Answer:
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Step-by-step explanation:
To calculate Alvin and Betty's marginal and total willingness to pay for four bottles of water, we need to substitute the quantity of four (Q = 4) into their respective demand functions and solve for the corresponding prices (P).
For Alvin:
QdA = 8 - 0.5P
4 = 8 - 0.5P
0.5P = 8 - 4
0.5P = 4
P = 4 / 0.5
P = 8
For Betty:
QdB = 6 - P
4 = 6 - P
P = 6 - 4
P = 2
Now we can calculate their marginal willingness to pay (MWP) and total willingness to pay (TWP) for four bottles of water.
For Alvin:
MWP_A = ΔTotal Willingness to Pay / ΔQuantity = (TWP_A - TWP_A-1) / (Q - Q-1)
= (P * Q - P * (Q - 1)) / (Q - (Q - 1))
= (8 * 4 - 8 * (4 - 1)) / (4 - (4 - 1))
= (32 - 8 * 3) / 1
= (32 - 24) / 1
= 8 / 1
= 8
TWP_A = P * Q = 8 * 4 = 32
For Betty:
MWP_B = ΔTotal Willingness to Pay / ΔQuantity = (TWP_B - TWP_B-1) / (Q - Q-1)
= (P * Q - P * (Q - 1)) / (Q - (Q - 1))
= (2 * 4 - 2 * (4 - 1)) / (4 - (4 - 1))
= (8 - 2 * 3) / 1
= (8 - 6) / 1
= 2 / 1
= 2
TWP_B = P * Q = 2 * 4 = 8
Graphically, we can plot the demand curves for Alvin and Betty, and indicate the prices at which they are willing to pay for four bottles of water. The quantity is fixed at Q = 4.
On the graph, plot the point (Q = 4, P = 8) for Alvin and the point (Q = 4, P = 2) for Betty. These represent the prices at which they are willing to pay for four bottles of water. The lines representing their respective demand curves can also be plotted on the same graph.
The graph will illustrate the intersection of the demand curves with the corresponding prices for Q = 4, indicating the willingness to pay for both Alvin and Betty.