# Mat 540 Chapter 4

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Chapter 8 1. Question #1, page 189 in text By allowing student to pick and choose between prices, they will pick price will below their reservation price and university cannot get to their surplus. For example, sleepers will have a consumer surplus of \$2,500 when they buy the dorm room by \$3,000. The eaters will have consumer surplus of \$ 3,500 when they buy the meal plan by \$2,500. The best price to consume the maximum consumer surplus and get the highest revenue is to charge a total of \$8,000 for a both dorm room and meal plan. Chapter 9 2. Problem #5, p. 221 in text. Total cost = 200 + 50 q Market demand: P = 290 –(1/3) Q Number of firms in market: n=14 The output level that maximizes profit: q = (a – c) / [(n+1)*b] q…show more content…
Problem #6, p. 221 in text. (You do not need to “derive” the Cournot equilibrium. Just solve for the values using the appropriate formulas.) Market demand: P = 400 – 2Q Unit cost production = 40 a. Firm’s quantity in equilibrium is : q1 = (a-c)/3b = (400-40)/(3*2)= 60 unit = q2 Firm’s revenue: P= 400 – 2 * (2*60) = \$160 Firm’s profit = (60*160) – (60*40) = \$7200 b. Monopoly output: MR=400-4q MC=40 MR=MC 400 – 4q = 40 then q=90 unit The reason that producing on half the monopoly output (90*1.5 = 135) a Nash equilibrium outcome is that it will exceed the market demand of Nash equilibrium (\$160). 4. Problem #8, p. 221-222 in text. (HINT: First calculate the profits of a market with two firms, and then continue this process for 3, 4, and 5 firms.) a. To obtain the long run equilibrium, number of firms in the industry should be infinity, and it is calculated by: qi= (a-c) / [(n+1)*b] b. For two firms: Quantity: q1=q2= (a-c)/[(n+1)*b]= (100-20)/3 = 26.67 Price: P=100-(2*26.67)=46.67 Cost: Cost= 20*26.67=789.4 Profit: Profit=46.67*26.67-789.4=0 For Three firms: Quantity: q1=q2= q3 = 20 Price: P=60 Cost: Cost= 296 Profit: Profit=904 For Four firms: Quantity: q1=q2= q3 =…show more content…
Suppose that Firm 1 is a domestic producer and Firm 2 is a foreign producer. The domestic government grants Firm 1 a subsidy of \$3 per unit of production. What will be the new Cournot firm quantities, market price, and profits? (HINT: Think about what the subsidy does for Firm 1’s marginal costs.) q1= (100-(10-3))/3=31 q2= 30 Q=31+30=61 Market Price=100-30-31=39 Firm’s one profit= 31*39-31*7=992 Firm’s two profit=30*39-30*10=870 c. Compare consumer surplus from parts a and b. Do consumers fare better with or without the subsidy? (Remember that consumer surplus is calculated from market quantity and market price.) The consumer surplus is bigger with subsidiary because they get more quantity with lower price while without subsidiary consumer’s surplus become smaller as they get less quantity with higher price. Chapter 11 6. Practice Problem 11.1, p. 249 in text. (For parts a and b, only perform the mathematical calculations/derivations. That is, only answer the first sentence for each part. Answer all of part c.) 7. Problem #1, part a only, p. 260 in text. P=200-q1-q2 MC=60 a. q2= (a-b*q1-c)/2*b = (a-c)/(48b) b. For the first firm: q1=200-60/2*1=70 For the second firms: