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Hi,
For this question of finding the optimum selling price why in the model answer they used to prices and substract one price from the other using the price equation.
When price : $1,350, demand : 8,000 units
When price : 51,400, demand : 7,000 units
So: (?) 1,350 = a ? 8,000b and (2) 1,400 = a ? 7,000?
so subtracting equation (1) from equation (2), 50 : 1,000b and b : 0.05
and substituting in equation (2):1,400 : a 7 0.05 >< 7,000 so a : 1,750
so Price : 1,750 7 0.05q and marginal revenue : 1,750 7 0.1qI am not able to understand why they use theses two prices,
Thanks,
The answer uses two different prices and their corresponding demand quantities to calculate the values of ‘a’ and ‘b’ in the price-demand equation.
The current selling price is $ 1350 and at this price the average weekly demand over lat four weeks has been 8,000 components. An analysis for the market show that for every $50 increase in price demand will falls by 1000 components per week. Equally for every $50 reduction in selling price, the demand will increase by 1,000 components per week.
By substituting the values of price and demand into the equation, they can solve for ‘a’ and ‘b’. In this case, the prices used are $1,350 and $1,400, with corresponding demand quantities of 8,000 units and 7,000 units, respectively
Subtracting equation (1) from equation (2) allows them to solve for ‘b’, which is found to be 0.05. Substituting this value into equation (2) allows them to solve for ‘a’, which is found to be 1,750.
Therefore, the optimum selling price is $1,750, and the marginal revenue equation is 1,750 – 0.1q.
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