Question

Car A initially costs $500 more than car B, but it consumes 0.04 gallons per mile versus 0.06 gallons per mile for B. Both last 8 years and B's salvage value is $100 smaller than A's. Fuel costs $1.7 per gallon. Do not consider the time value of money in the calculations. a) Other things being equal, determine the breakeven point, i.e. the miles of use per year at which both cars are equally preferable. b) Compute the incremental cost A-B (i.e. the difference in the net costs of A and B) considering the miles of use per year ranging from 0 to 4,000 miles with increments of 200 miles. Then plot the data on a chart where the x-axis represents the miles of use per year (ranging from 0 to 4,000 miles) and the y-axis represents "the incremental cost A-B." Determine the regions where A and B are the preferred alternatives. (Use Excel Chart type "X-Y Scatter with Smooth Lines").

          Car A initially costs $500 more than car B, but it consumes 0.04 gallons per mile versus 0.06 gallons per mile for B. Both last 8 years and B's salvage value is $100 smaller than A's. Fuel costs $1.7 per gallon. Do not consider the time value of money in the calculations.

a) Other things being equal, determine the breakeven point, i.e. the miles of use per year at which both cars are equally preferable.

b) Compute the incremental cost A-B (i.e. the difference in the net costs of A and B) considering the miles of use per year ranging from 0 to 4,000 miles with increments of 200 miles. Then plot the data on a chart where the x-axis represents the miles of use per year (ranging from 0 to 4,000 miles) and the y-axis represents "the incremental cost A-B." Determine the regions where A and B are the preferred alternatives. (Use Excel Chart type "X-Y Scatter with Smooth Lines").

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Added by Michael M.

Principles of Economics

Gregory Mankiw 8th Edition

Instant Answer

Solved by Expert Roee Shalom

01/02/2025

Step 1

Let's denote the initial cost of car B as \( C_B \) and the initial cost of car A as \( C_A \). According to the problem, \( C_A = C_B + $500 \). Let's denote the salvage value of car B as \( S_B \) and the salvage value of car A as \( S_A \). According to the Show more…

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Car A initially costs $500 more than car B, but it consumes 0.04 gallons per mile versus 0.06 gallons per mile for B. Both last 8 years and B's salvage value is $100 smaller than A's. Fuel costs $1.7 per gallon. Do not consider the time value of money in the calculations. a) Other things being equal, determine the breakeven point, i.e. the miles of use per year at which both cars are equally preferable. b) Compute the incremental cost A-B (i.e. the difference in the net costs of A and B) considering the miles of use per year ranging from 0 to 4,000 miles with increments of 200 miles. Then plot the data on a chart where the x-axis represents the miles of use per year (ranging from 0 to 4,000 miles) and the y-axis represents "the incremental cost A-B." Determine the regions where A and B are the preferred alternatives. (Use Excel Chart type "X-Y Scatter with Smooth Lines").

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Transcript

00:01 Hello, so let's solve this problem that we're given here.

00:03 We have some given information.

00:06 The initial cost difference, car a costs $500 more than car b.

00:09 We have the fuel consumption of both cars, 0 .04 and 0 .06.

00:14 The fuel cost is $8 .70.

00:16 The lifetime of both cars is $8, and the range of use per year is from 0 to 4 ,000 miles.

00:22 There's an increment of 200 miles per range.

00:27 So, or excuse me, per year.

00:29 So first of all, we need to look for the break -even point.

00:33 So at the break -even point, the total cost for both cars is the same.

00:36 This includes the initial cost difference and the fuel cost over eight years.

00:40 So let's look at the fuel cost per mile.

00:47 Car a, so we'll just write a and b for both cars.

00:51 Car a is 0 .04 times 1 .7, which is equal to $0 .068 dollars per mile.

00:59 So actually, we'll just write it like this, dollars per mile.

01:04 And car b is 0 .06 times 1 .7 is equal to $0 .102 dollars per mile.

01:13 Now we can look at the annual fuel cost.

01:16 We can move this up here.

01:24 Car a again and b, we have 0 .068 times the miles per year.

01:34 And then 0 .102 times the miles per year, and then the fuel cost over eight years.

01:45 So what i mean miles per year is that there is an increment of 200 miles, so there's 20 different calculations for the annual fuel cost, because we're going to start at zero, and we're moving up to 4 ,000.

01:56 At the end of all the calculations that i'll break down, we'll write a graph with all the calculations that we have, and you can plug that in exactly.

02:05 Same chart into excel and just and then put it into an xy scatter chart with some smooth lines for cart a and b...

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