Assume in a competitive market, where P is price per unit and Q is number of units. Sellers are not interested in offering this product if P 500, and for every 1 unit increases in P, sellers will offer 1 unit. Buyers are not interested in purchasing this product if P 2,000, and for every 1 unit drops in P, buyers will purchase 0.25 units.

(a)Based on the given information about sellers and buyers, write down the supply and demand equations. Show how to solve for equilibrium quantity Q^e and P^e, total revenue to sellers TR^e, consumer surplus CS^e, producer surplus PS^e, and total surplus TS^e.

(b)Suppose the prices of inputs required to produce this product increase such that the cost to produce each unit increases BY 100. Show how to solve for the new equilibrium quantity Q and price P, total revenue to sellersTR, consumer surplus CS, producer surplus PS, total surplus TS, and the demand elasticity n_D (mid- ? point formula). Calculate the quantity effect and the price effect to confirm TR =

TR TRe equals to "gain" minus "sacrifice" and it is consistent to the result on n_D . (Hint: We discussed quantity effect "gain" and price effect "sacrifice" in lecture using a decrease in price example. The opposite is true if there is a price increase.)

(c)Suppose after the increase in input prices, all buyers of this product receive an increase in income, which shifts the demand to right by 50 units at every price. Write down the new demand curve. (Hint: You need to re-write the demand curve and do not take the "shortcut.") Show how to solve for the new equilibrium quantity Q and price P, total revenue to sellers TR, consumer surplus CS, producer surplus PS, and total surplus TS.