity of leather purses on the horizontal axis and average cost on the vertical axis. Then plot the long-run average cost curve (LRAC) as the curve that "envelopes" are holds up each of these individual short-run average cost curves. Label your graph carefully and completely.

b. According to your graph from part (a), at what quantity is long-run minimum cost achieved?

c. If the Chinese government limits output to 5,000 purses per month, which plant size is the optimal one to build?

d. Does the envelope curve touch each short-run average cost curve at its minimum point? Why or why not?

2. a. The following tables give information about costs for a firm. Complete the two tables:

Table A

Q	Total Cost	Fixed Cost	Variable Cost	Marginal Cost	Total Average Cost	Fixed Average Cost	Variable Average Cost
0	$3,500	$3,500
1	$5,000	$3,500	$1,500
2	$5,650	$3,500		$650
3	$6,050	$3,500	$2,550
4	$6,250	$3,500				$875
5	$6,800	$3,500
6	$8,050	$3,500
7	$11,150	$3,500					$1,093
8	$17,500	$3,500			$2,188
9	$27,500	$3,500

Table B

Q	Total Cost	Fixed Cost	Variable Cost	Marginal Cost	Total Average Cost	Fixed Average Cost	Variable Average Cost
0	$0	$0	$0
1	$1,550
2	$2,900						$1,450
3	$4,170		$4,170
4	$5,440				$1,360
5	$6,750
6	$8,050			$1,300
7	$9,449
8	$10,880					$0
9	$12,510

b. Which table, A or B, represents firm's short run situation, and which represents firm's long run situation? How do you know?

c. At what output level would the firm's short run and long run average costs be the same?

3. Nominal and Real Prices-

Jack, Paul, and Robin graduated from UW-Madison in the spring of 2007 and they have worked in Tokyo, Paris, and Madison respectively Jack's monthly wage in 2007 was 100 (measured in hundred dollars-that means that his monthly wage was $100,000); Paul's monthly wage in 2007 was 60 (again, measured in hundred dollars); and Robin's monthly wage in 2007 was 96 (hundred dollars). In 2008, Jack's nominal wage increased by 4% and Paul's nominal wage decreased by 10% while Robin experienced no change in his nominal wage. Between 2007 and 2008 inflation rates were 30% for Tokyo, -28% for Paris, and 20% for Madison. (Assume that year 2007 is the base year for the CPI for Tokyo, Paris, and Madison)

a. Complete the following table based on the information you were given and assuming that 2007 is the base year.

	Jack in Tokyo	Paul in Paris	Robin in Madison
Nominal wage in 2007	100	60	96
Nominal wage in 2008
CPI 2007
CPI 2008
Real wage in 2007
Real wage in 2008

b. Did any of these three individuals experience an increase in their nominal wage and a decrease in their real wage?

c. Did any of these three individuals experience a decrease in their nominal wage and an increase in their real wage?

d. At the beginning of 2009, Paul was offered a raise to 81 for his position in Paris. But Paul decided to accept a job offer from a company in Madison. Working in Madison, Paul earned the nominal wage of 150 in 2009. Between 2008 and 2009, inflation rates were the same in Paris and Madison and Paul's real wage in 2009 turned out to be 100. What would Paul's real wage had been in 2009 had he stayed in Paris and earned a nominal wage of 81? You might find it helpful to organize your thinking by using the following table.

Year	Nominal Wage in Paris	Real Wage in Paris	CPI in Paris	Nominal Wage in Madison	Real Wage in Madison	CPI in Madison
2007				-----	-----	100
2008				----	----
2009

4. Elasticity and Total Revenue-

Guam and Hawaii initially both operate as closed economies, which means that they had consumed only domestically produced goods. Madison Coke Company (MCC) made an agreement with the government of Guam and Hawaii respectively to exclusively provide coke to the market in these two economies. Before opening the branches and providing soda to the market, MCC conducted a consumer survey and found out that the demand curve for soda was P=20-2Q in Hawaii and P=40-5Q in Guam.

a. Initially MCC provided coke to each island at the price of 5 dollars. Last month MCC increased the price to $20 in both islands. Calculate the price elasticity of demand for each island using the standard percentage method (that is, calculate the price elasticity of demand using the standard percentage formula and not the arc elasticity formula). Calculate the total revenue from each island at the price of $20.

b. Calculate the price elasticity of demand for each island using the mid-point method. Compare your result using the mid-point (or arc elasticity method) to the result from part (a) using the standard method.

c. Calculate the price elasticity of demand for Guam and Hawaii at the price of $10 using the point elasticity formula. Calculate the total revenue from each market at this price.

d. Find the price level that maximizes the total revenue from the coke market in Guam. Find the price level that maximizes the total revenue from the coke market in Hawaii. What is the sum of the total revenue from both islands if MCC prices coke in each market to maximize its revenue (i.e., MCC can charge different prices in the two markets)?

5. Income and Substitution Effects-

John loves eating blueberries (B) and almonds (A). During winter, the price of a pound of blueberries is $4 and the price of a pound of almonds is $2. John has an income of $60 in the winter to spend on blueberries and almonds.

a. With blueberries on the x-axis and almonds on the y-axis, draw John's winter budget line (BL^winter) and translate your drawn line into an equation for John's winter budget line.

b. Suppose that the optimal consumption bundle (A, B) satisfies MU_B(A, B)/MU_A(A, B) = A/AB. Under BL^winter, find the optimal consumption bundle and draw an indifference curve (IC^winter) passing through it.

c. During summer, the price of a pound of blueberries is $1 and the price of a pound of almonds is $2. Suppose John has an income of $60. With almonds on the y-axis and blueberries on the x-axis, draw John's budget line (BL^summer) and translate this information into an equation for John's summer budget line.

d. Find the optimal consumption bundle with John's summer budget line and draw an indifference curve (IC^summer) passing through it.

e. Now in your graph shift John's summer budget line to the left until it becomes tangent to John's winter indifference curve (IC^winter). (You are now drawing a budget line that can be labeled "budget line 3": this new budget line should be parallel to John's summer budget line and just tangent to the indifference curve representing John's utility or satisfaction in the winter.) You are told that this new point of tangency corresponds to approximately 12.6 pounds of blueberries and 12.6 pounds of almonds. Calculate the substitution effect and income effects for blueberries as the price of blueberries decreases from $4 a pound to $1 a pound. During summer, what is the income level that John would need to have in order for him to have the same utility level as he had during winter?