PNG'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: $\begin{array} { l l }
\ln ( 0.2 ) = - 1.609 & \ln ( 1.5 ) = 0.405 \
\ln ( 0.5 ) = - 0.693 & \ln ( 4,000 ) = 8.294 \
\ln ( 0.8 ) = - 0.223 & \ln ( 5,000 ) = 8.517
\end{array}$ PNG's price elasticity of demand is:
A) -0.252
B) +0.322
C) -3.973
D) +3.108

Question

PNG'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: $\begin{array} { l l } 
\ln ( 0.2 ) = - 1.609 & \ln ( 1.5 ) = 0.405 \
\ln ( 0.5 ) = - 0.693 & \ln ( 4,000 ) = 8.294 \
\ln ( 0.8 ) = - 0.223 & \ln ( 5,000 ) = 8.517
\end{array}$ PNG's price elasticity of demand is:
A) -0.252
B) +0.322
C) -3.973
D) +3.108

Quizplus · Accepted Answer

The price elasticity of demand is calculated using the formula: $$E_d = \frac{\%\ change\ in\ quantity\ demanded}{\%\ change\ in\ price}$$ Given a 50% increase in price and an 80% reduction in quantity sold, the elasticity is: $$E_d = \frac{-80\%}{50\%} = -1.6$$ However, none of the provided options match this calculation directly. The closest interpretation based on the given logarithmic values and the context of the question suggests a misunderstanding in the calculation or the presentation of options. The correct calculation method shows a significant elasticity, indicating a highly elastic demand. The provided options and values hint at a more complex calculation or a specific context not fully addressed in the question. Given the standard formula and the information provided, the expected answer deviates from the options, suggesting option C (-3.973) as the closest to a high elasticity value, despite not matching the standard calculation. This choice is selected based on the context of a significant change in demand relative to price, indicating a misunderstanding or a need for clarification in the question's context.

PNG's Managers Estimate That a 50% Increase in Price Would