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Multiple choice question: Joey earns £126 in period 1 and he will earn £63 in pe...
Apr 26, 2024
Multiple choice question: Joey earns £126 in period 1 and he will earn £63 in period 2. Joey can borrow orlend at an interest rate of 10%. There is no inflation. Suppose that c1 and c2 are hisconsumption in periods 1 and 2 respectively and that he has a utility function𝑈(𝑐1, 𝑐2) = 𝑚𝑖𝑛 {𝑐1, 2𝑐2}. a. Joey will consume £105 in period 2. b. Joey will earn £3 from his period 1 savings. c. Joey will neither borrow nor save and lend. d. Joey will save and lend £40.
C
Key Concept
Intertemporal Choice and Utility Maximization
Explanation
Joey's utility function is U(c1,c2)=min⁡{c1,2c2}U(c_1, c_2) = \min \{c_1, 2c_2\}. To maximize his utility, Joey will choose c1c_1 and c2c_2 such that c1=2c2c_1 = 2c_2. Given his income and the interest rate, he can allocate £126 in period 1 and £69.3 (which is £63 plus 10% of £63) in period 2 without borrowing or lending. To equalize c1c_1 and 2c22c_2, Joey will consume £126 in period 1 and £63 in period 2, thus he will neither borrow nor save and lend.
Mutiple choice question: Suppose in the context of a consumer’s utility maximisation problem over twogoods x1 and x2, you have found that x1 is an inferior good. Then you may concludethat: a. x1 is a luxury good. b. x2 is a luxury good. c. Both x1 and x2 will be necessary goods. d. x2 is a Giffen good.
B
Key Concept
Inferior Good and Luxury Good
Explanation
An inferior good is one for which demand decreases as income increases. This is different from a luxury good, which is a good for which demand increases more than proportionally as income increases. The fact that x1 is an inferior good does not imply anything about the nature of x2; it could be a normal good, a luxury good, or even another inferior good. However, the question implies a dichotomy between x1 and x2, suggesting that if x1 is inferior and we are to make a conclusion about x2, then by elimination of other options, x2 could be a luxury good.
Multiple choice question:Oskar's preferences over gambles, in which the probabilities of events 1 and 2are both ½, can be represented by the von Neumann-Morgenstern utility function𝑢 = 0.5𝑥^0.5 + 0.5𝑦^0.5, where x is his consumption if event 1 happens and y is hisconsumption if event 2 happens. A gamble that allows him a consumption of £9 ifevent 1 happens and £25 if event 2 happens is exactly as good for Oskar asbeing sure to have an income of a. £12.5. b. £9. c. £16. d. £17
C
Key Concept
Expected Utility
Explanation
To find the certain equivalent of a gamble, we calculate the expected utility of the gamble and then find the certain consumption that gives the same utility.
To solve for Oskar's certain equivalent, we calculate the expected utility of the gamble: EU=0.5⋅x0.5+0.5⋅y0.5=0.5⋅90.5+0.5⋅250.5=0.5⋅3+0.5⋅5=1.5+2.5=4EU = 0.5 \cdot x^{0.5} + 0.5 \cdot y^{0.5} = 0.5 \cdot 9^{0.5} + 0.5 \cdot 25^{0.5} = 0.5 \cdot 3 + 0.5 \cdot 5 = 1.5 + 2.5 = 4 Now we find the certain income zz that would give the same utility: u(z)=0.5⋅z0.5+0.5⋅z0.5=z0.5u(z) = 0.5 \cdot z^{0.5} + 0.5 \cdot z^{0.5} = z^{0.5} Setting the expected utility equal to the utility of the certain income: z0.5=4z^{0.5} = 4 Squaring both sides: z=16z = 16 Therefore, the certain equivalent income for Oskar is £16.
Multiple choice question: Lars consumes only potatoes and herring. When the price of potatoes was 9 crowns per sack and the price of herring was 5 crowns per crock, he spent his entire income to buy 5 sacks of potatoes and 10 crocks of herring per month. Nowthe government subsidizes potatoes. Market prices haven't changed, but consumers get a subsidy of 5 crowns for every sack of potatoes consumed. To payfor this subsidy, the government introduced an income tax. Lars pays an incometax of 20 crowns per month. If s is the number of sacks of potatoes and c is the number of crocks of herring, what is Lars's new budget equation? a. 4s + 5c = 75. b. 9s + 5c = 95. c. 4s + 5c = 95. d. 9s + 5c = 75.
C
Key Concept
Budget Constraint with Subsidy and Tax
Explanation
Lars's budget constraint is affected by both the subsidy on potatoes, which effectively reduces the price of potatoes from 9 to 4 crowns (9 - 5 subsidy), and the income tax of 20 crowns. Originally, Lars spent 45 crowns on potatoes (5 sacks * 9 crowns/sack) and 50 crowns on herring (10 crocks * 5 crowns/crock), totaling 95 crowns. After the subsidy and tax, his budget for potatoes and herring is still 95 crowns (his original budget minus the tax), but the cost of potatoes is reduced due to the subsidy. Therefore, the new budget equation is 4s (subsidized price of potatoes) + 5c (price of herring) = 95 (original budget - tax).
Multiple choice question: Tim has preferences represented by the utility function𝑈(𝑥, 𝑦) = 𝑚𝑖𝑛 {6𝑥 + 𝑦, 𝑥 + 2𝑦}. If x is on the horizontal axis and y is on the vertical axis, what is the slope of his indifference curve at the point (1, 6)? a. -1/6 b. -6 c. -1/2 d. -26
C
Key Concept
Marginal Rate of Substitution (MRS)
Explanation
The slope of the indifference curve at any point is given by the negative of the Marginal Rate of Substitution (MRS), which is the rate at which a consumer is willing to substitute one good for another while maintaining the same level of utility. For Tim's utility function U(x,y)=min⁡{6x+y,x+2y}U(x, y) = \min \{6x + y, x + 2y\}, we need to find the active part of the utility function at the point (1, 6). Since 6(1)+6=126(1) + 6 = 12 and 1+2(6)=131 + 2(6) = 13, the active part is 6x+y6x + y. The MRS is the negative of the ratio of the marginal utilities of the two goods. The marginal utility of xx is 6 and the marginal utility of yy is 1, so the MRS at the point (1, 6) is −6/1=−6-6/1 = -6. Therefore, the slope of the indifference curve at that point is -6.
A monopolist has the total cost function 𝑐(𝑞) = 800 + 8𝑞. The inverse demandfunction is 𝑝 = 80 – 6𝑞, Multiple choice question: where prices and costs are measured in pounds. If the firm is required by law to price its commodity at its marginal cost, a. the firm’s loss is £400. b. the firm’s profits are zero. c. the firm’s loss is £800. d. the firm is making positive profit but not as much profit as it would make if itwere allowed to choose its own price.
B
Key Concept
Marginal Cost Pricing
Explanation
When a monopolist prices its commodity at its marginal cost, it is operating at a point where price equals marginal cost, which is the condition for allocative efficiency in perfect competition. The monopolist's profit is zero because it is covering all its variable and fixed costs without any surplus. The total cost function is c(q)=800+8qc(q) = 800 + 8q, and the marginal cost (MC) is the derivative of the total cost with respect to quantity, which is MC=8MC = 8. The inverse demand function is p=80−6qp = 80 - 6q. Setting p=MCp = MC gives 80−6q=880 - 6q = 8, solving for qq gives q=12q = 12. Substituting q=12q = 12 into the total cost function gives c(12)=800+8(12)=896c(12) = 800 + 8(12) = 896. The total revenue (TR) at q=12q = 12 is TR=p×q=8×12=96TR = p \times q = 8 \times 12 = 96. Since TR=TCTR = TC at q=12q = 12, the firm's profits are zero.
A seller, who has the right to sell automobiles in Island Heybeli, imports automobiles from abroad at a cost of £10,000 each and sells them at a price that maximises his profit. One day, the island’s government annexes a neighbouring island and extends the seller’s monopoly rights to the annexed island. The demandfunction that the seller faces in the annexed island is the same as the demand function that he faces in Island Heybeli. Which of the following statements is true? a. The monopolist keeps its price constant and his sales double. b. The monopolist doubles its price and his sales stay constant. c. The monopolist raises its price but does not necessarily double it. d. The monopolist’s profits more than double
D
Key Concept
Monopoly and Market Expansion
Explanation
When a monopolist expands into a new market with the same demand function, total revenue and profits increase due to the larger market size. However, the monopolist will adjust the quantity supplied to maximize profit in each market, which does not necessarily imply that prices will double or sales will stay constant. The profit increase is due to the ability to sell more units in total across both markets, not due to a proportionate increase in price.
A competitive firm has a production function 𝐹(𝐾, 𝐿) = (𝐾 + 𝐿)^0.5 where 𝐾 and 𝐿 stand for inputs capital and labour respectively. The price of capital is 𝑣, and theprice of labour is 𝑤. Which of the following is true? a. Regardless of 𝑤 and 𝑣, cost minimisation requires that 𝐾 = 𝐿. b. If 𝑣 > 𝑤, contingent demand for labour is 0. c. The technology has increasing returns to scale. d. If 𝑣 < 𝑤, profit maximisation requires that no labour is used in production.
A
Key Concept
Cost Minimization
Explanation
In cost minimization, a firm chooses inputs to minimize costs for a given level of output. For the given production function F(K,L)=(K+L)0.5F(K, L) = (K + L)^{0.5}, the marginal products of capital and labor are equal, which implies that the cost-minimizing combination of KK and LL occurs when K=LK = L, regardless of the prices vv and ww. This is because the production function exhibits constant returns to scale, and the marginal rate of technical substitution (MRTS) is equal to 1, which should equal the ratio of input prices for cost minimization.
Multiple choice question: Consider a duopoly that faces a market demand 𝑝 = 4,500 – 4𝑄. Each firm hasone manufacturing plant and each firm i has a cost function 𝐶(𝑞𝑖) = 𝑞𝑖^2, where 𝑞𝑖is the output of firm 𝑖 and 𝑄 is the total output. The two firms form a cartel andarrange to split total industry profits equally. Under this cartel arrangement, they will maximise joint profits if a. they produce a total of 500 units, no matter which firm produces them. b. each firm produces 250 units in its plant. c. they each produce a total of 562.50 units. d. they shut down one of the two plants, having the other operate as amonopoly and produce 450 units and then splitting the profits.
B
Key Concept
Cartel Production and Profit Maximization
Explanation
In a cartel arrangement, firms act as a monopoly to maximize joint profits. They will set the total output to the monopolist's output level and then split this output equally to maximize profits and maintain the agreement. Given the demand function p=4,500−4Qp = 4,500 - 4Q and the cost function C(qi)=qi2C(q_i) = q_i^2, the firms will produce where marginal revenue equals marginal cost. The total quantity that maximizes joint profits can be found by setting the derivative of the total profit function with respect to QQ equal to zero and solving for QQ. Then, since the profits are split equally, each firm will produce half of the total quantity.
Multiple question: A competitive firm has a production function 𝐹(𝐾, 𝐿) = (𝐾 + 𝐿)^0.5 where 𝐾 and 𝐿 stand for inputs capital and labour respectively. The price of capital is 𝑣, and theprice of labour is 𝑤. Which of the following is true? a. Regardless of 𝑤 and 𝑣, cost minimisation requires that 𝐾 = 𝐿. b. If 𝑣 > 𝑤, contingent demand for labour is 0. c. The technology has increasing returns to scale. d. If 𝑣 < 𝑤, profit maximisation requires that no labour is used in production.
A
Key Concept
Cost Minimization
Explanation
In cost minimization, a firm chooses inputs to minimize costs for a given level of output. For the given production function F(K,L)=(K+L)0.5F(K, L) = (K + L)^{0.5}, the marginal products of capital and labor are equal, which implies that the cost is minimized when K=LK = L, regardless of the prices vv and ww. This is because the production function exhibits constant returns to scale, and the marginal rate of technical substitution (MRTS) is equal to 1, meaning that one unit of capital can be perfectly substituted for one unit of labor without affecting the output
Multiple choice question: A seller, who has the right to sell automobiles in Island Heybeli, imports automobiles from abroad at a cost of £10,000 each and sells them at a price that maximises his profit. One day, the island’s government annexes a neighbouring island and extends the seller’s monopoly rights to the annexed island. The demandfunction that the seller faces in the annexed island is the same as the demand function that he faces in Island Heybeli. Which of the following statements is true? a. The monopolist keeps its price constant and his sales double. b. The monopolist doubles its price and his sales stay constant. c. The monopolist raises its price but does not necessarily double it. d. The monopolist’s profits more than double
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