Question

2. A market for a commodity is modelled by taking the demand and supply functions to be $q^P(p) = 1 - p$ and $q^S(p) = p$. The price change in year $t$, i.e. $p_t - p_{t-1}$, depends upon the excess demand in the previous two years and is given by $p_t - p_{t-1} = \frac{7}{12}(q^P(p_{t-1}) - q^S(p_{t-1})) - \frac{1}{12}(q^P(p_{t-2}) - q^S(p_{t-2})).$ Given that $p_0 = 5/2$ and $p_1 = 1/3$, find a formula for $p_t$.

          2. A market for a commodity is modelled by taking the demand and supply functions to be
$q^P(p) = 1 - p$ and $q^S(p) = p$.
The price change in year $t$, i.e. $p_t - p_{t-1}$, depends upon the excess demand in the previous two years
and is given by
$p_t - p_{t-1} = \frac{7}{12}(q^P(p_{t-1}) - q^S(p_{t-1})) - \frac{1}{12}(q^P(p_{t-2}) - q^S(p_{t-2})).$
Given that $p_0 = 5/2$ and $p_1 = 1/3$, find a formula for $p_t$.

2. A market for a commodity is modelled by taking the demand and supply functions to be
q^P(p) = 1 - p and q^S(p) = p.
The price change in year t, i.e. pt - pt-1, depends upon the excess demand in the previous two years
and is given by
pt - pt-1 = (7)/(12)(q^P(pt-1) - q^S(pt-1)) - (1)/(12)(q^P(pt-2) - q^S(pt-2)).
Given that p0 = 5/2 and p1 = 1/3, find a formula for pt.

Added by Dylan G.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Vincenzo Zaccaro

03/20/2023

Step 1

p(t) - p(t-1) = (7/12)(1 - p(t-1)) - (1/12)(1 - p(t-2)) - p(t-1) p(t) - p(t-1) = (7/12) - (7/12)p(t-1) - (1/12) + (1/12)p(t-2) - p(t-1) p(t) = (7/12) - (7/12)p(t-1) - (1/12) + (1/12)p(t-2) + p(t-1) Show more…

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A market for a commodity is modelled by taking the demand and supply functions to be q^(D)(p)=1-p, and ,q^(S)(p)=p. The price change in year t, i.e. p_(t)-p_(t-1), depends upon the excess demand in the previous two years and is given by p_(t)-p_(t-1)=(7)/(12)(q^(D)(p_(t-1))-q^(S)(p_(t-1)))-(1)/(12)(q^(D)(p_(t-2))-q^(S)(p_(t-2))). Given that p_(0)=(5)/(2) and p_(1)=(1)/(3), find a formula for p_(t). 2. A market for a commodity is modelled by taking the demand and supply functions to be qP(p)=1-p and d=(a)sb The price change in year t, i.e. pt -- pt-1, depends upon the excess demand in the previous two years and is given by Pt - Pt-1= ((1-d)sb-(1-d)ab) 12 qP(pt2) -qS(pt2)) Given that po = 5/2 and p1 = 1/3, find a formula for Pt