Economics Problem (Find equilibrium price and quantity)

[Jacob_10329]

The demand for cookies is given by QD = 425 – 2P where QD is the quantity demanded of the cookies (number of cookies per day) and P is the price of cookies ($/cookie). The supply of cookies is given by QS = 5 + 3P where QS is the quantity supplied of the cookies (number of cookies per day) and P is the price of cookies ($/cookie).

a) Find the equilibrium price and quantity.

b) Let’s say, other things equal, bakers have improved their technology to produce cookies and the supply increases – the quantity supplied increases by 60 cookies per day at every possible price. Find the new equilibrium price and quantity.

For question a. I got P = $84 and Q = 257 and
for question b. I got P = $72 and Q = 281

I was wondering if someone can double check to see if I got this question correct, thanks!

 

[Jacob Lee]

The demand for cookies is given by QD = 425 – 2P where QD is the quantity demanded of the cookies (number of cookies per day) and P is the price of cookies ($/cookie). The supply of cookies is given by QS = 5 + 3P where QS is the quantity supplied of the cookies (number of cookies per day) and P is the price of cookies ($/cookie).

a) Find the equilibrium price and quantity.

b) Let’s say, other things equal, bakers have improved their technology to produce cookies and the supply increases – the quantity supplied increases by 60 cookies per day at every possible price. Find the new equilibrium price and quantity.

For question a. I got P = $84 and Q = 257 and
for question b. I got P = $72 and Q = 281

I was wondering if someone can double check to see if I got this question correct, thanks!

 

[tieboa]

Hi Jacob
your answer for question a. is correct (those two equation will be solved by using the simultaneous=substitutionmethods).

 

[JeffM]

Your answers are correct mathematically although they make no practical sense: a cookie costing 84 dollars is a joke!

You may notice that tieboa is a brand new member and has never answered a question before. There is an easier method to solve this problem than what he or she proposed. Notice that there actually are three independent variables, and to solve for three variables, you need three equations. I suspect you used that fact to find p.

[MATH]p = \text {market price per cookie;}\\ q_d(p) = \text {quantity demanded per day at a unit price of } p; \text { and}\\ q_s((p) = \text {quantity supplied per day at a unit price of } p.\\ q_d(p) = 425 - 2p, \text { and}\\ q_s(p) = 5 + 3p.[/MATH]Three variables and two equations. The third equation is not given, but it is necessary to solve the problem. Instead you are given the clue of equilibrium. What happens to supply and demand when the market is at equilibrium? They are equal. So the third equation is

[MATH]q_d(p) = q_s(p) \implies 425 - 2p = 5 + 3p \implies 5p = 420 \implies p = 84.[/MATH]
From a purely mathematical perspective, QS and QD are different variables and cannot be substituted for each other in general. It is the conditions implicit in the word "equilibrium" that both make the problem soluble and make the solution simple. Notice that the algebra immediately reduces to one equation in one unknown. Equilibrium simplifies the math a lot.