Ok I know this is long, but I am not getting parts of this right. Given : market

Question

Ok I know this is long, but I am not getting parts of this right. Given : market demand q=8-2p and MC =2. I determined the maximizing price and quantity to be p=3 and q=2.

Part II - Welfare Measures a. Find CS (consumer surplus), PS (producer surplus which is equal to profit), and TS (total surplus) in this market. b. Find the portion of TS that goes to consumers ( CS/ T S ) and the portion that goes to monopolist (P S/ T S ). c. Find DWL. d. Now suppose that market demand shifts upward. New market demand is q = 122p. Repeat parts i iii. You have to find monopoly price and quantity for the new market demand first.

Part III - Welfare Analysis Here we are trying to make welfare judgment about the upward shift in demand. a. Compare CS, PS, TS before and after change. What welfare judgment can you make with these comparisons? Explain. b. Compare CS T S and P S T S before and after change. What welfare judgment can you make with this information? Explain. c. Compare DWL before and after the shift. What judgment can be made with this information about the inefficiency in the market before and after? d. Let TSCM be the total surplus in the competitive market. Find DWL, TCCM before and after. What welfare judgment can you make with this comparison? Explain.

Explanation / Answer

Demand: q = 8 - 2p

2p = 8 - q

p = 4 - 0.5q

MC = 2

Equilibrium p = 3 and q = 2 (given).

PART - II

(a) From demand function, when q = 0, p = 4 (Reservation price).

CS = Area between demand curve & market price = (1/2) x (4 - 3) x 2 = (1/2) x 1 x 2 = 1

PS = Area between supply curve & market price = (1/2) x (3 - 2)** x 2 = (1/2) x 1 x 2 = 1

TS = CS + PS = 1 + 1 = 2

**MC = supply price = 2 (given)

(b)

CS / TS = 1 / 2 = 0.5 (50%)

PS / TS = 1 / 2 = 0.5 (50%)

(c)

If the market is perfectly competitive, profit is maximized by equating price with MC:

4 - 0.5q = 2

0.5q = 4 - 2 = 2

q = 4

p = MC = 2

Deadweight loss = (1/2 x Difference in price x Difference in quantity = (1/2) x (3 - 2) x (4 - 2) = (1/2) x 1 x 2 = 1

(d) New demand: q = 12 - 2p

2p = 12 - q

p = 6 - 0.5q

Total revenue, TR = p x q = 6q - 0.5q2

Marginal revenue, MR = dTR / dq = 6 - q

Equating with MC,

6 - q = 2

q = 6 - 2 = 4

p = 6 - 0.5q = 6 - (0.5 x 4) = 6 - 2 = 4

(i) For new demand curve, when q = 0, p = 6 (Reservation price)

CS = (1/2) x (6 - 4) x 4 = (1/2) x 2 x 4 = 4

PS = (1/2) x (4 - 2) x 4 = (1/2) x 2 x 4 = 4

TS = 4 + 4 = 8

(ii)

CS / TS = 4 / 8 = 0.5 (50%)

PS / TS = 4 / 8 = 0.5 (50%)

(iii)

If the market is perfectly competitive, profit is maximized by equating price with MC:

6 - 0.5q = 2

0.5q = 6 - 2 = 4

q = 8

p = MC = 2

Deadweight loss = (1/2 x Difference in price x Difference in quantity = (1/2) x (4 - 2) x (8 - 4) = (1/2) x 2 x 4 = 4

NOTE: The first multi-part sub-question is answered in full.

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