Jane is the manager of a local bank branch in College Station where he consumes bundles of two commodities x and y. Prices in Co
1 answer:
Answer:
Remain the same
Explanation:
......................................................... (1)
ICS = Income in College Station = $6,000
CSpx = Price of x in College Station = 1
CSpy = Price of y in College Station = 5
ID = Income in Dallas = ?
Dpx = Price of x in Dallas = 4
Dpy = Price of y in Dallas = 5
Step 1
Assume that Jane always divides his income in College Station equally into two, i.e. $3,000 each, to buy x and y, the quantities of x and y he can buy in College Station can be calculated by dividing the $3,000 by the prices of x and y. This is calculated as follows:
CSqx = Quantity of x in College Station = $3,000 ÷ 1
= 3,000 units
CSqy = Quantiy of y in College Station = 3,000 ÷ 5
= 600 units
Jane's utility in College Station can be calculated by amending equation (1) and substituting 3,000 units for x and 600 units for y as follows:
= 3,000 * 360,000
CSU(3000, 600) = 1,080,000,000 utils .......................... (2)
Step 2
Since Jane is guaranteed a salary in Dallas with which he would be able to buy exactly what he buys in College Station, this implies that the salary in Dallas will make him to be able to buy 3,000 units of good x and 600 units of good which he currently buys in College Station.
Since
CSpx = 1, which is less than Dpx = 4
But
CSpy = 5, is equal to Dpy = 5
We need to calculate how much his Income will increase in Dallas to be able to buy 3,000 units of good x in Dallas given that its price is $4. Therefore, his income will increase by multiplying $4 by 3000 units and deduct $3,000 he was spending in College Station on x as follows:
IID = Increase in Income in Dallas = (3,000 * $4) - $3,000
= $12,000 - $3,000
= $9,000
Therefore, ID (Income in Dallas) is the addition of IDD and ICS (Income in College Station) calculated as:
ID = IID + ICS
= $9,000 + $6,000
= $15,000
Conclusion
With the ID of $15,000, Jane will be spending $12,000 to buy 3,000 units of good x in Dallas and continue to spend $3,000 to buy 600 units of good y in Dallas.
This will make Jan's utility in Dallas (DU) to be equal to 1,080,000,000 utils as obtained in equation (2) above.
Therefore, Jane's utility will remain the same based on the tangency rule which states that a consumer will choose a combination of two goods at which an indifference curve is tangent to the budget line, i.e. his income.
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Answer:
The step by step answer to your problem is given below:
Explanation:
1A) Break even point for option 1:
Sales- Variable cost= Fixed cost
Q* $950-Q*$760= $7410
Q*$190= $7410
Q=$7410/$190
Q= 39 carpets
1B) Breakeven point for Option 2
Sales- variable cost-rent cost= 0
Q*$950- $760*Q- (Q*950*10%)= 0
95Q= 0
Q= 0
2. At what level of revenues will Cover Rugs earn the same operating income under either option?
Operating income under Option 1 = $190Q - $7140
Operating income under Option 2 = $95Q
We have to find Q such that $190Q - $7140 = $95Q
Q=$7410/$95= 78 Carpets
Revenue= $950 x 78 = $74,100
For Q = 78 Carpets, operating income under both option 1 and 2 will be = $7410
a. For what range of unit sales will Cover Rugs prefer Option 1? b. For what range of unit sales will Cover Rugs prefer Option 2?
For Q > 78, say 79 carpets:
Option 1 gives operating income= (190*79) - 7410= $7600
Option 2 gives operating income= 95*79= $7505
So color rugs will prefer Option 1.
For Q < 78, say 77 carpets:
Option 1 gives operating income= (190*77) - 7410= $7220
Option 2 gives operating income= 95*77= $7315
So color rugs will prefer Option 2.
3. Calculate the degree of operating leverage at sales of 65 units for the two rental options.
Operating Leverage=
= Contribution margin per unit x Numbers of Carpet Sold= Contribution Margin
Under Option 1,
Contribution Margin per unit= $950-$760=$190,
Operating income= $190*65-$7410= $4940.
Degree of Operating Leverage=
=2.5
Under Option 2,
Contribution Margin per unit= $950-$760-$760-0.10*$950=$95,
Operating income= $95x65-$0= $6175.
=1.0
4. Briefly explain and interpret your answer to requirement 3.
The degree of operating leverage helps managers calculate and anticipate the effects of fluctuations in sales on operating income. The calculation in requirement 3 show that when sales are 65 units, a % change in sales and contribution margin will result in 2.5 times that % change in operating income for option 1. But the same % change in Option 2 because there are no fix costs attached in option 2.
Answer
The answer and procedures of the exercise are attached in the following archives.
Explanation
You will find the procedures, formulas or necessary explanations in the archive attached below. If you have any question ask and I will aclare your doubts kindly.
