# Simple supply and demand problem

Data: $$Q_{s}=P/2$$ $$Q_{d}=P-42$$
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. • Check your demand function, it should be decreasing. Feb 22, 2021 at 12:07 • Thanks for your reply. Not sure I follow you. A demand function is always decreasing. Do you mean by that that I'm incorrect somewhere? I would like more assurance, not less so I would be grateful if you can be more specific. 1) I'm not sure if I should use 17 instead of 17.5. Is 17 correct? 2) I only used the supply function to plug my variables as there is a shortage not a surplus. Therefore I never used the demand function here. Am I wrong then? Thanks. Feb 22, 2021 at 12:12 • Your demand is$Q_d=P-42$, which is increasing in price. I guess it should be$42-P\$. Then your calculations will change accordingly. And in general you shouldn't round to integers (if not instructed to do so) since units could well be divisible. Feb 22, 2021 at 12:59