Question

4. (Aggregating Demand Curves and finding Inverse Demand) The demand function for a certain good is: Qu(p) - 100 -p in the US, and Q. (p) - 150 - 2p in Japan. The price p is in a common currency. a. In a single diagram, graph the individual country demand functions in the US and Japan. b. In the same diagram, draw the aggregate demand function (for US + Japan): Qup). c. In your diagram, there will be three relevant price ranges: (i) where QAp) -0; (ii) where only the US demands positive output; and (iii) where both the US and Japan de Specify these three relevant ranges of p, and for each range give the expression for QNP). (In range (1). Q.(p) 0, but for (ii) and (iii) you need to provide expressions involving p.) d. Referring to your graph, give the equation for the aggregate inverse demand function (P as a function of Q) for the three relevant ranges of Q. (One of those three ranges is where , PA(0) - 0.)

Answer 1

a. Demand for a certain good in US is Q_U(p)=100-p

When p=0,Q_U=100 and when Q_U=0,p=100

Thus, plotting price on vertical axis and quantity on horizontal axis, the demand curve for US has a vertical intercept of 100 and a horizontal intercept of 100 as shown below in the diagram.

Now, demand for a certain good in Japan is Q_J(p)=150-2p

When p=0,Q_J=150 and when Q_J=0,p=75

Thus, plotting price on vertical axis and quantity on horizontal axis, the demand curve for japan has a vertical intercept of 75 and a horizontal intercept of 150 as shown below in the diagram.

b. Now, the aggregate demand curve is given by Q_A(p) = Q_U(p) + Q_J(p)

or, Q_A = 100-p+150-2p

or, Q_A = 250-3p

For the aggregate demand curve, when p=0,Q_A=250 and when Q_A=0,p=83.33. Thus, the vertical and horizontal intercepts of the aggregate demand curve are 83.33 and 250 respectively. We have shown the aggregate demand curve on the same diagram below.

Price 100 Demand for US QU 83.33 75 Qemand for Japan QJ Aggregate Demand QA Quantity 100 150 250

c. In the above diagram, we can find three price ranges, i.e, p=75, p=83.33 and p=100.

d. Inverse demand curve is given by p(Q_A) = 250/3 - Q_A/3.