Question

Consider a small, isolated town in which a brewery faces the following inverse demand: ?=15−0.33?P=15−0.33Q. The brewery can produce beer at a constant marginal and average total cost of $1 per bottle.

a. Calculate the profit-maximizing quantity and price. Specify all amounts to two decimal places.

Q ≈

P ≈ $

b. Calculate consumer and producer surplus and the deadweight loss from market power.

CS = $

PS = $

DWL = $

c. If it were possible to organize the townsfolk, how much would they be willing to pay the brewery to sell beer at a price equal to its marginal cost?

$74.24

$222.71

$340.88

$148.47

d. What is the minimum payment the brewery would be willing to accept to sell beer at a price equal to marginal cost?

$148.47

$74.24

$340.88

$222.71

e. Could the townsfolk and the brewery strike a bargain? Would there by any deadweight loss if such a bargain were struck?

Yes. The townsfolk could pay the brewery an amount that lies between the amounts you specified in parts c and d. There would then be no deadweight loss.

Yes. The townsfolk could pay the brewery an amount that lies between the amounts you specified in parts c and d. There would then be a deadweight loss smaller than the deadweight loss you specified in part b.

No. The amount the townsfolk require exceeds what the brewery is willing to pay.

No. The amount the brewery requires exceeds what the townsfolk are willing to pay.

Answer 1

a) at profit Maximizing eqm

MR = MC

15-.66Q = 1

14= .66Q

Q*= 21.21

P*= 15-.33*21.21 = 8

.

b) CS = .5*(15-8)*21.21

= .5*7*21.21

= 74.235

.

PS = profit = (P-ATC)*Q

= (8-1)*21.21

= 148.47

.

DWL= .5*(8-1)*(42.42-21)

= .5*7*21.21

= 74.235

( In Perfect Competition, P = MC,

So, 15- .33Q = 1

Q= 42.42)

C) option B)

Willingness to pay = deadweight loss incurred in Monopoly + profit in monopoly

= 74.24+ 148.47

= 222.71

D)

Minimum payment equals the reduction in profit , from moving to monopoly to Perfect Competitive firm

So it equals = 148.47, option A)

E) option 1)

Yes, as Max payment, willingness to pay is more than Minimum willingness to accept, so bargaining is possible, total welfare is maximized with no deadweight loss