Question

Upscale hotels in the United States recently cut their prices by $\mathbf{25}$percent in an effort to bolster dwindling occupancy rates among business travellers. A survey performed by a major research organization indicated that businesses are wary of current economic conditions and are now resorting to electronic media, such as the Internet and the telephone, to transact business. Assume a company’s budget permits it to spend$\mathbf{\backslash (}\mathbf{6}\mathbf{,}\mathbf{000}$per month on either business travel or electronic media to transact business. Graphically illustrate how a$\mathbf{25}$percent decline in the price of business travel would impact this company’s budget set if the price of business travel was initially$\mathbf{\backslash )}\mathbf{1}\mathbf{,}\mathbf{200}$per trip and the price of electronic media was$\mathbf{\$}\mathbf{600}$per hour. Suppose that, after the price of business travel drops, the company issues a report indicating that its marginal rate of substitution between electronic media and business travel is$\mathbf{-}\mathbf{1}$. Is the company allocating resources efficiently? Explain.

Short answer

The company is not using their resources efficiently because the Marginal Rate of Substitution should be equal to $\mathrm{\$}1.5$and not -1.

Step-by-step solution

Finding the horizontal and vertical intercept

Use the following equation,

$\mathrm{X}=\frac{\mathrm{M}}{{\mathrm{P}}_{\mathrm{x}}}$

Here,

$M$is the Company’s monthly budget

$X$is the maximum affordable quantity for business trips

$P_x$is the Price of the business travel per trip

$\mathrm{M}=\mathrm{\$}6,000$

${\mathrm{P}}_{\mathrm{x}}=\mathrm{\$}1200$

By substituting we will get,

$\begin{array}{c}\mathrm{X}=\frac{\mathrm{M}}{{\mathrm{P}}_{\mathrm{x}}}\\ =\frac{\mathrm{\$}6000}{\mathrm{\$}1200}\\ =5\end{array}$

Therefore, the maximum affordable quantity for business trips is $5$.

When,

$\mathrm{M}=\mathrm{\$}6,000$

${\mathrm{P}}_{\mathrm{x}}=\mathrm{\$}600$

By substituting we will get,

$\begin{array}{c}\mathrm{X}=\frac{\mathrm{M}}{{\mathrm{P}}_{\mathrm{x}}}\\ =\frac{\mathrm{\$}6000}{\mathrm{\$}600}\\ =10\end{array}$

Therefore, the maximum affordable quantity for business trips is$10$ .

Plotting the graph

Since, the upscale hotels in the United States cuts their price by $25\%$. Here,

$\mathrm{M}=\mathrm{\$}6,000$

${\mathrm{P}}_{\mathrm{x}}=\mathrm{\$}900$

By substituting we will get,

$\begin{array}{c}\mathrm{X}=\frac{\mathrm{M}}{{\mathrm{P}}_{\mathrm{x}}}\\ =\frac{\mathrm{\$}6000}{\mathrm{\$}900}\\ =6.67\end{array}$

Therefore, the maximum affordable quantity for business trips is$6.67$ .

Finding the Marginal Rate of Substitution

Now, to determine if the company is using its resources efficiently, use the Marginal Rate of Substitution's equation:

$\begin{array}{c}\mathrm{MRS}=\frac{-{\mathrm{P}}_{\mathrm{x}}}{{\mathrm{P}}_{\mathrm{y}}}\\ =\frac{-{\mathrm{P}}_{\mathrm{x}}}{{\mathrm{P}}_{\mathrm{y}}}=\frac{900}{600}\\ \mathrm{MRS}=1.5\end{array}$

Hence, the company is not using their resources efficiently because the Marginal Rate of Substitution should be equal to $1.5$, and not -1.