I'm not sure about this, can I ask you if I'm wrong? Thanks.
Data: $$Q_{s}=P/2$$ $$Q_{d}=P-42$$
Questions:
a) How many units will be traded at 35 dollars? At $14 dollars?
b) What quantity at what price will be in equilibrium?
c) What is the total revenue from sales?
Answer a
$$Q_{s}=P/2 => P=2Q_{s}$$ $$Q_{d}=P-42 => P=Q_{d}+42$$ $$P/2=P-42$$ $$P_{eq}=84$$
35 dollars is below 84 dollars, therefore, there is a shortage (we should plug the 35 dollars into the supply equation)
=> 17 units will be sold at that price (am I correct to round down?)
$$Q_{s}=35/2 = 17.5$$
14 dollars also is below 84 dollars, therefore, there is a shortage too (we should plug the 14 dollars into the supply equation)
=> 7 units will be sold at that price
$$Q_{s}=14/2 = 7$$
Answer b
$$P_{eq}=84$$ $$Q_{eq}=P_{eq} /2 = P_{eq}-42$$ $$Q_{eq}= 42$$
Answer c
The total revenue would be, respectively: $$84*42 = 3528$$ $$35*17 = 595$$ $$14*7 = 98$$
I know it's supposed to be simple but not sure if I'm rounding correctly (17.5 to 17) and if those dramatic drops in revenue are to be expected.
Thank you.
