Question

PLEASE HELP WILL MARK BRAINLIEST

The data provided below describe an ice-cream store’s daily production possibilities for milkshakes and sundaes.
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Milkshakes 0 20 40 60 80 100 120
Sundaes 210 200 180 150 110 60 0
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(a) Draw a correctly labeled graph of the store’s production possibilities curve (PPC) with milkshakes on the horizontal axis and sundaes on the vertical axis and label the endpoints using the numbers provided above.

(b) Is the opportunity cost of producing milkshakes increasing, decreasing, or constant? Explain using numbers in the table.

(c) The store is currently producing 80 milkshakes and 110 sundaes. Calculate the opportunity cost of increasing milkshake production from 80 to 100 milkshakes. Show your work.

(d) Would it be efficient for the store to produce 80 milkshakes and 150 sundaes? Explain using numbers in the table.

(e) Suppose the ice-cream store purchases a new machine that increases the output of milkshakes and sundaes. Show the effect of the change on the store’s PPC on your graph in part (a).

Answer 1

(a) Please see the attached graph

(b) The opportunity cost is increasing

(c) The opportunity cost is the -77.5 units of sundae not produced

(d) The function is note defined at c = (80, 150)

(e) The slope of the graph will change less rapidly, and the opportunity cost of producing milkshake will increase

Reason:

(a) The given data in a tabular form is presented here;

$\begin{array}{|c|cc|}\mathbf{Milkshakes} &&\mathbf{Sundaes}\\0&&210\\20&&200\\40&&180\\60&&150\\80&&110\\100&&60\\120&&0\end{array}$

Please find attached the required drawing of the Production Possibility Curve (PPC) created with MS Excel

The endpoints are;

A(0, 210): Sundaes are the goods mainly produced while no milkshakes is produced

B(120, 0): No sundaes is being produced while milkshakes are the goods mainly in production

(b) The opportunity cost producing milkshakes is the amount of sundaes forgone

$\begin{array}{|c|c|c|}\mathbf{Milkshakes} &\mathbf{Sundaes}& \mathbf{\dfrac{\Delta Sundaes}{\Delta Milkshakes} }\\0&210&-0.5\\20&200&-1\\40&180&-1.5\\60&150&-2\\80&110&-2.5\\100&60&-3\\120&0&\end{array}$

$\mathbf{\dfrac{\Delta Sundaes}{\Delta Milkshakes} } = Rate \ of \ Change \ of \ Sundaes \ to \ Milkshakes$

From the rate of change column of the above table, as the quantity of milkshake produced is increasing, the quantity of sundaes produced decreases more as shown by the progressively increasingly negative rate of change of sundae to milkshake produced

Therefore, the opportunity cost of producing milkshake, which is the quantity of sundae produced, is increasing

(c) The number of sundae produced when producing 80 milkshakes is 110

When the production of milkshakes is increased from 80 to 100, the expected quantity of sundae produced is (110/80) × 100/1 = 137.5

Therefore, 137.5 units of sundae is expected to be produced from 100 units of milkshakes

The actual quantity of sundae produced when the quantity of milkshake produced is 100 is 60

Therefore, the opportunity cost is the extra 20 milkshakes, is the deficit (137.5 - 60 = 77.5

The opportunity cost = -77.5 units of sundae not produced

(d) When the quantity of milkshakes produced = 80, the maximum quantity of sundae that can be produced is 100

Therefore, the condition (80, 150) is not feasible

(e) Given that the quantity of milkshake produced by the new machine is increasing, the rate of change of the sundae to milkshake will decrease, but the the opportunity cost of producing milkshake will continue to increase

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