1. a. true b. true c. false d. true e. true f. false g. true h. uncertain 2. Only labour 3. MPL/MPK=K/2L=1 K=2L 500=L1/2K= L1/22L= 2L3/2

optimal L=(250) 2/3 optimal K=2(250) 2/3

4. False, see problem 2 5. False, consider y= K2/3L2/3 6. a. DRS, cost more than twice as much b. CRS, cost twice as much c. IRS, cost less than twice as much 7. AVC=600-2q minimized at q=0 8. MC1=20+2q MC2=40, for the first 10 units MC1< MC2, hence the first 10 units are produced on plant 1 the rest on plant 2 9. There will be entry by the other firms otherwise 10. They cannot affect the price, so MR=p and MR=MC implies p=MC 11. MCi = 20qi : hence each firm’s supply curve is q=p/20 and total industry supply is Q=5p, equating this to the demand 75-0.05Q=0.20Q, Q=300, P=60, q=3, Each firm earns 180 in revenue and bears 190 in costs, so they earn -10 in profits. Firms will be leaving the industry in the long run. 12. MR=p(1+1/e)=MC, where e is the elasticity of demand. Since p>MC, e must be <-1 13. The monopoly has more instruments to extract profits when discriminates. 14. False, it is 0.

15. MR1=50-4q1 MR2=70-4q2, MC=10 MR=MC implies q1 = 10, q2 = 15, P1 = 30, P2 = 40 It should be able to identify to which demand the customer belongs and prevent resale. 16. e1 = -3/2, e2 = -4/3, yes the formulae in 12 above holds. 17. MC=6q, the monopoly will set the price P where demand=MC, so 60-9q=6q, q=4, P=24. And set the membership fee = to consumer surplus after this F=72 18. Each member of the cartel has an incentive to increase her own output. 19. The firms will end up setting p=MC and there will be negative profits in case there are any fixed costs. 20. a. MR=180 - 3y, optimal y=100/3, price P=130 b. for the first 50 units p=180-1.5y is >105 so if the monopoly will decide to operate on this portion of demand it will be constrained by the price ceiling, if they decide to sell >50 the monopoly will not be constrained by the price ceiling. Since p=105 for y<50, the MR is 105 for y<50 and follows 180 - 3y for y>50. c. They will sell 50 at the price of 105. d. they will sell 100/3 at the price of 130. the price ceiling like this is not binding.

21. He faces a residual demand equal to the total demand for food minus the supply of all other types of food offered.

22. On A: MR=60-2y, optimal y=27 and P=33

On B: MR=36-y, optimal y=30 and P=19 b. since the price on A is more than 6 higher than on B every customer from A is buying at market B. The total demand on B market is then (60-p)+(72-2p)=132-3p Profit =(132-3p)(p-6) and optimal price p=25 c. price per unit is 6 on both markets, the membership fees: on A: F=(54)2/2=1458, on B, F=30x60/2=900.

23. a. combined demand of two consumers of two different types Y=20-p+24-2p=44-3p

profit =(44-3p)(p-3), optimal price p=53/6 b. Each consumer of type I will be offered q=17 for the price per unit p=3 and the fee for the right to purchase F=consumer surplus after that = (17) 2/2=144.5. Each consumer of type II will be offered q=18 for the price per unit p=3 and the fee for the right to purchase F=consumer surplus after that = 81

c. These two demands intersect so our approach to the second degree price discrimination cannot be applied here. DISREGARD THIS PART OF THE EXERCISE. Or consider type II demand p=12-y. Then for type II the quantity is determined from 20-y-(12-y)=8=12-y-3, so y=1 and the fee for the right to buy this quantity is the type II

consumer surplus = area of the trapezoid with the bases of 9 and 8 and the height of 1. So the fee for them is 9.5. It is assumed that the customers cover the marginal cost of the service as well. For type I customers the quantity is 17, and the fee for the right to use the service is their entire consumer surplus minus the area between the two demands with the height of 1. Thus the fee for type I customer is (17) 2/2-8=136.5

24. b. Lisa will choose the bigger piece if Bart cuts the cake into unequal pieces, therefore Bart will cut the cake into equal pieces. c. No Bart will still cut into equal pieces. Lisa will do the same if it is her chance to cut.

25. a. Firm 1 profit if the two firms act simultaneously = (130-y1-y2-10)y1 Firm 2 profit if the two firms act simultaneously = (130-y1-y2-5)y2 Firm 1 best response curve is 120-y2=2y1 Firm 2 best response curve is 125-y1=2y2 Optimal pairs of outputs y1=115/3; y2=130/3 Profits approximately $1469 and $1877 b. If firm 2 follows its own decision is given by the same best response curve 125-y1=2y2

or 125/2-.5y1=y2 Firm 1 profit taking this into account is (130-y1-(125/2-.5y1)-10)y1=(115/2-.5y1))y1= =.5((115-y1)y1) Optimal y1=115/2 and y2 that follows is 125/2-115/4=135/4 The profits change to $1653 for firm 1 and $1139 for firm 2. c. clearly manager of firm 1 should act first. d. Both pairs of outputs are on the best response curve of firm 2. the Cournot point is where the best responses intersect and the Stackelberg point is to the right of that where the isoprofit curve of firm 1 touches the best response curve of firm 2.