Question

Find another set of equilibrium prices for the economy in Example 1. Suppose the same economy used Japanese yen instead of dollars to measure the value of the various sectors’ outputs. Would this change the problem in any way? Discuss.

Short answer

Currency does not affect equilibrium prices as it is goverened by the ratio of prices.

Step-by-step solution

Find another set of equilibrium prices

From example 1, let the annual output of the steel sector be \({p_s} = \$ 200\;{\rm{billion}}\)

The outputs of the coal and electric sector according to the results of example 1 are:

\(\begin{aligned}{c}{p_C} = 0.94{p_S}\\ = 0.94\left( {200} \right)\\ = 188\end{aligned}\)

And

\(\begin{aligned}{c}{p_E} = 0.85{p_s}\\ = 0.85\left( {200} \right)\\ = 170\end{aligned}\)

Conversion of currency

\(\$ 1\)is equivalent to \(110.13\;{\rm{JPY}}\).

The equivalent Japanese Yen for \(\$ 188\;{\rm{billion}}\) is:

\({p_C} = 188 \times 110.13\;{\rm{billion}}\,{\rm{JPY}}\)

The equivalent Japanese Yen for \(\$ 170\;{\rm{billion}}\) is:

\({p_E} = 170 \times 110.13\;{\rm{billion}}\;{\rm{JPY}}\)

Ratio of prices

Find the ratio of prices \({p_C}\) to \({p_E}\).

\(\begin{array}{c}\frac{{{p_C}}}{{{p_E}}} = \frac{{188 \times 110.13}}{{170 \times 110.13}}\\ = \frac{{94}}{{85}}\end{array}\)

Discussion

From the equations \({p_c} = 0.94{p_s}\) and \({p_E} = 0.94{p_S},\) it is clear that the output of the coal and electric field is a non-negative multiple of the output of the steel sector.

On changing the unit of currency, from dollars to Japanese Yen, the effect will be the same effect as it will be by multiplying with any other constants.

So, the ratio of the prices will remain the same irrespective of the type of currency.