TTV Corporation's managers estimate that a 50% increase in price would cause an 80% reduction in the quantity of product sold. Total fixed costs for the product are $5,000 and total variable costs are $4,000, based on production of 400 units. The following values may be useful: $$\begin{array} { l }
\ln ( 0.2 ) = - 1.609 \quad \ln ( 1.5 ) = 0.405 \
\ln ( 0.5 ) = - 0.693 \quad \ln ( 4,000 ) = 8.294 \
\ln ( 0.8 ) = - 0.223 \quad \ln ( 5,000 ) = 8.517 \
\end{array}$$ TTV's price elasticity of demand is:

Question

TTV Corporation's managers estimate that a 50% increase in price would cause an 80% reduction in the quantity of product sold. Total fixed costs for the product are $5,000 and total variable costs are $4,000, based on production of 400 units. The following values may be useful: $$\begin{array} { l } 
\ln ( 0.2 ) = - 1.609 \quad \ln ( 1.5 ) = 0.405 \
\ln ( 0.5 ) = - 0.693 \quad \ln ( 4,000 ) = 8.294 \
\ln ( 0.8 ) = - 0.223 \quad \ln ( 5,000 ) = 8.517 \
\end{array}$$ TTV's price elasticity of demand is:

Quizplus · Accepted Answer

The price elasticity of demand is calculated as the percentage change in quantity demanded divided by the percentage change in price, which gives -80% / 50% = -1.6. However, using the given logarithmic values for a more precise calculation, we use the formula $\ln(Q_2/Q_1) / \ln(P_2/P_1)$, which results in $\ln(0.2)/\ln(1.5) = -1.609/0.405 = -3.973$, indicating option A is correct.

TTV Corporation's Managers Estimate That a 50% Increase in Price