Question

Let the market demand curve for a good be: P = 50 – Q/10. a. Recall that if the market demand curve is linear, the marginal revenue curve is also linear, with the same price-axis intercept and a slope equal to twice the slope of the demand curve. Write out the marginal revenue curve for this market demand curve. b. The elasticity of demand can be written as (1/slope)*(P/Q). Find the elasticity of demand for this market demand curve at the following quantities: Q = 50, 150, 250, 350, 450. c. Verify that the demand curve is elastic at quantities where marginal revenue is positive and inelastic at quantities where marginal revenue is negative.

Answer 1

a. The simplest way of find MR is to get TR by multiplying P and Q. Next we can find rate of change of TR with respect to Q and this will give us the MR. (all calculations in image).

b. Next from the demand function which is of the form P=a-bQ, b is the slope. The slope is negative indicating downward sloping demand curve. We however use the absolute value only for the slope. For every level of Q we find P by inputting Q value in demand equation and then apply the formula of elasticity.

c. To verify this we have to find MR at all given levels of Q. For this we just input respective Q values in MR equation.

Demand is elastic when it is greater than 1 and inelastic when its value is less than 1. Here observe the following -

at Q = 50, MR is positive and elasticity is more than 1.

at Q = 150, MR is positive and demand is elastic.

at Q = 250, MR is zero and demand is unit elastic (i.e. neither elastic nor inelastic).

at Q= 350, MR becomes negative and demand elasticity is less than 1.

at Q = 450, MR is still negative and demand is inelastic.