Given the following demand function for medical care:
Q=100-5p
Where:
P = is the price of health service.
Q = quantity demanded.
What is the quantity demanded at p = 5.
Draw the demand curve for medical care.
Suppose the price rise to (6), calculate the change in consumer surplus.
What is the elasticity of demand for this demand function?
What implications the result in (d) has for government policy toward the health service?
To calculate the quantity demanded at p = 5, substitute p = 5 into the demand function Q = 100 - 5p:
Q = 100 - 5(5) = 100 - 25 = 75
So, the quantity demanded at p = 5 is 75.
To draw the demand curve for medical care, we can plot the quantity demanded (Q) on the vertical axis and the price (p) on the horizontal axis. The equation Q = 100 - 5p represents a linear downward-sloping demand curve. Plotting a few points and connecting them will give us the demand curve. For example, when p = 0, Q = 100, so one point on the curve will be (0,100). When p = 20, Q = 0, so another point on the curve will be (20,0). By connecting these points, we can draw the demand curve.
To calculate the change in consumer surplus when the price rises to 6, we need to find the area under the original demand curve and above the new price of 6. The formula for consumer surplus is given by the equation CS = 0.5 * (Q1 + Q2) * (P1 - P2), where Q1 and Q2 are quantities demanded at prices P1 and P2, respectively. In this case, P1 = 5, P2 = 6, Q1 = 75 (quantity demanded at p = 5), and Q2 can be found by substituting p = 6 into the demand function: Q2 = 100 - 5(6) = 100 - 30 = 70. Plugging these values into the equation, we get:
CS = 0.5 * (75 + 70) * (5 - 6) = 0.5 * 145 * (-1) = -72.5
So, the change in consumer surplus is -72.5.
To find the elasticity of demand for this demand function, we can use the formula:
E = (dQ / Q) / (dp / p)
where dQ is the change in quantity demanded, Q is the original quantity demanded, dp is the change in price, and p is the original price. From the demand function Q = 100 - 5p, we can see that the coefficient of p is -5, which means the elasticity of demand is constant and equal to -5 for all price levels.
The result implies that the demand for medical care is relatively inelastic, as the absolute value of the elasticity is greater than 1. This suggests that a change in price, such as an increase, will result in a proportionally smaller change in quantity demanded. In terms of government policy, it suggests that increasing prices may not significantly reduce the demand for medical care. However, it is important to note that the elasticity of demand is just one factor to consider, and other factors such as income and substitutes should also be taken into account when formulating healthcare policies.