Imagine the market for good x has a demand function of qdx...

Imagine the market for Good X has a demand function of QDX = 100 - 2PX - 4PY + 0.05M + 0.1AX and a supply function of QSX = 4PX - 10, where PX is the price of Good X, PY is the price of Good Y, M is the average consumer income, and AX is the amount spent to advertise Good X. If the price of Good Y is $5, M is $5000, and AX is $10,000, find the equilibrium price of Good X.

Transcript

00:01 So here we're talking about equilibrium.

00:02 We're told that the quantity demand is 100.

00:05 Quantity demanded of x is 100 minus two times the price of x, minus four times the price of y plus 0 .05m plus 0 .1ax.

00:22 We know that the supply function quantity supplied of x is equal to, 4 px minus 10.

00:33 Well, that's a little bit easier.

00:34 We're given a whole bunch of information, so i'm going to plug that in, right? if we simplify the quantity demand, we have 100 minus 2 px, minus 4.

00:45 The price of y is 5 plus 0 .05m, m is 5 ,000, plus 0 .1ax, and a x is 10 ,000.

00:57 So this is equal to 100 minus 2 px minus 20 minus 250 plus 1 ,000, right? if you multiply all those things out.

01:16 Yeah.

01:18 So 100, 1100, 900, 900, 850.

01:23 So this is equal to 830 minus 2 px, right? so we sub in, we get the demand function.

01:30 Now we can say that equilibrium is where quantity supplied of x is equal to quantity demanded of x.

01:40 So i can set 4 px minus 10 is equal to 830 minus 2 px.

01:47 6 px is equal to 820.

01:51 The price of x is equal to, again, with the calculator coming into play here.

02:03 13 .667.

02:05 Now what i do to the price of x is i substitute it back in here and i get the quantity is equal to 4 .13 .6667 minus 10 is equal to with an assist from the calculator 44 .667.

02:35 So this doesn't actually come out to be integers and and i don't think this, that i'm a little surprised by that.

02:41 I thought it would be raped to come out with integer.

02:43 So i'm just checking my math.

02:45 But everything looks okay.

02:46 Yeah, i can't find any mistake.

02:48 So again, demand and supply functions are two variables, their own price, their own quantity.

02:53 Get rid of everything else by subbing it in.

02:56 Set the quantities equal to each other.

02:58 Solve for price.

02:59 Sub back in to get the quantity.

03:02 I could also sub this.

03:05 Oh, and i have done something wrong.