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Final Exam Study Guide (2020 Fall) Main Topics (New) 1.

2.

3.

Perfect Competition,Monopoly, and Monopolistic Competition a. Characteristics of Perfect Competition,Monopoly, and Monopolistic Competition b. Perfect Competition in short-run and Long-run c. Profit maximization d. Shut down vs Exit decision under perfect competition e. Deadweight loss under Monopoly f. Monopolistic Competition in short-run and Long-run Oligopoly a. Four Oligopoly settings b. Reaction function and profit for Cournot Oligopoly Price Descrimination a. First/ Second/ Third Price descrimination b. Other Surplus extraction: Two-part pricing

Main Topics (Old) 4. 5. 6. 7. 8. 9. 10.

Cost and Cost Functions Cost Minimization in Short-Run and Long-Run Production Function, MPL, MPK, increasing/decreasing/constant, returns to scale Demand/Supply Shifts and Market Equilibrium Consumer and Producer Surplus Price Restrictions (floors/ceilings) and Taxes Elasticity

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MULTIPLE CHOICE QUESTIONS Elasticity 1.

2.

Assume that the price elasticity of demand is -2 for a certain firm’s product. If the firm raises the price, the firm’s managers can expect total revenue to: a. Decrease b. Increase c. Remain constant d. Either increase or remain constant depending upon the size of the price increase. Answer: A. This firm is facing an elastic demand, thus an increase in price by 1% would decrease quantity by more than 1%. Revenues decline. If a price increase from $5 to $7 causes quantity demanded to fall from 150 to 100, what is the absolute value of the own-price elasticity at a price of $7? a. 0.57 b. 1.75 c. 0.02 d. 1.24 Answer: B. 𝐸𝑄𝑥 ,𝑃𝑥 =

3.

𝛥𝑃𝑥

∗

𝑃𝑥 𝑄𝑥

=

100−150 7−5

∗

7 100

= −1.75. The absolute value is 1.75

The own-price elasticity of demand for apples is -1.5. If the price of apples falls by 6%, what will happen to the quantity of apples demanded? a. It will increase 4% b. It will increase 9% c. It will fall 4% d. It will fall 6% Answer: B. 𝐸𝑄𝑥 ,𝑃𝑥 =

4.

𝛥𝑄𝑥

%𝛥𝑄𝑥 %𝛥𝑃𝑥

→ %𝛥𝑄𝑥 = 𝐸𝑄𝑥 ,𝑃𝑥 ∗ %𝛥𝑃𝑥 = (−1.5) ∗ %6 = −9% Demannd

increases by 9%. A 3 percent increase in price causes a 10 percent decrease in quantity demanded for a good. Which of the following statements is most likely applicable to this good? a. The relevant time horizon is short. b. The good is a necessity. c. The market for the good is broadly defined. d. There are many close substitutes for this good. %𝛥𝑄

Answer: D. 𝐸𝑄𝑥 ,𝑃𝑥 = %𝛥𝑃𝑥 = 𝑥

−%10 %3

= −3.33 The absolute value of E is greater than 1, the

demand is elastic. Among given options, a good with many close substitutes is the one with elastic demand.

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CS, PS, Price Restrictions (floors/ceilings) and Taxes 5.

6.

7.

The market demand is 𝑄𝐷 = 60 − 6𝑃 and the market supply is 𝑄𝑆 = 4𝑃. A price ceiling of $3 will result in a a. Quantity shortage of 30 units b. Quantity surplus of 30 units c. Quantity surplus of 12 units d. Quantity shortage of 12 units Answer: A. After a price ceiling of $3, consumers would like to purchase 𝑄𝐷 = 60 − 3 ∗ 6 = 42 and the producer will produce 𝑄𝑆 = 4 ∗ 3 = 12. Thus, there is a shortage of 4212=30. A tax of $10 per unit is imposed on good X. The tax reduces the equilibrium quantity in the market by 200 units. The deadweight loss from the tax is: a. $2,000. b. $1,000. c. $500. d. $250. Answer: B. Deadweight loss is the area of the triangle that is created by imposing the tax and because the market shrinks (Q after tax is smaller than 𝑄 ∗). The Tax reduces equilibrium quantity by 200 units. This, by the way, is also the height of the triangle that is associated with the deadweight loss. The base of the deadweight loss is actually the amount of per unit tax: Tax=$10. So the amount of the deadweight loss is: 𝐷𝑊𝐿 = 1/2 ∗ 200 ∗ 10 = $1,000. The demand and supply for headphones are given as: Qd= 30- 2P and Qs =2P-10. If government imposes a price ceiling of P=$8. What are the CS and PS? a. CS= 33, PS= 9 b. CS= 9, PS= 33 c. CS=20, PS= 12 d. CS=12, PS= 20 Answer: A. When a price ceiling of $8 is imposed, to get the quantity traded in the market, we plug in 𝑃 = $8 into the supply function:𝑄𝑇 = 2𝑃 − 10 = 2 ∗ 8 − 10 = 6. Given the quantity traded in the market now is 6 unit, we can find the full economic price by plug in 𝑄𝑇 = 6 into the demand function.30 − 2𝑃 = 6 , we can solve for P and the get the full economic price. Thus, the full economic price would be P = 12 New consumer surplus = Area A = (15 − 12) ∗ 6 ∗ 0.5 + (12 − 8) ∗ 6 = 9 + 24 = 33 New producer surplus = Area B = (8 − 5) ∗ 6 ∗ 0.5 = 9

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Demand and Supply 8.

New cars are normal goods. What will happen to the equilibrium price of new cars if the price of gasoline rises, the price of steel falls, public transportation becomes cheaper and more comfortable, auto- workers accept lower wages, and automobile insurance becomes more expensive? a. Price will rise. b. Price will fall. c. Price will stay exactly the same. d. The price change will be ambiguous. Answer: B. If price of gas rises, people will buy fewer cars, so demand decreases. If public transportation also becomes cheaper and more comfortable, fewer people will drive and more will use public transportation, which also decreases Demand for new cars. If auto insurance becomes more expensive, this also decreases demand since people won’t buy as many new cars as before the increase in the price of insurance. All these factors decrease the Demand for new cars. Auto workers accepting lower wages affects supply: since wages are an input for autos, a decrease in wages will increase the supply of cars. A decrease in Demand and an increase in Supply will lower equilibrium price unambiguously. On the other hand, the equilibrium quantity is ambiguous.

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9.

If steak is a normal good, what would happen to equilibrium price and quantity during a recession? a. Price would increase and quantity decrease b. Price and quantity would both increase c. Price and quantity would both decrease d. Price would decrease and quantity increase Answer: C. During a recession, aggregate income declines. Income is a demand shifter. Since steak is a normal good, demand shifts downward, so that equilibrium price and quantity both decline. 10. Which of the following events will definitely cause equilibrium quantity to fall? a. demand increases and supply decreases b. demand and supply both decrease c. demand decreases and supply increases d. demand and supply both increase Answer: B. Equilibrium Quantity decreases unambiguously when D decreases and S decreases. When D decreases, this means that people don’t want to purchase the good – so quantity (and price) decline. When S declines, that means less quantity is available, so Q also declines. 11. Beer and wine are substitutes. Suppose that higher minimum wage in breweries has reduced the amount of beer in the market. What impact does this have on the equilibrium price and quantity for wine? a. Price increases, quantity increase b. Price decreases, quantity decreases c. Price increase, quantity is ambiguous d. price is ambiguous, quantity decreases Answer: A. In the market for beer, as the supply of beer decreases, it shifts the supply curve to the left. At the new equilibrium, the price for beer increases. Beer and wine are substitutes. When the price for beer increases, the demand for wine would increase. An increase in demand in the wine marker would shift the demand for wine to the right. At the new euiqlibrium, the price and quantity for wine both increase.

Cost and Cost function 12. Suppose the production function is given by: 𝐹(𝐿, 𝐾) = 𝐿0.5 𝐾 0.5 . Suppose that you have employed L=4 and K=9 units of inputs. What is the marginal product of the fourth worker? What is the average product of labor? 3 3 a. 𝑀𝑃𝐿 = 4; 𝐴𝑃𝐿 = 4

2 3

3

2 2

1

3 1

b.

𝑀𝑃𝐿 = 3; 𝐴𝑃𝐿 =

c.

𝑀𝑃𝐿 = 4; 𝐴𝑃𝐿 =

d.

𝑀𝑃𝐿 = ; 𝐴𝑃𝐿 = 2

2

Answer: A. We can find 𝑀𝑃𝐿 = 0.5𝐿−0.5𝐾 0.5. Substutting K=9 and L =4, we can get 3 𝑀𝑃𝐿 = 0.5𝐿−0.5𝐾 0.5 = 0.5 ∗ 4 −0.5 ∗ 9 0.5 = 4.To find 𝐴𝑃𝐿 we need to find the total output Q 5

produced with L=4 and K=9 and then divide that number by the total amount worker L =4. 𝑄 6 3 𝑄 = 𝐿0.5 𝐾 0.5 = 2 ∗ 3 = 6,𝐴𝑃𝐿 = = = 𝐿

4

2

13. Total product begins to fall when: a. Marginal product is maximized b. Marginal product begins to decline c. Marginal product is negative d. Marginal product is positive but declining Answer: C. Output begins to decline when if you add more input, total output (Q) is diminished. This means that the last unit of input has to have a negative MP (negative productivity), since it destroys total output. 14. For the cost function 𝑇𝐶 = 100 + 2𝑄 + 3𝑄2 , the marginal cost of producing 2 units of output is a. MC=$2 b. MC=$14 c. MC=$12 d. MC=$3 Answer:B. 𝑀𝐶 = 2 + 6𝑄. Evaluate at Q=2; MC=2+6*2=14 15. Which of the following statements best summarizes the law of diminishing marginal returns? a. In the short run, as more labor is hired, output diminishes. b. In the short run, as more labor is hired, output increases at a diminishing rate. c. In the short run, the amount of labor a firm will hire diminishes as output increases. d. As more labor is hired, the length of time that defines the short run diminishes. Answer: B. Diminishing marginal returns (another term for diminishing marginal product) means that when more of an input is used (in this case labor), output increases but at a diminishing rate. This is so because each additional worker gives us fewer and fewer units of output compared to the previous workers. 16. The marginal cost curve: a. Lies always below the average total cost curve (ATC) b. Lies always above the average variable cost curve (AVC) c. Intersects the ATC and AVC at their maximum points d. Intersects the ATC and AVC at their minimum points Answer: D. Marginal cost always goes through the lowest point of ATC and AVC. We gave an intuition for this in the lecture and we proved/showed this in examples.

Cost min in short/long run 17. The production function is 𝑄 = 𝐾 0.5 𝐿0.5. In the short-run, the firm sells its output at a price of $10 per unit, and can hire labor at a wage of $5 per unit. Capital is fixed at 25 units. The amount of labor that minimizes costs is: a. L=1 b. L = 25 c. L = 10 d. None is correct

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Answer: B. Cost-Minimizing (Profit maximizing) with one input (or in the short-run if K is fixed): 𝑃 ∗ 𝑀𝑃𝐿 = 𝑤. Since 𝑀𝑃𝐿 = 0.5𝐾 0.5 𝐿−0.5 = .5 ∗ 250.5𝐿−0.5 = .5 ∗ 5𝐿−0.5, plug this equation into the short-run miximizing condition. Thus, 𝑃 ∗ 𝑀𝑃𝐿 = 𝑤 → 10 ∗ .5 ∗ 5𝐿−0.5 = 25 25, we get 0.5 = 5. Thus L=25 𝐿 18. Suppose the marginal product of labor is 8 and the marginal product of capital is 2. If the wage rate is $4 and the price of capital is $2, then in order to minimize costs the firm should a. use more capital and less labor. b. use more labor and less capital. c. use three times more capital than labor. d. none of the above. Answer:B. First we check 𝑀𝑃𝐿 /𝑀𝑃𝑘 = 8/2 = 4 > 4/2 = 𝑤/𝑟, so we are not the cost minimization point. You need to moive from 𝑀𝑃𝐿 /𝑀𝑃𝑘 > 𝑤/𝑟 towards 𝑀𝑃𝐿 /𝑀𝑃𝑘 = 𝑤/𝑟. Currently we have 𝑀𝑃𝐿 /𝑤 > 𝑀𝑃𝑘 /𝑟, which means the productivity of labor relative to its cost is more than the productivity of Capital relative to its cost. we should higher more workers. As we increase L, 𝑀𝑃𝐿 increases, and as you decrease K ,𝑀𝑃𝑘 inncreases, so the ratio 𝑀𝑃𝐿 /𝑤 decreases while 𝑀𝑃𝑘 /𝑟 increases. You keep subtracting L and adding K until the two ratios are equal to each other. 19. A firm produces according to the following production function: 𝐹(𝑘, 𝐿) = 𝐿0.7 𝐾 0.3 . The price of capital is $3 and the wage rate is $7. What is the optimal combination of labor and capital to produce 100 units of output? a. L=50 and K=50 b. L=100 and K=50 c. L=100 and K=100 d. L=10 and K=10 Answer: C. At cost minimization point, we have 𝑀𝑃𝐿 /𝑀𝑃𝑘 = 𝑤/𝑟. 𝑀𝑃𝐿 /𝑀𝑃𝑘 = 0.7𝐿−0.3 𝐾0.3 0.3𝐿0.7 𝐾 −0.7 0.7 0.3

7𝐾

= = 7/3. Thus, K=L. Plug this into the production function, we have 100 = 3𝐿 0.7 𝐿 𝐾 → 𝐿 𝐿0.3 = 100 → L=100 and k=100 20. A firm produces output according to a production function: F(L,K) =4K +8L. If the wage rate i s $60 per hour and the rental rate on capital is $20 per hour, what is the cost-minimizing input mix for producing 32 units of output? a. L=2;K=4 b. L=0;K=8 c. K=4;L=0 d. K=1;L=6 Answer: B. The production function in this case is linear (inputs are perfectly substitutable), which means that the firm can substitute Labor for Capital (or vice versa) at a constant rate throughout the isoquant. We know that 𝑀𝑃𝐿 = 8 and 𝑀𝑃𝐾 = 4. Using the tangency condition, we have: 𝑀𝑃𝐿 /𝑤 = 8/60 < 𝑀𝑃𝐾 /𝑟 = 4/20 Normally we would say we have hired too much labor – to get to the tangency condition and restore the equilibrium we would fire labor and hire more capital until the two sides of the equation are equal. The issue in this case is that the productivity of labor and capital does not change (they are constant) throughout the isoquant: no matter how much labor we have, its productivity is 𝑀𝑃𝐿 = 8 and capital productivity is 𝑀𝑃𝐾 = 4. This means the two ratios in the tangency condition WILL NEVER be equal. This means that we have a corner solution: either we hire 7

all labor or hire all capital, whichever is more productive relative to its cost. In this case, capital is more productive relative to its cost, so we produce Q =32 using only capital ( K = 8 ) and no labor.

Oligopoly 21. Which of the following is NOT a feature of Sweezy oligopoly? a. There are few firms in the market serving many consumers. b. The firms produce homogeneous products. c. Each firm believes that rivals will cut their prices in response to a price reduction, but will not raise their prices in response to a price increase. d. Barriers to entry exist. Answer: B. The firms produce differentiated products under Sweezy oligopoly. 22. Which of the following is a profit-maximizing condition for a Cournot oligopolist? a. MR=MC b. 𝑄1 = 𝑄2 = 𝑄3 =. . . = 𝑄𝑛 c. P= MR d. All above are correct Answer: A. For profit maximization, MR=MC holds for any types of markst structure. However, if firms in a cournot oligopolist are not identical, 𝑄1 = 𝑄2 = 𝑄3 =. . . = 𝑄𝑛 would not hold. 23. If firms compete in a Cournot fashion, then each firm views the: a. output of rivals as given. b. prices of rivals as given. c. profits of rivals as given. d. All of the statements associated with this question are correct. Answer: A. Under Cournot Oligopoly, each firm believes rivals will hold their output constant if it changes its output. 24. Two identical firms compete as a Cournot duopoly. The demand they face is P = 100 − 2Q. The cost function for each firm is C(Q) = 4Q. The equilibrium output of each firm is: b. 16 c. 32 d. 36 Answer: B. As we have two identical firms compete as a Cournot duopoly, the demand in the market is 𝑃 = 100 − 2(𝑄1 + 𝑄2 ). The marginal revenue for firm 1 is 𝑀𝑅 = 100 − 4𝑄1 − 2𝑄2 , the marginnal cost for firm 1 is 𝑀𝐶1 = 4. At profit maximization, 𝑀𝑅1 = 𝑀𝐶1 . → 100 − 4𝑄1 − 2𝑄2 = 4 → 𝑄1 = 24 − 0.5𝑄2 (1).Similarily, we can get the reaction functionn for firm 2 𝑀𝑅2 = 𝑀𝐶2 . → 100 − 4𝑄2 − 2𝑄1 = 4 → 𝑄2 = 24 − 0.5𝑄1 (2). To solve for 𝑄1 and 𝑄2 , plug in equation (2) into equation (1) and get 𝑄1 = 24 − 0.5(24 − 0.5𝑄1 ) → 𝑄1 = 12 + 0.25𝑄1 → 𝑄1 = 16. We can also solve for 𝑄2 by plugging 𝑄1 = 16 into equation (2)

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25. Two identical firms compete as a Cournot duopoly. The demand they face is P = 100 − 2Q. The cost function for each firm is C(Q) = 4Q. Each firm earns equilibrium profits of: a. 1024 b. 2048 c. 4096 d. 512 Answer: D. Based on Q24, we know that 𝑄2 =𝑄1 = 16. From the demand function, we can get the price 𝑃 = 100 − 2(𝑄1 + 𝑄2 ) = 100 − 2 ∗ (16 + 16) = 36. Hence the profit for Firm 1: 𝑝𝑟𝑜𝑓𝑖𝑡 = 𝑃 ∗ 𝑄1 − 4 ∗ 𝑄1 = 16 ∗ 36 − 4 ∗ 16 = 512 26. From a consumer’s point of view, which type of oligopoly is most desirable? a. Sweezy b. Cournot c. Stackelberg D. Bertrand Answer: D. Consumers have perfect information and there are no transaction costs under Bertrand oligopoly. 27. Sue and Jane own two local gas stations. They have identical constant marginal costs, but earn zero economic profits. Sue and Jane constitute: a. a Sweezy oligopoly. b. a Cournot oligopoly. c. a Bertrand oligopoly. d. None of the answers is correct. Answer: C. Firms produce identical products at a constant marginal cost in a Bertrand oligopoly 28. Two identical firms serve a market where demand is described by: P = 100 – 10(Q1 + Q2). Each firm’s marginal cost is $40. Suppose each firm maximizes its own profit, treating the other’s output as constant. At the Cournot equilibrium, how many units of output will each firm produce? Suppose, instead, that the firms collude in setting their outputs (form a monopoly). What outputs should they set ? a. At Cournot equilibrium, 𝑄1 = 𝑄2 = 2; when firms collude 𝑄1 = 𝑄2 = 3 b. At Cournot equilibrium, 𝑄1 = 𝑄2 = 2; when firms collude 𝑄1 = 𝑄2 = 1.5 c. At Cournot equilibrium, 𝑄1 = 𝑄2 = 1.5; when firms collude 𝑄1 = 𝑄2 = 2 d. At Cournot equilibrium, 𝑄1 = 𝑄2 = 3; when firms collude 𝑄1 = 𝑄2 = 2 Answer: B.At Cournot equilibrium, Firm 1 maximizes its profit based on firm 2’s output. Since 𝑀𝑅1 = 100 − 20𝑄1 − 10𝑄2 and 𝑀𝐶 = 40. To maximize firm 1’s profit, we have 𝑀𝑅1 = 𝑀𝐶 → 100 − 20𝑄1 − 10𝑄2 = 40. The firm 1’s reaction function is 𝑄1 = 3 − 0.5𝑄2 . Likewise, we can get Firm 2’s rection function: 𝑄2 = 3 − 0.5𝑄1 Solve the above two reaction function simultaneously will result in:Q1=Q2=2. If the firms collude in setting their outputs, we firt need to find the output level under monopoly. In this case the monopoly’s demand will be P = 100 - 10Q. As MR=100 - 20Q, we set MR= MC =40 and get Q =3 as the monoploy output level. In perfect collusion, each firm produces half of the monopoly output. Hence, 𝑄1 = 𝑄2 = 1.5

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29. Consider a Cournot duopoly with the following inverse demand function: P = 100 − 2Q 1 − 2Q2. The firms’ marginal costs are identical and are given by MCi(Q i) = 2Qi. Based on this information, firm 1 and 2’s reaction functions are: a. 𝑄1 = 24.5 − 0.5𝑄1 and 𝑄2 = 24.5 − 0.5𝑄2 b. 𝑄1 = 24.5 − 0.5𝑄2 and 𝑄2 = 24.5 − 0.5𝑄1 c. 𝑄1 = 49 − 0.5𝑄2 and 𝑄2 = 49 − 0.5𝑄1 d. 𝑄1 = 49 − 0.25𝑄2 and 𝑄2 = 49 − 0.25𝑄1 Answer: B. For Firm 1 to maximize its profit: 𝑀𝑅1 = 100 − 4𝑄1 − 2𝑄2 = 𝑀𝐶 = 2 → 4𝑄1 = 98 − 2𝑄2 → 𝑄1 = 24.5 − 0.5𝑄2 . Similarily, you can get 𝑄2 = 24.5 − 0.5𝑄1 . 30. Two firms compete in a Stackelberg fashion. If firm 2 is the leader, then: a. firm 1 views the output of firm 2 as given. b. firm 2 views the output of firm 1 as given. c. Both firm 1 views the output of firm 2 as given and firm 2 views the output of firm 1 as given are correct. d. None of the answers is correct. Answer: A. An a Stackelberg oligopoly, a single firm (the leader) chooses an output before all other firms choose their outputs. All other firms (the followers) take as given the output of the leader and choose outputs that maximize profits given the leader’s output.

Price descrimination 31. A local video store estimates its average customer’s demand per year is Q = 7 − 2P, and it knows the marginal cost of each rental is $0.5. How much should the store charge for each rental if it engages in optimal two-part pricing? a. $0.35 b. $0.5 c. $0.7 d. $1.00 Answer: B. In optimal two-part pricing, the store will charge a fixed fee that captures all CS and charge a per unit price that equals to the marginal cost. Thus P=MC=0.5 32. A local video store estimates its average customer’s demand per year is Q = 20 − 4P, and it knows the marginal cost of each rental is $1.00. How much should the store charge for an annual membership in order to extract the entire consumer surplus via an optimal two-part pricing strategy? a. $20 b. $32 c. $40 d. $64 Answer: B. In optimal two-part pricing, the store w...