Question

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6. Consider the following demand and supply functions for commodity i: qp = 500 - 10pi +5p; + 20y qi = -100+ 10pi - 10px where y = income, p; = price of substitute j, and pk = price of input k. (a) Solve for and graph the inverse demand and supply functions under the assumption that P; = 4, y = 4, and P = 10. 2pt Solve for equilibrium quantity and price, q* and p*, as well as the consumer surplus and producer surplus at these equilibrium quantities. Please provide a graph along with your answer. 2pt How would equilibrium values change in income, y, increased from 4 to 9? Please provide a graph along with your answer. 2pt

Answer 1

= 500- 10 Pi + 5Pjt zou = 500 - Topi + 5(4+ 2014) = 500-10Pi + 20+ 0 qd; = 6oo-lopi loPi = 60o- qli Pi = 60 0.12i inverse demand the Pi= 6o- 0.12i qs; = -200 + 10 Pi - 10px = -100 + lopi - 100102 = -100 + lo Pi - 100 = - 200 + lopi bqsi = - 200 + lopi Direct ssen qi + 200 = 10 li - Pi = 20 to 12i This is inverse supply the با ما DD = SS ( In equilibrium) 66-0-18i = 2ot oli 60-20 = 0.12ito.lqi 40= 0. 2qi 2i = 40 0.2 que P = = 200 20+ 0.1 (200) = 20 + 20 = 40

S ९ ५०० - - - Ds 200 * cs = (60 -- ५०) (200) = PS = । (५०-२०) (३००) = २००० २०००

Now income fer from 4 to 9 qd;= 500 - lopi + 5 Pj + zoy = 500- lopi + 5(4) + 2018) = 500- lopit zot 180 q: 70o- loli lopi = 700- qi - Piz z o- oolzi DO = ss 70 - 0.lei = Zot o lei - 70-20 = 0.12; toolei 50= 0.22i li = 50 0.2 qi = 250 q* =250 p* = 20+ 0-1 (250) = 20+ 25 = 45

_ Do 200 250 250 600 700 g A As income fer from u to g demand cuerue Shifts to the right from Do to Di. The equilibrium point moves from point to A. As a result equilibrium price fes from 40 to 45 and equilibrium quantity шло •е» че bьт goo ta5o.