If P1 = $5, Q1 = 10,000, P2 = $6 and Q2 = 5,000, then a linear estimate of the demand curve is:a.Q = 35,000 - 5,000Pb.P = $5 + $10,000Qc.Q = 7 - 0.002Pd.P = $7 - $0.002Q
Question
If P1 = 6 and Q2 = 5,000, then a linear estimate of the demand curve is:a.Q = 35,000 - 5,000Pb.P = 10,000Qc.Q = 7 - 0.002Pd.P = 0.002Q
Solution
The demand curve is a graphical representation of the relationship between the price of a good or service and the quantity demanded for a given period of time. In this case, we are given two points on the demand curve: (P1, Q1) = (6, 5,000).
We can use these two points to find the slope (m) and y-intercept (b) of the linear demand curve, which is typically written in the form Q = mP + b.
-
Calculate the slope (m): m = (Q2 - Q1) / (P2 - P1) m = (5,000 - 10,000) / (5) m = -5,000
-
Substitute one of the points and the slope into the equation to solve for the y-intercept (b): 10,000 = -5,000*$5 + b b = 35,000
So, the linear estimate of the demand curve is Q = -5,000P + 35,000, which corresponds to option a.
Similar Questions
In a market there are two consumers. Each consumer has a demand curve of P = 10–0.5q. What is the market demand curve? Group of answer choicesP = 10 – QP = 10 – 0.25QP = 20 – QP = 10 – 2QP = 20 – 0.5Q
Use the following graph to answer the question below. The horizontal axis ranges from Q1 through Q4 and the vertical axis ranges from P1 through P4. A decreasing line is labeled demand. The data points at the demand curve (Q1, P4), (Q2, P3), (Q3, P2), and (Q4, P1) connects to both the axes with dotted lines, forming 10 squares. From left to right and top to bottom, the squares are labeled A, B, C, and D; E, F and G; H and I; and J.If the price increases from P1 to P2, then the total revenue will gain areasMultiple ChoiceA + B + C, but it will lose areas G + I + J.E + F + G, but it will lose area J.C + F + H, but it will lose area J.B + E, but it will lose areas H + I + J.
For Demand Curve D2:Change in Price from R200 to R250:Change in Price=𝑅250−𝑅200=𝑅50Change in Price=R250−R200=R50Percentage Change in Price:Percentage Change in Price=(𝑅250−𝑅200𝑅200)×100=25%Percentage Change in Price=( R200R250−R200 )×100=25%Change in Quantity if Price Increases from R200 to R250:Assume the initial quantity demanded at R200 is 𝑄1Q 1 and at R250 is 𝑄2Q 2 .\text{Change in Quantity} = Q_2 - Q_1]Percentage Change in Quantity:Percentage Change in Quantity=(𝑄2−𝑄1𝑄1)×100Percentage Change in Quantity=( Q 1 Q 2 −Q 1 )×100Determine Elasticity:PED=Percentage Change in QuantityPercentage Change in PricePED= Percentage Change in PricePercentage Change in Quantity Use the calculated percentage changes to determine if D2 is elastic or inelastic.
If 20 individual consumers have the following demand curve: p=30−3q. what is market demand
A monopoly faces a demand curve given by P = 100 - 0.5Q, where P is the price and Q is the quantity. Calculate the total revenue and marginal revenue when the quantity sold is 40 units.
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.