Given the following supply and demand functions find the Market Equilibrium point: Qs = 10 +15P Qd = 150 -5P. Now assume there is a positive shock in demand: Qd2 = 200 - 5P find the new Equilibrium Price and Quantity.

Market Equilibrium is one of the fundamental concepts in Economics. Graphically our equilibrium will be the point of intersection between Demand and Supply function. On the order hand, In order to solve it algebrically we need to create a system of simultaneous equation. This simply means solving for both Supply and Demand simultaneously. To do so we first equate Quantity Demanded and Supplied (since at equilibrium they must be the same) to solve for the Equilibrium Price. So given Qs = 10 + 15P and Qd= 150 -5P we impose Qd = Qs, by plugging in the respective function for Qd and Qs, we get 10 + 15P = 150 - 5P, now we have to solve for P so we rearrange the equation by moving all the constants to the RHS and all the Variables (in this case only P) to the LHS. This will give us 20P = 140, therefor P*=7 (the star indicates that this is the price at Equilibrium). Now we can plug P* into either supply or demand to get our Q*. We'll plug it into the demand so we get that Q*= 150 - 5x7= 150 - 35= 115. So our Equilibrium[P*,Q*] will be (7,115). Note that if we plug P* into the Supply we'll get the same result since both equations were solved simultaneously. Q*=10 +15x7=115. Now, let's analyse the shock in demand. This positive shock shifted our demand function rightwards, graphically we would see that the intercept of the function with the Y-axis changed from 150 to 200. This happened because the constant in both functions indicates where the function is going to intercept the Y-axis, if the shock changed the coefficient of P instead of the constant we would have seen a pivot instead of a shift in the function. We can solve for the new equilibrium in the same way as before and get our new Equilibrium price and quantity which will respectively be: P*=9.5 and Q*=152.5.