Question

Need assistance with this! Thanks in advance!

• Label all axes (P, Q)
• Label all lines/curves (Demand, Supply)
• Label all relevant equilibrium points
• Label intercepts for your linear demand and supply. (Intercepts are the points where the lines intersect the axes. For example, if a demand curve intersects the price axis at P=100, indicating that at P=100, 0 units are demanded, you should label that point on the axis with the price of 100).
• Please limit your depictions of supply and demand only to the non-negative values of P and Q (e.g., utilize only Quadrant 1 of the coordinate plane)

Question 1

Suppose you have been hired by a research firm trying to understand the market for Widgets (a hypothetical product). Your analysis of the data indicates that the Demand curve for Widgets is estimated to be linear and given by equation Q_d = 100 – P and the Supply curve for Widgets appears to be linear as well and is estimated as Q_s = 3P – 20. Graphically draw these two curves, labeling all relevant points (such as intercepts for each line) on the horizontal and vertical axes.

Question 2

Given that Demand is Q_d = 100 –P and Supply is Q_s = 3P – 20, your next assignment is to compute the equilibrium Price and Quantity in the market for Widgets. Indicate these values on the graph.

Question 3

The firm that hired you has estimated that improvements in Widget quality tastes will cause the Demand curve to change to Q_d = 140 –P.   If the Supply curve remains the same (Q_s = 3P – 20), graphically draw these two curves, labeling all relevant points on the horizontal and vertical axes.

Question 4

Given that New Demand is Q_d = 140 – P and Supply is Q_s = 3P – 20, your next assignment is to compute the new equilibrium Price and Quantity in the market for Widgets. Indicate these values on the graph.

Answer 1

Answer

Question 1

The equation of the demand curve for Widgets is as follows,

Q_d = 100 – P .............................(1)

The equation of the supply curve for Widgets is as follows,

Q_s = 3P – 20 .............................(2)

The following graph shows the demand and supply curves of widgets.

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Question 2

The equation of the demand curve for Widgets is as follows,

Q_d = 100 – P .............................(1)

The equation of the supply curve for Widgets is as follows,

Q_s = 3P – 20 .............................(2)

At the equilibrium, Qd = Qs

  100 – P =  3P – 20

Or,   – P - 3P = -20 - 100

Or, - 4P = - 120

Or, P = -120 / - 4

Or, P = 30

Now, putting the value of 'P' in equation(1), we get,

Q_d = 100 – 30

Or, Qd = 70

Again, putting the value of 'P' in equation(2), we get,

Q_s = 3 * 30 – 20

Or, Q_s = 90 - 20

Or, Qs = 70

So, at price $30, we see that Qd = Qs = 70. Thus, the equilibrium price and quantity in the market for Widgets are $30 and 70 units respectively.

These values are shown in the following graph.

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Question 3

The new demand curve with the same supply curve of widgets are shown in the following graph.

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Question 4

The equation of the new demand curve for Widgets is as follows,

Q_d = 140 – P

The equation of the supply curve for Widgets is same as before, which is as follows,

Q_s = 3P – 20

At the equilibrium, Qd = Qs

  140 – P =  3P – 20

Or,   – P - 3P = -20 - 140

Or, - 4P = - 160

Or, P = -160 / - 4

Or, P = 40

Now, putting the value of 'P' in new demand equation, we get,

Q_d = 140 – 40

Or, Qd = 100

Again, putting the value of 'P' in supply equation, we get,

Q_s = 3 * 40 – 20

Or, Q_s = 120 - 20

Or, Qs = 100

So, at price $40, we see that Qd = Qs = 100. Thus, the new equilibrium price and quantity in the market for Widgets are $40 and 100 units respectively.

These values are shown in the following graph.

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