Question

2. Points = 26. Consider Market Model: Demand: Supply: Q=a-bP Q=-c+dP (a, b>0) (c,d > 0) 1) Discuss in words the meaning of each equation in the model (3 points); 2) Find the equilibrium levels of P* and Q* (3 points); 3) Draw qualitative conclusions about changes in P* and Q* when each of the parameters change. (Qualitative conclusion shows the direction of change.) Explain economic meaning of these changes. (Total 6 points: 3 points for P*; 3 points for Q*); 4) If a= 10, c=5, b= 2; d = 3, draw quantitative conclusions about changes in P* and Q when each of the parameters change. (Quantitative conclusion shows the magnitude of change.) Explain economic meaning of these changes. (Total 6 points: 3 points for P; 3 points for Q*); 5) Show your conclusions in (4) graphically. Note: Carefully label everything on your graphs. Make the graphs neat and understandable. Points will be deducted for missing labeling and for hard-to- understand graphs. (Total 8 points: 4 graphs -- change in a; change in b; change in c, change in d; -- 2 pts each).

Answer 1

1) The first equation is the demand curve which gives the market demand which varies with the prevailing price of the good. The quantity demanded by the consumers varies negatively with price, satisfying the law of demand. The lower the price, the higher is the demand of the good.

The second, being the supply curve gives the quantity supplied given the price of the good. As expected, the producers supply more to higher price and hence there is a positive relationship between Q and P.

2) At equilibrium, Demand = Supply. Hence,

$a-bP=-c+dP => P^{*}=\frac{a+c}{b+d}$

Replacing this value of P in either the demand or supply curve gives us, $Q* = a-b(\frac{a+c}{b+d}) = \frac{ab+ad-ab-bc}{b+d}=\frac{ad-bc}{b+d}$

3)

$\frac{dP*}{da}=\frac{1}{b+d}> 0 ; \frac{dQ*}{da}=\frac{d}{b+d}>0$

As 'a' increases, quantity demanded at all prices increase, resulting in higher equilibrium price and quantity.

$\frac{dP*}{db}=\frac{-(a&plus;c)}{(b&plus;d)^{2}}< 0 ; \frac{dQ*}{db}=\frac{-a(c&plus;d)}{(b&plus;d)^{2}}<0$

As 'b' increases, the absolute slope of the demand curve increases, the demand curve becomes steeper. Consumers demand lower quantities than before for lower prices which results in a decline of the equilibrium price and quantity.

$\frac{dP*}{dc}=\frac{1}{(b&plus;d)}>0 ; \frac{dQ*}{db}=\frac{-b}{(b&plus;d)}<0$

As 'c' increases, quantity supplied is less at all prices which results in a scarcity, driving the equilibrium price up but the equilibrium quantity down.

$\frac{dP*}{d\textrm{d}}=\frac{-(a&plus;c)}{(b&plus;d)^2}<0 ; \frac{dQ*}{d\textrm{d}}=\frac{b(a&plus;c)}{(b&plus;d)^2}>0$

As 'd' increases, slope of the supply curve decreases, higher quantity is supplied than before for higher prices. Supply curve is This leads to a fall in equilibrium price but a rise in equilibrium quantity.

4)

$\frac{dP*}{da}=\frac{1}{5} ; \frac{dQ*}{da}=\frac{3}{5}$

$\frac{dP*}{db}=\frac{-3}{5} ; \frac{dQ*}{db}=\frac{-16}{5}$

$\frac{dP*}{dc}=\frac{1}{5} ; \frac{dQ*}{db}=\frac{-16}{5}$

$\frac{dP*}{d\textrm{d}}=\frac{-3}{5} ; \frac{dQ*}{d\textrm{d}}=\frac{6}{5}$

For every unit change in 'a', equilibrium price will change by 1/5 and the equilibrium quantity by 3/5. The interpretation will be the same for the rest.

5) Label the diagrams according to the first diagram.

Rise a = 10 b=2, en c c =5, d = 3 8 = 10 - 2 P. 21 = 10-8 P = 5-2 l 8 = - 5 + 3 P. => 3P = g + 5 >> P Tots 5 Rise in V loco Change in a (say, rise in a). Rise in bo