Directions: The homework will be collected in a box before

b. We can set this problem up as a simple ratio: (390 + 2.5x)/600= 80/100 and then solve for x. Take a moment to look at this ratio and make sure you understand it. The 390 is the number of points you have on a 500 point scale from part (a) of this problem. The 2.5x is the conversion of the sixth assignment from a 40 point scale to a 100 point scale. The 600 in the denominator is the total number of available points you could get from the six assignments if they were each measured on a 100 point scale. The 80/100 is the average score you would like after the sixth assignments are completed. Solving this ratio for x, we get x = 36. You would need to make a 36 out of 40 points on the sixth assignment in order to have an average of 80 in the class.

6. Joey is taking a class that has ten quizzes over the course of the semester. He has taken five quizzes and his average score on the five quizzes is 78 points on a 100 point scale.

a. Suppose that he takes two more quizzes and scores an 80 on the first of these quizzes and a 90 on the second. What is his average score now?

b. Suppose Joey wants his final quiz score average to be a 83. If he has already taken seven quizzes with the scores discussed earlier, what must his average on the last three quizzes be in order for him to have a final quiz score average of 83 in the class?

Answers:

b. From part (a) we know that Joey has earned 560 points out of a possible 700 points on the first seven quizzes. There are three more quizzes and let’s denote the average score on each of these quizzes as x. Joey will therefore at the end of the ten quizzes have a total number of points of 560 + 3x on the ten quizzes. We can use this information to set up a ratio: (560 + 3x)/1000 = 83/100. The “1000” refers to the total number of points that are available after from the ten quizzes. The “83/100” represents the average that Joey wants to have after the ten quizzes have been taken. Solve for x to find the average score Joey must make on the last three quizzes in order to have an 83 average in the class. The value of x is 90. So, if Joey has an average of 90 on the last three quizzes then his overall average from the ten quizzes will be an 83.

7. Consider the small closed economy of Islandia and its market for bananas. Currently, the domestic demand and supply curves for bananas are given by the following equations:

Domestic Demand: P = 1000 – (1/5)Q

Domestic Supply: P = 200 + (1/15)Q

Furthermore, you know that the world price of bananas is equal to $300 per unit of bananas. Hint: you will likely find it helpful to draw a sketch or several sketches as you proceed with this problem.

a. If Islandia remains a closed economy, what will be the equilibrium price and quantity in the market for bananas in this economy?

b. Suppose Islandia opens the banana market to trade. Will Islandia import or export bananas when it changes its status from a closed economy to an open economy? Explain your answer.

c. Calculate the value of consumer surplus in the banana market when Islandia is a closed economy and the value of consumer surplus in the banana market when Islandia is an open economy. Will domestic consumers be in favor of opening the market to trade? Explain your answer.

d. Calculate the value of producer surplus in the banana market when Islandia is a closed economy and the value of producer surplus in the banana market when Islandia is an open economy. Will domestic producers be in favor of opening the market to trade? Explain your answer.

e. Suppose that the market for bananas in Islandia is open to trade but that the government of Islandia wishes to reduce imports of bananas to 1000 units of bananas through the imposition of a tariff. How big will the tariff need to be in order for Islandia to reach their goal? Explain your answer.

f. How much tariff revenue will be raised with the imposition of the tariff described in part (e)?

g. What is the deadweight loss from the imposition of the tariff described in part (e)?

Answers:

b. If Islandia opens its banana market to trade, bananas will sell for the world price of $300 per unit of bananas. At this price domestic suppliers will be willing to supply 1500 units of bananas while domestic demanders will demand 3500 units of bananas. There will be an excess demand or shortage of 2000 units of bananas. This shortage will be satisfied by Islandia importing 2000 units of bananas at the world price of $300 per unit of bananas. The sketch below provides an image of this outcome.

c. Consumer surplus in the banana market when Islandia is closed to trade is equal to (1/2)($1000 per unit - $400 per unit)(3000 units) = $900,000. After the banana market opens to trade consumer surplus is equal to (1/2)($1000 per unit - $300 per unit)(3500 units) = $1,225,000. Opening the banana market to trade is favored by consumers since it results in consumer surplus increasing by $325,000. The graph below shows these two different areas:

d. Producer surplus in the banana market when Islandia is closed to trade is equal to (1/2)($400 per unit - $200 per unit)(3000 units) = $300,000. After the banana market opens to trade producer surplus is equal to (1/2)($300 per unit - $200 per unit)(1500 units) = $75,000. Opening the banana market to trade is not favored by producers since it results in producer surplus decreasing by $225,000. The graph below shows these two different areas: