Chapter 9, Problem 6NP

A

To determine

To describe:

By using the data from earlier problem and derive the numerical values of the given parameters in the provided appendix.

Answer to Problem 6NP

If there is a rise in the demand for a dashboard GPS which follows the prices of automobiles can result in complement decrease.

Explanation of Solution

  $Y=A(5N-0.0025N^2)$

  $MPN=5A-0.005AN$

  $\begin{array}{l}{C}^d=300+0.8(Y-T)-200r\\ I^d=258.5-250r\end{array}$

  $\begin{array}{l}A\left(f_{1}N-\frac{1}{2}{f}_2{N}^2\right)=A\left(5N-0.0025N^2\right)\\ =A\left(5N-\frac{0.0025}{0.5}{N}^2\right)\\ =A\left(5N-\frac{1}{2}\times 0.005N^2\right)\end{array}$

  $\begin{array}{l}NS=n_0+n_w(1-t)w\\ n_0+n_w(1-t)w=55+10(1-t)w\end{array}$

  $\begin{array}{l}{C}^d=c_0+c_Y(Y-T)-C_{r}r\\ c_0+c_Y(Y-T)-c_{r}r=300+0.8(Y-T)-200r\end{array}$

  $\begin{array}{l}T=t_0+tY\\ =20+0.25Y\end{array}$

  $I^d=i_0-i_{r}r=258.5-250r$

  $\begin{array}{l}\frac{M^d}{P}=l_0+l_{y}Y-l_r(r+{\pi }^e)\\ l_0+l_{y}Y-l_r(r+{\pi }^e)=0.5Y-250(r+{\pi }^e)\end{array}$

Economics Concept Introduction

Introduction: Shifts of demands can also result in the increase or decrease of pricing on account of the substitutes and the complement goods.

B

To determine

To describe:

By substituting the above derived values into the equations that relevant in the provided appendix and obtain the general equilibrium values of employment, output, real interest rate, real wage and price level.

Answer to Problem 6NP

If there is a fall in the demand for the e book as it is following the change in the prices of e books it would result in an increase of complement.

Explanation of Solution

  $\begin{array}{l}w=A\left[\frac{f_1-f_2{n}_0}{1+(1-t)A{f}_2{n}_w}\right]\\ =2\left[\frac{5-0.005\times 55}{1+(1-0.5)\times 2\times 0.005\times 10}\right]\\ =2\left[\frac{4.725}{1.05}\right]\\ =9\end{array}$

  $\begin{array}{l}N=\frac{n_0+(1-t)A{f}_1{n}_w}{1+(1-0.5)\times 2\times 0.005\times 10}\\ =\frac{105}{1.05}\\ =100\end{array}$

  $\begin{array}{l}\overline{Y}=A\left[f_1\overline{N}-\frac{1}{2}{f}_2\overline{N^2}\right]\\ =2\left[5\times 100-\frac{1}{2}\times 0.005\times {100}^2\right]\\ =2\left[500-25\right]\\ =950\end{array}$

  $\begin{array}{l}{\alpha }_{IS}=\frac{c_0+i_0+G-c_Y{t}_0}{c_r+i_r}\\ =\frac{300+258.5+50-0.8\times 20}{200+250}\\ =\frac{592.5}{450}\\ =\frac{79}{60}\end{array}$

  $\begin{array}{l}{\beta }_{IS}=\frac{1-(1-t)c_Y}{c_r+i_r}\\ =\frac{1-(1-0.5)\times 0.8}{200+250}\\ =\frac{0.6}{450}\\ =\frac{1}{750}\end{array}$

  $\begin{array}{l}r={\alpha }_{IS}-{\beta }_{IS}Y\\ =\frac{79}{60}-\frac{1}{750}\times 950\\ =\frac{1}{20}\\ =0.05\end{array}$

  $\begin{array}{l}P=\frac{M}{l_0+l_Y\overline{Y}-l_r({\alpha }_{IS}-{\beta }_{IS}\overline{Y}+{\pi }^e)}\\ P=\frac{9150}{0+0.5\times 950-250\left(\frac{79}{60}-\frac{1}{750}\times 950+0.02\right)}\\ =\frac{9150}{475-17.5}\\ =\frac{9150}{457.5}\end{array}$

Economics Concept Introduction

Introduction: If there is a high demand of the particular product and there are low substitutes and high complements, it can results in high pricing of complements and creating a pressure for the alternatives.

C

To determine

To describe:

Assuming the proposed given condition, repeat the solution derived in the above part.

Answer to Problem 6NP

If there is a fall in the demand for the e book as it is following the change in the prices of e-books it would result in an increase of complement.

Explanation of Solution

  $\begin{array}{l}{\alpha }_{IS}=\frac{c_0+i_0+G-c_Y{t}_0}{c_r+i_r}\\ =\frac{300+258.5+72.5-0.8\times 20}{200+250}\\ =\frac{592.5}{450}\\ =\frac{41}{30}\end{array}$

  $\begin{array}{l}r={\alpha }_{IS}-{\beta }_{IS}Y\\ =\frac{41}{30}-\frac{1}{750}\times 950\\ =\frac{1}{10}\\ =0.10\end{array}$

  $\begin{array}{l}P=\frac{M}{l_0+l_Y\overline{Y}-l_r({\alpha }_{IS}-{\beta }_{IS}\overline{Y}+{\pi }_e)}\\ =\frac{9150}{0+0.5\times 950-250\left(\frac{41}{30}-\frac{1}{750}\times 950+0.02\right)}\\ =\frac{9150}{475-30}\\ =\frac{9150}{445}=20.56\end{array}$

Economics Concept Introduction

Introduction: If there is a high demand of the particular product and there are low substitutes and high complements, it can results in high pricing of complements and creating a pressure for the alternatives.