hi ive been getting my head around a few multiple choice questions..here are a couple of them.. 1. If the ratio of marginal revenue to price is 1:2, what is the absolute value of the elasticity of demand ? soln:2 2.Increase in the absolute value of interest rate sensitivity of investment demand..........INCREASES the absolute value of slope in the IS curve...???! my understanding is that when investment is interest elastic,the IS curve is flat..im not sure how u would come to a conclusion like this... any help will be appreciated!! thanks in advance.
I can answer Q1. elasticity of demand = % increase in demand/% increase in price = dQ/dP*P/Q total revenue=Q*P hence marginal revenue=d(total revenue)/dQ=d(Q*P)/dQ=P+Q*dP/dQ (by chain rule) therefore, MR/P=1+Q/P*dP/dQ=1/2 so Q/P*dP/dQ=-1/2 which is the inverse of the first equation i derived for elasticity of demand. hence, elasticity is -2. I used a very mathematical way to calculate that, but there must be a better and quicker way.
Re. Q1 Revenue (R) = price(P) x Quantity (Q) Differentiating wrt Q then gives: dR/dQ = P + Q.dP/dQ i.e. MR = P (1+(Q/P).(dP/dQ)) MR/P = (1 + (1/e)) where e = price elasticity of demand. So, in this question: 1/2 = (1 + (1/e)) So, e must equal -2, i.e. e has an absolute value of 2. Re. Q2 Yes, if investment is interest-elastic, then the IS curve will tend to be flatter rather than steeper. So, on the face of it, this question does appear to be wrong. However, I do not know where the question you are referring to comes from, so I cannot help any further or say if there is anything else that needs to be taken into account in answering the question.
Thanks for the response. Graham, as you required, the question is from IAI paper (India) May 2006. The question reads as : An increase in the absolute value of interest rate sensitivity of investment demand...... The solution given is - "increases the absolute value of the slope of the IS curve."
I agree with Graham here - the answer seems wrong to me. If there is an increase in the sensitivity of investment to a change in interest rate the IS curve becomes flatter, ie with a higher absolute value of elasticity so that a change in interest rates will lead to a greater change in investment and hence Agg D. I think the answer is thinking of elasticity but saying slope!
