Question

Statistics

Posted 6 months ago

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Use the figure shown to answer the question.
Two supply curves
According to each supply curve, what quantities would be produced at $\$ 30$ ?
Choose 1 answer:
(A) \begin{tabular}{|ll|} \hline$Q_{S}$ on $S_{1}$ & $Q_{S}$ on $S_{2}$ \\ \hline 30 & 30 \\ \hline \end{tabular}
(B) \begin{tabular}{|ll} \hline$Q_{S}$ on $S_{1}$ & $Q_{S}$ on $S_{2}$ \\ \hline 30 & 10 \end{tabular}
(c) \begin{tabular}{ll|} \hline$Q_{S}$ on $S_{1}$ & $Q_{S}$ on $S_{2}$ \\ \hline $\mathbf{0}$ & $\mathbf{0}$ \end{tabular}
(D) \begin{tabular}{|ll|} \hline$Q_{S}$ on $S_{1}$ & $Q_{S}$ on $S_{2}$ \\ \hline 0 & 30 \end{tabular}
(E) \begin{tabular}{ll} $Q_{S}$ on $S_{1}$ & $Q_{S}$ on $S_{2}$ \\ \hline 40 & 0 \end{tabular}
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Answer from Sia

Posted 6 months ago

Solution by Steps

step 1

To determine the quantity produced at a price of $30 on supply curve S1, we need to find the point on the line S1 that corresponds to a price (P) of$30

step 2

Using the two points given for S1, (0,10) and (80,60), we can find the slope of the line using the formula $m = \frac{y_2 - y_1}{x_2 - x_1}$

step 3

Substituting the points into the slope formula: $m = \frac{60 - 10}{80 - 0} = \frac{50}{80} = \frac{5}{8}$

step 4

With the slope $m = \frac{5}{8}$ and the point (0,10), we can use the point-slope form of the equation of a line, $y - y_1 = m(x - x_1)$, to find the equation of S1

step 5

Substituting the slope and point into the point-slope form: $P - 10 = \frac{5}{8}(Q - 0)$, which simplifies to $P = \frac{5}{8}Q + 10$

step 6

To find the quantity produced at $P =$30 on S1, we substitute $P = 30$ into the equation: $30 = \frac{5}{8}Q + 10$

step 7

Solving for $Q$: $30 - 10 = \frac{5}{8}Q$, which simplifies to $20 = \frac{5}{8}Q$

step 8

Multiplying both sides by $\frac{8}{5}$ to isolate $Q$: $Q = \frac{8}{5} \times 20 = 32$

step 9

To determine the quantity produced at a price of $30 on supply curve S2, we need to find the point on the line S2 that corresponds to a price (P) of$30

step 10

Using the two points given for S2, (0,30) and (80,70), we can find the slope of the line using the formula $m = \frac{y_2 - y_1}{x_2 - x_1}$

step 11

Substituting the points into the slope formula: $m = \frac{70 - 30}{80 - 0} = \frac{40}{80} = \frac{1}{2}$

step 12

With the slope $m = \frac{1}{2}$ and the point (0,30), we can use the point-slope form of the equation of a line, $y - y_1 = m(x - x_1)$, to find the equation of S2

step 13

Substituting the slope and point into the point-slope form: $P - 30 = \frac{1}{2}(Q - 0)$, which simplifies to $P = \frac{1}{2}Q + 30$

step 14

To find the quantity produced at $P =$30 on S2, we substitute $P = 30$ into the equation: $30 = \frac{1}{2}Q + 30$

step 15

Solving for $Q$: $30 - 30 = \frac{1}{2}Q$, which simplifies to $0 = \frac{1}{2}Q$

step 16

Since $0 = \frac{1}{2}Q$, the quantity produced at $P =$30 on S2 is $Q = 0$

Answer

The quantities produced at a price of $30 are 32 units on supply curve S1 and 0 units on supply curve S2.

B

Key Concept

Interpreting supply curves

Explanation

To find the quantity supplied at a given price, locate the price on the y-axis and find the corresponding quantity on the x-axis where the price level intersects the supply curve.

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