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This question refers to a market in which quantity demanded is given by $q = a - bp$ and quantity supplied by $q = c + dp$.

In this market, an increase in the parameter $a$ would:

a. increase quantity and decrease price.

b. decrease both price and quantity.

c. increase both price and quantity.

d. increase price and decrease quantity.

callculus42
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Joyce
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  • What are your own thoughts? The parameter $a$ appears only in the first equation ... Also, why are both quantity demanded and quantity supplied set to $q$? Is $q=q$? – Matti P. Jul 23 '18 at 07:21
  • No Idea. This is my confusion. I read the text and the notes and now have to complete these hw problems and this is the only one I am having an issue with because of what you mentioned. – Joyce Jul 23 '18 at 07:22
  • Also, we don't have any information about the price here. Since the sign of $a$ in the first equation is positive, we can be pretty sure that the answers B and D are not correct. So the correct answer is either A or C. – Matti P. Jul 23 '18 at 07:25
  • Maybe i will take a guess then. Ughhh! – Joyce Jul 23 '18 at 07:30
  • @Joyce On what price and what quantity does the statements relate? Equilibrium quantity and equlibrium quatity? This should has been mentioned in the statments. – callculus42 Jul 23 '18 at 08:19
  • Usually, $q$ is the same in both equations to give you the hint that in equilibrium quantity demanded equals quantity supplied. You could answer the question using that condition, solve for $p$ and then solve for $q.$ I suggest it's faster to draw a diagram with supply and demand curves, and note how the curves and thus the equilibrium changes when you change $a$. – Trurl Jul 23 '18 at 17:40

2 Answers2

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One of the tenets of economics is that in equilibrium $$Supply=Demand$$ Both supply and demand are functions of price. So in order to find an equilibrium we need find a price that satisfy the above equation. If supply and demand equations are well-behaved (i.e., supply equation increasing in price and demand equation decreasing in price) then there is a unique equilibrium price such that demand=supply.

So in your case $$ a-bp = c+dp$$

Solving this equation for $p$ you obtain $$ p = \frac{a-c}{b+d} $$ Note that the price needs to be non-negative and finite, which imposes restrictions on the parameters. Assuming that $b,d>0$ so that demand and supply functions are well behaved, we have requirement that $a-c>0$.

We can now answer your question. Differentiating $p$ wrt $a$ we obtain $$\frac{\partial p}{\partial a} = \frac{1}{b+d}>0$$

Therefore, equilibrium price increases following an increase in $a$. Moreover, since equilibrium $p$ increases, the supply function implies that the equilibrium quantity will increase as well.

So answer C is correct: Both equilibrium price and equilibrium quantity will increase.

Mdoc
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If $a$ increases to $a'$, the Demand function $D$ goes to $D'$ and the equilibrium point $E$ goes to $E'$; that is both quantity and price increase.

See the following picture: enter image description here

alexjo
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