# A perfectly discriminating monopoly has 2 potential consumers. Each consumer has the same demand curve q1=10-2p. The monopoly’s cost function is c(Q)=Q2/2. Find the total quantity Q the monopoly will sell.

A perfectly discriminating monopoly has 2 potential consumers. Each consumer has the same demand curve q1=10-2p. The monopoly’s cost function is c(Q)=Q2/2. Find the total quantity Q the monopoly will sell.

Persons A and B are roommates. Person A smokes and Person B does not. The index s measures how smoky the room is. It varies from s=0, where there is no smoke in the room, to s=1, when the room is filled with smoke. Thus, 1-s measures how “clean” the air in the room is. Person A’s utility function is uA(xA,s)=xA+ln(1+s), where xA is the amount of money Person A owns. Person B’s utility function is uB(xB,1s)=3xB+2(1-s), where xB is the amount of money Person B owns. Each person starts with an endowment of 5 units of money. Person B has the legal right to a smoke-free room. If Persons A and B can exchange money for the right to smoke and make any deal that would make them both better off, what final amounts of money may Person A be left with?

xA may take the values in [0.13;0.23]

xA may take the values in [0.24;0.34]

xA may only take the value 5

xA may take the values in [0.35;0.45]

A monopolist engages in 3rd degree price discrimination and charges the price pA in Market A and the price pB in Market B. The aggregate demand from Market B is QB=10p-3. If the prices that maximize the monopoly’s profits are pA=20 and pB=10, what is the absolute value of the price elasticity of the demand from Market A at the price pA=20?

3

1.5

2.5

2

. A perfectly discriminating monopoly has 2 potential consumers: consumer 1 and consumer 2. Consumer 1’s demand curve is q1=12-2p and q2=12-p. The monopoly’s cost function is c(Q)=3Q2 /4. What will be the quantities q1,q2 the consumers will consume?

q1=0;q2=3

q1=1;q2=2

q1=4;q2=0

q1=0;q2=4

A monopolist engages in 3rd degree price discrimination and charges the price pA in Market A and the price pB in Market B. The aggregate demand from Market B is QB=10p-3. If the prices that maximize the monopoly’s profits are pA=20 and pB=25, what is the absolute value of the price elasticity of the demand from Market A at the price pA=20?

4

6

3

5

Consider the pure exchange economy with 2 goods, good 1 and good 2, and two consumers, consumer A and consumer B. Each consumer is initially endowed with 5 units of each good. The consumers have the following Cobb-Douglas utility functions: uA(x1A,x2A)=x1Ax2A2; uB(x1B,x2B)=x1B2x2B. Is there a point on the contract curve where consumer A’s consumption is strictly below her consumption of good 2?

Yes

Not enough information to answer question.

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