Economics 102 Introductory Macroeconomics - Spring 2006, Professor J. Wissink

Problem Set 1 – ANSWERS

  1. Consider the production function information below for Malmsbury, England which can make only shortbread and ale with their labor supply of 10 hours.

a)Graph the production function for shortbread and the production function for ale.

b)Yes, it does. The law of diminishing returns sets in after the 2nd hour of labor in the shortbread sector because the additional unit of labor adds less to the total output compared to the previous unit. It sets in right from the start in the ale sector.

c)

d)The Total Opportunity Cost of 75 gallons of ale is 53.6 - 32 = 21.6 lbs of shortbread

e)The Marginal Opportunity Cost of the 75th gallon of ale is the (change in SB)/(change in ale) = (40-32)/(75-71) = 8/4 = 2 lbs of shortbread. Note: since this is an approximation, there are other ok approximations, too. This is the way most people would do it. But it would also be OK if you did the following:
(change in SB)/(change in ale) = (40-22)/(77-71) = 18/6 = 3 lbs of shortbread, "sandwiching" the point you are looking at with the data from the row before and the row after. Both answers are correct.

f)Technological advancement in ale production pushes out the PPF to the new PPF. Note that Malmsbury could move to point C (same ale, more shortbread) or point B (same shortbread, more ale) or any combination of points between B and C (more of both).

  1. Consider an economy producing only bread and clothing. Bread is produced with land and labor as inputs, while clothing is produced with capital and labor as inputs.

a)See PPFo in graph.

b)Draw the possible consequences of the following on the economy’s PPF. Assume each event below occurs separately (and not in combination with other events noted), and use a separate diagram for each answer.

i)See PPFtech in graph.

ii)See PPFimm in graph.

  1. Consider a small community which consists of three producers: Jay, Kay and Dee. The following table shows how many hours it takes each person to produce one pound of food or 1 yard of cloth. Assume that each person works a total of 48 hours/week.

a)See tableshown above. The marginal opportunity costs of producing 1 pound of food and 1 yard of cloth are shown in the last 2 columns above. Notice that for Jay to get 1 pound of food he needs 1 hour of time. One hour of time taken out of cloth production will reduce cloth output by 1/2 yard. Therefore, Jay's marginal opportunity cost of food in terms of cloth is 1/2 yard of cloth. The other opportunity costs are calculated based on the same reasoning. For completeness, the maximum rates of production of food and cloth are also shown. From table (a), Jay has the comparative advantage in food production because he has the lowest opportunity cost for food production. Kay has the comparative advantage in cloth production.

b)If Jay is self sufficient and he wants to consume 36 pounds of food, he needs to spend 36 hours in food production. Hence he can use only 12 hours to produce cloth which yields him 6 yards of cloth. Following the same reasoning, if Dee wants to consume 8 yards of cloth, she can produce, at most, 6 pounds of food.

c)Between Jay and Dee, Jay has the comparative advantage in food production and Dee has the comparative advantage in cloth production. If they work together, Jay specializes in food production and produces 48 pounds of food. Dee specializes in cloth production and she produces 16 yards of cloth. Since Jay still wants to consume 36 pounds of food and Dee still wants to consume 8 yards of cloth, Jay can trade 12 pounds of food to Dee in exchange for 8 yards of cloth. After this, Jay consumes 36 pounds of food and 8 yards of cloth. Dee consumes 12 pounds of food and 8 yards of cloth. Comparing this situation with the answer in part (b), it is clear that both Jay and Dee are better off.

d)See graph below:

  1. True or False and EXPLAIN: The law of diminishing marginal productivityapplied to labor implies that the total product of labor curve must eventually be downward sloping.
    False: It merely implies that the total product of labor curve must eventually increase at a decreasing rate.
  2. MULTIPLE CHOICE ANSWERS: D, C, D, C, C, A, C

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