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Jeremy is deeply in love with Jasmine. Jasmine lives where cell phone coverage is poor, so he can either call her on the land-line phone for five cents per minute or he can drive to see her, at a round-trip cost of $2 in gasoline money. He has a total of $10 per week to spend on staying in touch. To make his preferred choice, Jeremy uses a handy utilitometer that measures his total utility from personal visits and from phone minutes

Round Trips Total Utility Phone minutes Total utility
0 0 0 0
1 120 20 200
2 180 40 380
3 230 60 540
4 270 80 680
5 300 100 800
6 330 120 900
7 200 140 980
8 180 160 1040
9 160 180 1080
10 140 200 1100

Jeremy is deeply in love with Jasmine

  1. Using the values given in the table above and the marginal utility approach, determine the choice of phone minutes and round trips that maximize Jeremy’s utility given his budget.

Find total utility in order to solve for marginal utility, the table doesn’t represent actual choice available for the budget. If Jeremy has only $10 to spend and a round trip costs $2 and phone calls cost $0.05 per minute, he could spend his entire budget on five round trips but no phone calls or 200 minutes of phone calls, but no round trips or any combination of the two in between. It is easy to see all of his budget options with a little algebra. The equation for a budget line is:

Budget=PRT×QRT+PPC×QPC

Where P and Q are price and quantity of round trips (RT) and phone calls (PC) (per minute). In Jeremy’s case the equation for the budget line is:Jeremy is deeply in love with Jasmine

$10=$2×QRT+$0.05×QPC

$10/$0.05= ($2QRT+$0.05QPC)/$0.05

200=40QRT+QPC

QPC=200−40QRT

Choose zero through five round trips (column 1), the table below shows how many phone minutes can be afforded with the budget (column 3). The total utility figures are given in the table below.

Round trips Total utility for trips Phone minutes Total utility for minutes Total utility
0 0 200 1100 1100
1 80 160 1040 1120
2 150 120 900 1050
3 210 80 680 890
4 260 40 380 640
5 300 0 0 300

Marginal utility is equal to the change in total utility divided by the change in trips or minutes.

Jeremy is deeply in love with Jasmine

 

 

Round trips Total utility for trips Marginal utility(per trip) Phone minutes Total utility for minutes Total utility Marginal utility(per minute)
0 0 0 200 1100 1100
1 80 80 160 1040 1120 60/40=1.5
2 150 70 120 900 1050 140/40=3.5
3 210 60 80 680 890 220/40=5.5
4 260 50 40 380 640 300/40=7.5
5 300 40 0 0 300 380/40=9.5

Note that it is impossible to directly compare marginal utilities, since the units are trips versus phone minutes. There is need of a common denominator for comparison, which is price. Dividing MU by the price, yields columns 4 and 8 in the table below.

Round trips Total utility for trips Marginal utility (per trip) MU/P Phone minutes Total utility for minutes Total utility Marginal utility(per minute) MU/P
0 0 0 200 1100 1100 1.5/$0.005=30
1 80 80 80/$2=40 160 040 1120 1.5 3.5/$0.05 = 70
2 150 70 70/$2=35 120 900 1050 3.5 5.5/$0.05 = 110
3 210 60 60/$2=30 80 680 890 5.5 7.5/$0.05 = 150
4 260 50 50/$2=25 40 380 640 7.5 9.5/$0.05 = 190
5 300 40 40/$2=20 0 0 300 9.5

 

Start at the bottom of the table where the combination of round trips and phone minutes is (5, 0). This starting point is arbitrary, but the numbers in this example work best starting from the bottom. Suppose we consider moving to the next point up. At (4, 40), the marginal utility per dollar spent on a round trip is 25. The marginal utility per dollar spent on phone minutes is 190.Since 25<190, we are getting much more utility per dollar spent on phone minutes, so let’s choose more of those. At (3, 80), MU/PRT is 30<150 (the MU/PM), but notice that the difference is narrowing. We keep trading round trips for phone minutes until we get to (1,160), which is the best we can do. The MU/P comparison is as close as it is going to get (40vs.70). Often in the real world, it is not possible to get MU/P exactly equal for both products, so you get as close as you can. Jeremy is deeply in love with Jasmine

 

 

Quantity Fixed cost Variable cost Total cost Average Variable

Cost

 

Average total cost Marginal cost
0 $30 0        
1   $10        
2   $25        
3   $45        
4   $70        
5   $100        
6   $135        

The above table represents a Ski Company. They sell pairs of skis. Use the information provided to answer the following 8 questions.

  1. What is the fixed cost of producing 2 pairs of skis?

Fixed cost remains constant regardless of the quantity of production.

Fixed cost= $30

  1. What is the total cost of producing 4 pairs of skis?

Total cost= fixed cost + variable cost

Total cost=$30+$70= $100

  1. What is the average variable cost of producing 5 skis?

Average variable cost= total variable cost/ total output

Average variable cost = $100/5= $20

  1. What is the marginal cost of producing the 6th pair of skis?

Marginal cost = change in total cost/ change in quantity

Change in total cost=total cost for 6 skis – total cost for 5 skis

Total cost for 6 skis= $135+$30=$165

Total cost for 5 skis=$100+$30=$130

Change in total cost=$165-$130= $35

Change in quantity = 6-5= 1

Marginal cost= $35/1=$35

Assume this firm is perfectly competitive.

  1. If the price of a pair of skis was $20, how many pairs of skis will they choose to produce?

He will choose to produce 3 pairs of skis because he will incur the least amount of loss.

  1. What will be their profit or loss?

Loss/ profit = revenue – total cost

Revenue = $20*3= $60

Total cost= $30+$45= $75

Loss=$60-$75=$15

  1. If the price of skis were $30 a pair, what quantity would they produce?

He will produce 5 pairs of skis because he will incur the at most profit.

  1. What will be their profit or loss?

Loss/ profit = revenue – total cost

Revenue =5*$30=$150

Total cost =$30+$100=$130

Profit =$150-$130=$20

 

The chart above represents the costs in the short-run and long-run for a firm. Use it to answer the following 4 questions.

  1. What do economists call the phenomenon occurring with the LRATC curve from 1,000 to 3,000 units of output?

Economies of scale; cost goes down as output increases.

  1. What do economists call the phenomenon occurring with the LRATC curve from 3,000 to 5,000 units of output?

Diseconomies of scale; cost goes up as output increases

  1. If this firm needed to produce 1,500 units of output, which SRATC curve will they choose?

SR ATC 1

  1. If this firm needed to produce 2,800 units of output, which SRATC curve will they choose?

SR ATC 3