Tüm alıştırma soruları

1526 soru

Soru 1101Soru

A consumer's maximum willingness to pay for four successive bags of rice is ₦15,000, ₦13,000, ₦11,000, and ₦9,000 respectively. If the prevailing market price per bag is ₦9,000, what is the total consumer surplus derived in Naira?

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Cevap: 12000

Cevap

The total consumer surplus derived by the consumer is ₦12,000.
Consumer surplus is the difference between total willingness to pay and total actual expenditure. The total willingness to pay for the 4 bags of rice is ₦15,000 + ₦13,000 + ₦11,000 + ₦9,000 = ₦48,000. Since each bag costs ₦9,000, total expenditure for 4 bags is 4 × ₦9,000 = ₦36,000. Subtracting ₦36,000 from ₦48,000 gives a consumer surplus of ₦12,000.

Adım Adım Çözüm

1
Sum the maximum willingness to pay for all consumed units to find Total Willingness to Pay.
Total Willingness to Pay = ₦15,000 + ₦13,000 + ₦11,000 + ₦9,000 = ₦48,000.
Total utility or willingness to pay is the cumulative value derived from consuming all 4 units.
2
Multiply the number of purchased units by the market price per unit to calculate Total Actual Expenditure.
Total Expenditure = 4 × ₦9,000 = ₦36,000.
The market price applies uniformly to all units purchased.
3
Subtract Total Expenditure from Total Willingness to Pay to calculate Consumer Surplus.
Consumer Surplus = ₦48,000 - ₦36,000 = ₦12,000.
Consumer surplus is defined as the net benefit (Total Willingness to Pay minus Total Expenditure).

Anahtar Kavram

Concept and Calculation of Consumer Surplus

Alternatif Yöntem

Alternatively, calculate the individual surplus for each unit (Willingness to Pay - Market Price) and sum them up: 1st unit (₦15,000 - ₦9,000 = ₦6,000), 2nd unit (₦13,000 - ₦9,000 = ₦4,000), 3rd unit (₦11,000 - ₦9,000 = ₦2,000), 4th unit (₦9,000 - ₦9,000 = ₦0). Total Consumer Surplus = ₦6,000 + ₦4,000 + ₦2,000 + ₦0 = ₦12,000.
Tahmini Süre:1m 0s
Soru 1102Soru

A firm operating under monopolistic competition faces an inverse demand function P=1204QP = 120 - 4Q and a marginal revenue function MR=1208QMR = 120 - 8Q, where PP is price in Naira and QQ is quantity of output. Its total cost function is TC=200+20Q+Q2TC = 200 + 20Q + Q^2 and its marginal cost function is MC=20+2QMC = 20 + 2Q. What is the firm's maximum short-run economic profit in Naira?

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Cevap: 300

Cevap

The firm's maximum short-run economic profit is 300 Naira.
The profit-maximizing condition for a monopolistically competitive firm is MR=MCMR = MC. Setting 1208Q=20+2Q120 - 8Q = 20 + 2Q yields Q=10Q = 10 units. Substituting Q=10Q = 10 into the demand function gives a price of 8080 Naira, producing Total Revenue of 800800 Naira (80×1080 \times 10). Substituting Q=10Q = 10 into the Total Cost function yields 500500 Naira (200+200+100200 + 200 + 100). Short-run economic profit is TRTC=800500=300TR - TC = 800 - 500 = 300 Naira.

Adım Adım Çözüm

1
Equate Marginal Revenue (MR) to Marginal Cost (MC) to find the profit-maximizing output
1208Q=20+2Q    10Q=100    Q=10120 - 8Q = 20 + 2Q \implies 10Q = 100 \implies Q = 10 units
Like all imperfectly competitive firms, a monopolistically competitive firm maximizes profit at the output level where marginal revenue equals marginal cost.
2
Determine the price using the demand curve at the optimal output level
P=1204(10)=80P = 120 - 4(10) = 80 Naira
The demand curve indicates the maximum price per unit consumers are willing to pay for 10 units.
3
Calculate Total Revenue (TR) and Total Cost (TC)
TR=80×10=800TR = 80 \times 10 = 800 Naira and TC=200+20(10)+102=500TC = 200 + 20(10) + 10^2 = 500 Naira
Total revenue is price multiplied by quantity produced, while total cost is evaluated directly from the given total cost equation.
4
Subtract Total Cost from Total Revenue to determine short-run economic profit
Economic profit =800500=300= 800 - 500 = 300 Naira
Economic profit represents the excess of total revenue over total economic cost in the short run.

Anahtar Kavram

Short-Run Profit Maximization in Monopolistic Competition
Soru 1103Soru

A Nigerian importer requires British Pounds (GBP\text{GBP}) to settle an international trade transaction. In the foreign exchange market, the exchange rate between the US Dollar (USD\text{USD}) and the Nigerian Naira (NGN\text{NGN}) is $1.00=NGN 750\$1.00 = \text{NGN } 750, while the exchange rate between the British Pound (GBP\text{GBP}) and the US Dollar (USD\text{USD}) is £1.00=$1.40£1.00 = \$1.40. What is the cross exchange rate of one British Pound (£1.00£1.00) in terms of Nigerian Naira (NGN\text{NGN})?

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Cevap: 1050

Cevap

1050 NGN
The cross exchange rate determines the exchange rate between two currencies via a third currency. By multiplying the exchange value of 1 GBP in USD (1.401.40) by the exchange value of 1 USD in NGN (750750), we obtain £1.00=1.40×750=NGN 1050£1.00 = 1.40 \times 750 = \text{NGN } 1050.

Adım Adım Çözüm

1
Identify the exchange rate relations against the common intermediate currency (US Dollar).
1.00 USD=NGN 7501.00 \text{ USD} = \text{NGN } 750 and £1.00 GBP=$1.40£1.00 \text{ GBP} = \$1.40
Both currency pairs are quoted relative to the US Dollar.
2
Multiply the GBP/USD rate by the USD/NGN rate to determine the cross rate.
£1.00 \text{ GBP} = 1.40 \times 750 = \text{NGN } 1050
Since each Pound is worth 1.40USDandeachUSDisworth750NGN,1GBPequals1.40 USD and each USD is worth 750 NGN, 1 GBP equals 1.40 \times 750$ NGN.

Anahtar Kavram

Cross Exchange Rate Determination
Tahmini Süre:1m 30s
Soru 1104Soru

In a foreign exchange market operating under a flexible exchange rate system, the quantity demanded of US Dollars (USD\text{USD}) in millions is given by Qd=12002EQ_d = 1200 - 2E, and the quantity supplied is given by Qs=400+3EQ_s = 400 + 3E, where EE is the exchange rate in Nigerian Naira per US Dollar (NGN/USD\text{NGN/USD}). If an increase in import demand shifts the dollar demand curve upward by 250250 million dollars at every exchange rate level, by how many Naira per Dollar will the equilibrium exchange rate increase?

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Cevap: 50

Cevap

The equilibrium exchange rate increases by 50 NGN/USD.
Under a floating exchange rate system, the equilibrium exchange rate is determined by the intersection of foreign currency supply and demand. Initially, setting 12002E=400+3E1200 - 2E = 400 + 3E yields E1=160 NGN/USDE_1 = 160\text{ NGN/USD}. When demand for foreign currency increases autonomously by 250250 million dollars, the demand curve shifts rightward to Qd=14502EQ_d' = 1450 - 2E. Equating this new demand with supply gives 14502E=400+3E    E2=210 NGN/USD1450 - 2E = 400 + 3E \implies E_2 = 210\text{ NGN/USD}. The net increase in the rate is 210160=50 NGN/USD210 - 160 = 50\text{ NGN/USD}.

Adım Adım Çözüm

1
Find initial equilibrium exchange rate
E_1 = 160 NGN/USD
Equilibrium occurs where foreign exchange quantity demanded equals quantity supplied: 1200 - 2E = 400 + 3E.
2
Formulate new foreign exchange demand equation
Q_d' = 1450 - 2E
An autonomous increase in demand adds 250 million units to the existing demand function.
3
Find new equilibrium exchange rate
E_2 = 210 NGN/USD
Set the new demand equal to supply: 1450 - 2E = 400 + 3E.
4
Calculate the difference between the new and original exchange rates
210 - 160 = 50 NGN/USD
The question specifically asks for the increase in the equilibrium exchange rate.

Anahtar Kavram

Determination of Equilibrium Exchange Rates and Demand Curve Shifts
Soru 1105Soru

A consumer's evaluation of total utility derived from consuming successive tubers of yam in a local Nigerian market (expressed in monetary terms) is presented in the table below:

Quantity of Yam (Tubers)Total Utility (₦)
11,800
23,300
34,500
45,400
56,000
66,300

If the prevailing market price of a tuber of yam is ₦900, what is the total value of consumer surplus (in ₦) enjoyed by the consumer at equilibrium?

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Cevap: 1800

Cevap

The consumer surplus enjoyed by the consumer at equilibrium is ₦1,800.
To find consumer surplus, one must first establish the consumer's profit-maximizing equilibrium quantity where Marginal Utility (MU) equals Price (P). From the Total Utility (TU) values, the MU for successive units is ₦1,800, ₦1,500, ₦1,200, and ₦900. At the 4th unit, MU equals the market price of ₦900. Total utility for 4 units is ₦5,400 and total outlay is 4×900=3,6004 \times 900 = \text{₦}3,600. Subtracting total outlay from total utility yields a consumer surplus of ₦1,800.

Adım Adım Çözüm

1
Calculate Marginal Utility (MU) for each unit consumed
MU values are ₦1,800 for the 1st tuber, ₦1,500 for the 2nd, ₦1,200 for the 3rd, ₦900 for the 4th, ₦600 for the 5th, and ₦300 for the 6th tuber.
Consumer equilibrium is reached when the marginal utility of a unit equals its market price.
2
Determine the equilibrium quantity consumed
The consumer purchases 4 tubers of yam.
For the 4th tuber, MU=900MU = \text{₦}900, which matches the prevailing market price of ₦900. Consuming a 5th tuber yields MU=600<900MU = \text{₦}600 < \text{₦}900, which reduces net utility.
3
Calculate the actual total expenditure
Total Expenditure=4×900=3,600\text{Total Expenditure} = 4 \times \text{₦}900 = \text{₦}3,600.
Total expenditure is equal to the quantity purchased multiplied by the market price per unit.
4
Subtract Total Expenditure from Total Utility to find Consumer Surplus
Consumer Surplus=5,4003,600=1,800\text{Consumer Surplus} = \text{₦}5,400 - \text{₦}3,600 = \text{₦}1,800.
Consumer surplus measures the difference between total willingness to pay (Total Utility at 4 units) and actual expenditure.

Anahtar Kavram

Calculation of Consumer Surplus from Discrete Utility Schedules
Soru 1106Soru

In a given fiscal year, a nation recorded a Nominal Gross Domestic Product (GDP) of 600 billion\text{₦}600\text{ billion} while its GDP deflator stood at 150150. Calculate the Real GDP of the nation for that year in billions of Naira.

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Cevap: 400

Cevap

The Real GDP of the nation for that year is ₦400 billion.
Real GDP isolates physical output change from price fluctuations by dividing Nominal GDP by the price level index (GDP deflator) and scaling by the base value of 100. Substituting ₦600 billion and 150 gives 600150×100=400\frac{600}{150} \times 100 = 400 billion Naira.

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1
Identify the relationship between Nominal GDP, Real GDP, and the GDP Deflator.
The formula to adjust Nominal GDP for price inflation is Real GDP=(Nominal GDPGDP Deflator)×100\text{Real GDP} = \left( \frac{\text{Nominal GDP}}{\text{GDP Deflator}} \right) \times 100.
The GDP deflator measures the level of prices relative to the base year.
2
Substitute Nominal GDP (₦600 billion) and GDP Deflator (150) into the equation.
Real GDP=(600150)×100=4×100=400\text{Real GDP} = \left( \frac{600}{150} \right) \times 100 = 4 \times 100 = 400.
Dividing Nominal GDP by the GDP deflator strips out the price increase to reflect physical output quantity.

Anahtar Kavram

Adjustment of Nominal GDP to Real GDP using the price index/deflator.
Tahmini Süre:45s
Soru 1107Soru

A specific tax of 15\text{₦}15 per unit is imposed on a luxury commodity. Prior to the imposition of the tax, the equilibrium market price was 100\text{₦}100 per unit. Following the tax, the market price paid by consumers increases to 109\text{₦}109 per unit. What is the amount of the unit tax borne by the producer in Naira (\text{₦})?

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Cevap: 6

Cevap

The producer bears ₦6 of the ₦15 per unit tax.
Tax incidence refers to how the ultimate economic burden of a tax is divided between buyers and sellers. When a unit tax of 15\text{₦}15 raises the consumer price from 100\text{₦}100 to 109\text{₦}109, consumers bear 9\text{₦}9 of the tax burden per unit. The producer receives 10915=94\text{₦}109 - \text{₦}15 = \text{₦}94 per unit after paying the tax to the government. The net price reduction for the producer is 10094=6\text{₦}100 - \text{₦}94 = \text{₦}6, which represents the producer's incidence of the tax.

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1
Calculate the consumer's share of the tax incidence per unit.
Consumer tax share = 109100=9\text{₦}109 - \text{₦}100 = \text{₦}9.
The portion of an indirect tax passed forward to consumers equals the increase in the market price paid by buyers.
2
Calculate the producer's share of the tax incidence per unit.
Producer tax share = 159=6\text{₦}15 - \text{₦}9 = \text{₦}6.
The total per-unit tax is distributed between the consumer and the producer. Deducting the consumer's share from the total tax leaves the producer's share.

Anahtar Kavram

Tax Incidence Distribution
Tahmini Süre:1m 30s
Soru 1108Soru

A concrete block manufacturing factory operates in the short run with fixed molding machinery and variable labor (LL). When 44 workers are employed, the average product of labor (APLAP_L) is 3030 blocks per worker. When a 5th5\text{th} worker is hired, the total product of labor (TPLTP_L) increases to 145145 blocks. What is the marginal product (MPLMP_L) of the 5th5\text{th} worker?

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Cevap: 25

Cevap

The marginal product of the 5th worker is 25 blocks.
To find the marginal product of the 5th worker, first determine total product for 4 workers by multiplying 4 workers by their average product of 30 blocks, giving 120 blocks. The marginal product of the 5th worker is the difference between the total product with 5 workers (145 blocks) and total product with 4 workers (120 blocks), which equals 25 blocks.

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1
Calculate the total output produced by 4 workers using the average product formula
Total Product for 4 workers (TP4TP_4) = 4×30=1204 \times 30 = 120 blocks.
Average Product (APAP) equals Total Product (TPTP) divided by Labor (LL), so TP=L×APTP = L \times AP.
2
Calculate the change in total output resulting from employing the 5th worker
Marginal Product (MP5MP_5) = 145120=25145 - 120 = 25 blocks.
Marginal Product is the addition to total output when one additional unit of variable input is employed (MPL=ΔTP/ΔLMP_L = \Delta TP / \Delta L).

Anahtar Kavram

Short-Run Marginal Product and Total Product Relationships
Soru 1109Soru

In a regional market for poultry feed, the daily quantity demanded is expressed as Qd=48012PQ_d = 480 - 12P and the daily quantity supplied is expressed as Qs=120+18PQ_s = -120 + 18P, where PP represents the price per bag in hundreds of Naira and QQ represents quantity in bags. What is the market equilibrium price per bag in hundreds of Naira?

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Cevap: 20

Cevap

The market equilibrium price is 20 (in hundreds of Naira).
Equilibrium price is established when quantity demanded equals quantity supplied (Qd=QsQ_d = Q_s). Setting 48012P=120+18P480 - 12P = -120 + 18P yields 30P=60030P = 600, resulting in an equilibrium price of 20 (in hundreds of Naira).

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1
Equate the demand and supply equations to find market equilibrium.
48012P=120+18P480 - 12P = -120 + 18P
Market equilibrium occurs at the price level where the quantity buyers wish to purchase equals the quantity sellers wish to supply.
2
Rearrange the equation by grouping constant terms on one side and price variables on the other.
30P=60030P = 600
Adding 12P12P to both sides eliminates 12P-12P on the left, and adding 120120 to both sides eliminates 120-120 on the right.
3
Divide the total value by the coefficient of price to determine equilibrium price.
P=20P = 20
Dividing 600600 by 3030 isolates PP to give the equilibrium price.

Anahtar Kavram

Market Equilibrium Price Determination
Soru 1110Soru

A country recorded an Income Terms of Trade index of 144144 and an export volume index of 120120 relative to the base year index of 100100. If the country's import price index stood at 125125 during the same period, what was its export price index?

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Cevap: 150

Cevap

The export price index is 150.
The Income Terms of Trade (ITTITT) formula is ITT=(PxPm)×QxITT = \left(\frac{P_x}{P_m}\right) \times Q_x. Substituting the given values (ITT=144ITT = 144, Qx=120Q_x = 120, Pm=125P_m = 125) gives 144=(Px125)×120144 = \left(\frac{P_x}{125}\right) \times 120. Rearranging the equation to solve for the export price index yields Px=144×125120=150P_x = \frac{144 \times 125}{120} = 150.

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1
Identify the relationship between Income Terms of Trade, price indices, and volume index
ITT=(PxPm)×QxITT = \left(\frac{P_x}{P_m}\right) \times Q_x
Income Terms of Trade measures a nation's capacity to import based on export earnings, combining the net barter terms of trade with export quantity.
2
Substitute given values into the formula
144=(Px125)×120144 = \left(\frac{P_x}{125}\right) \times 120
The given values are ITT=144ITT = 144, Qx=120Q_x = 120, and Pm=125P_m = 125.
3
Isolate the unknown variable PxP_x
Px=144×125120=150P_x = \frac{144 \times 125}{120} = 150
Multiplying both sides by 125125 and dividing by 120120 isolates PxP_x to determine the export price index.

Anahtar Kavram

Income Terms of Trade Calculation
Soru 1111Soru

In a regional agricultural market, the total stock of money in circulation (MM) is ₦80,000 and the average price level (PP) per unit of output is ₦250. If the physical volume of transactions (TT) recorded during the period is 1,600 units, calculate the velocity of circulation (VV) of money.

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Cevap: 5

Cevap

The velocity of circulation of money (VV) is 5.
According to Irving Fisher's Quantity Theory of Money (MV=PTMV = PT), the total monetary flow in an economy (MVMV) equals the total nominal value of transactions (PTPT). Substituting M=80,000M = 80,000, P=250P = 250, and T=1,600T = 1,600 into the equation gives 80,000×V=400,00080,000 \times V = 400,000. Solving for VV yields V=5V = 5, meaning each unit of currency changed hands 5 times on average during the period.

Adım Adım Çözüm

1
Identify the given parameters and select the appropriate formula
Money supply (MM) = ₦80,000, Price level (PP) = ₦250, Volume of transactions (TT) = 1,600. Use Fisher's Equation of Exchange: MV=PTMV = PT.
Irving Fisher's equation establishes that total money spending (MVMV) equals total value of goods and services traded (PTPT).
2
Substitute the numerical values into the equation
80,000×V=250×1,60080,000 \times V = 250 \times 1,600
Plugging the known quantitative values isolates VV as the single unknown variable.
3
Solve for the velocity of circulation (VV)
80,000×V=400,000    V=400,00080,000=580,000 \times V = 400,000 \implies V = \frac{400,000}{80,000} = 5
Dividing total monetary outlay (PTPT) by total money stock (MM) determines how many times a unit of currency changes hands on average.

Anahtar Kavram

Fisher's Quantity Theory of Money Equation of Exchange (MV=PTMV = PT)
Soru 1112Soru

In a financial year, a government collected 650 billion\text{₦}650\text{ billion} in tax revenue and 180 billion\text{₦}180\text{ billion} in non-tax revenue. During the same period, its recurrent expenditure was 520 billion\text{₦}520\text{ billion} and its capital expenditure was 460 billion\text{₦}460\text{ billion}. What is the government's budget deficit in billions of Naira (\text{₦})?

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Cevap: 150

Cevap

The government's budget deficit is 150 billion\text{₦}150\text{ billion}.
The budget deficit represents the excess of total expenditure over total revenue in a fiscal period. Adding tax revenue (650 billion\text{₦}650\text{ billion}) and non-tax revenue (180 billion\text{₦}180\text{ billion}) gives a total revenue of 830 billion\text{₦}830\text{ billion}. Adding recurrent expenditure (520 billion\text{₦}520\text{ billion}) and capital expenditure (460 billion\text{₦}460\text{ billion}) yields a total expenditure of 980 billion\text{₦}980\text{ billion}. The difference (980 billion830 billion\text{₦}980\text{ billion} - \text{₦}830\text{ billion}) results in a budget deficit of 150 billion\text{₦}150\text{ billion}.

Adım Adım Çözüm

1
Calculate Total Revenue
Total Revenue = 830 billion\text{₦}830\text{ billion}
Total revenue is the sum of tax revenue and non-tax revenue: 650 billion+180 billion=830 billion\text{₦}650\text{ billion} + \text{₦}180\text{ billion} = \text{₦}830\text{ billion}.
2
Calculate Total Expenditure
Total Expenditure = 980 billion\text{₦}980\text{ billion}
Total expenditure is the sum of recurrent expenditure and capital expenditure: 520 billion+460 billion=980 billion\text{₦}520\text{ billion} + \text{₦}460\text{ billion} = \text{₦}980\text{ billion}.
3
Calculate Budget Deficit
Budget Deficit = 150 billion\text{₦}150\text{ billion}
A budget deficit occurs when total expenditure exceeds total revenue. Deficit = Total Expenditure - Total Revenue = 980 billion830 billion=150 billion\text{₦}980\text{ billion} - \text{₦}830\text{ billion} = \text{₦}150\text{ billion}.

Anahtar Kavram

Budget Deficit Calculation
Soru 1113Soru

At the beginning of a given trading period, the nominal exchange rate between the Nigerian Naira (NGN\text{NGN}) and the US Dollar (USD\text{USD}) is $1=NGN 500\$1 = \text{NGN } 500. During the period, Nigeria records an annual inflation rate of 26%26\%, whereas the United States records an annual inflation rate of 5%5\%. According to the relative Purchasing Power Parity (PPP) theory of exchange rate determination, what is the new equilibrium nominal exchange rate in NGN\text{NGN} per USD\text{USD}?

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Cevap: 600

Cevap

The new equilibrium nominal exchange rate is 600 NGN per USD.
Under relative Purchasing Power Parity, an inflation differential between two trading partners leads to a proportional depreciation of the currency with higher inflation. Dividing the domestic price index factor (1.26) by the foreign price index factor (1.05) yields an adjustment multiplier of 1.20. Multiplying the initial rate of 500 NGN/USD by 1.20 gives 600 NGN/USD.

Adım Adım Çözüm

1
Identify the relative Purchasing Power Parity (PPP) formula for exchange rate adjustment based on inflation differentials.
Formula: E1=E0×1+idomestic1+iforeignE_1 = E_0 \times \frac{1 + i_{\text{domestic}}}{1 + i_{\text{foreign}}}
Relative PPP states that exchange rates change to offset differences in inflation rates between two nations.
2
Substitute the initial rate (500), domestic inflation (0.26), and foreign inflation (0.05) into the equation.
E1=500×1.261.05E_1 = 500 \times \frac{1.26}{1.05}
This adjusts the currency valuation proportionally to the change in relative purchasing power.
3
Perform the division and multiplication.
E1=500×1.20=600E_1 = 500 \times 1.20 = 600
Evaluating the expression yields the depreciated exchange rate for the domestic currency.

Anahtar Kavram

Purchasing Power Parity (PPP) and Exchange Rate Determination
Tahmini Süre:2m 0s
Soru 1114Soru

A firm facing a downward-sloping demand curve sells 1212 units of an item at a price of 75\text{₦}75 per unit. In order to sell 1313 units, it must lower the price of all units to 71\text{₦}71. Calculate the Marginal Revenue of the 13th13\text{th} unit in Naira (\text{₦}).

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Cevap: 23

Cevap

The Marginal Revenue of the 13th unit is ₦23.
Marginal Revenue (MR) measures the change in Total Revenue (TR) when output increases by one unit. Selling 12 units at ₦75 gives TR₁ = ₦900. Selling 13 units at ₦71 gives TR₂ = ₦923. The difference, ₦923 - ₦900 = ₦23, is the additional revenue generated by the 13th unit.

Adım Adım Çözüm

1
Calculate the initial Total Revenue (TR₁) before expanding output
TR₁ = 12 units × ₦75 = ₦900
Total Revenue is calculated as Price multiplied by Quantity (TR = P × Q).
2
Calculate the new Total Revenue (TR₂) after expanding output to 13 units
TR₂ = 13 units × ₦71 = ₦923
When output increases to 13 units, the lower price of ₦71 applies to all units sold.
3
Determine the Marginal Revenue (MR) of the 13th unit
MR = TR₂ - TR₁ = ₦923 - ₦900 = ₦23
Marginal Revenue is the change in Total Revenue resulting from selling one additional unit of output (MR = ΔTR / ΔQ).

Anahtar Kavram

Marginal Revenue and Total Revenue Relationship in Imperfect Competition
Soru 1115Soru

In a domestic agricultural market, the weekly demand function for palm oil is given by Qd=80020PQ_d = 800 - 20P and the supply function is given by Qs=100+10PQ_s = -100 + 10P, where PP is the price per litre in Naira and QQ is the quantity in litres. What is the equilibrium quantity in litres?

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Cevap: 200

Cevap

The equilibrium quantity is 200 litres.
Market equilibrium occurs where quantity demanded equals quantity supplied (Qd=QsQ_d = Q_s). Setting 80020P=100+10P800 - 20P = -100 + 10P yields 30P=90030P = 900, which gives an equilibrium price of P=30P = 30 Naira. Substituting P=30P = 30 into the demand function Qd=80020(30)Q_d = 800 - 20(30) gives an equilibrium quantity of 200200 litres.

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1
Equate the demand function QdQ_d and the supply function QsQ_s to find the market equilibrium condition.
80020P=100+10P800 - 20P = -100 + 10P
At market equilibrium, quantity demanded equals quantity supplied.
2
Rearrange the equation to isolate PP and calculate the equilibrium price.
30P=900    P=3030P = 900 \implies P = 30
Adding 20P20P and 100100 to both sides groups variable terms and constant terms together.
3
Substitute the equilibrium price (P=30P = 30) into the demand equation to determine the equilibrium quantity.
Q=80020(30)=200Q^* = 800 - 20(30) = 200
Evaluating QdQ_d at P=30P = 30 gives the total quantity traded at equilibrium.

Anahtar Kavram

Market Equilibrium Price and Quantity
Soru 1116Soru

A manufacturing firm operating in an imperfectly competitive market sells 55 units of its commodity at a price of 30\text{₦}30 per unit. In order to increase its sales to 66 units, the firm lowers the price to 27\text{₦}27 per unit. What is the marginal revenue (MR\text{MR}) of the 6th6\text{th} unit in Naira (\text{₦})?

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Cevap: 12

Cevap

The marginal revenue of the 6th unit is 12 Naira.
Marginal revenue is calculated as the change in total revenue (ΔTR\Delta TR) divided by the change in total output (ΔQ\Delta Q). Initial total revenue (TR1TR_1) is 5×30=1505 \times 30 = \text{₦}150. Total revenue after expanding output (TR2TR_2) is 6×27=1626 \times 27 = \text{₦}162. Thus, MR=162150=12MR = 162 - 150 = \text{₦}12.

Adım Adım Çözüm

1
Calculate initial Total Revenue (TR_1)
TR_1 = 30 * 5 = 150 Naira
Total revenue is equal to price per unit multiplied by quantity sold.
2
Calculate new Total Revenue (TR_2)
TR_2 = 27 * 6 = 162 Naira
The new price applies to all 6 units sold in an imperfectly competitive market.
3
Subtract initial Total Revenue from new Total Revenue to find Marginal Revenue (MR)
MR = 162 - 150 = 12 Naira
Marginal revenue measures the change in total revenue resulting from selling one additional unit of output.

Anahtar Kavram

Marginal Revenue and Total Revenue Relationship
Soru 1117Soru

The market demand and supply equations for fertilizer in an agricultural district are given by Qd=1,80040PQ_d = 1,800 - 40P and Qs=200+40PQ_s = 200 + 40P, where PP is the price per bag in Naira (N\text{N}) and QQ is the quantity in bags. The government introduces a price ceiling of N12\text{N} 12 per bag to lower farming input costs. By how many bags does the quantity of fertilizer actually traded in the market decrease as a result of this price control policy?

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Cevap: 320

Cevap

The quantity of fertilizer actually traded in the market decreases by 320 bags.
Prior to government regulation, free market equilibrium is established where quantity demanded equals quantity supplied (1,80040P=200+40P1,800 - 40P = 200 + 40P), yielding an equilibrium price of 2020 Naira and an equilibrium volume of 1,0001,000 bags. When a maximum price ceiling of 1212 Naira is imposed, quantity demanded expands to 1,3201,320 bags while quantity supplied shrinks to 680680 bags. Because trade is voluntary, the quantity exchanged is constrained by the short side of the market (quantity supplied = 680680 bags). Comparing this volume to the initial equilibrium (1,0006801,000 - 680), the actual quantity of fertilizer traded decreases by 320320 bags.

Adım Adım Çözüm

1
Determine the initial free-market equilibrium price and quantity
Pe=20P_e = 20 Naira and Qe=1,000Q_e = 1,000 bags
Equilibrium occurs where quantity demanded equals quantity supplied (Qd=QsQ_d = Q_s).
2
Calculate quantity demanded and quantity supplied at the price ceiling of P=12P = 12
Qd=1,320Q_d = 1,320 bags and Qs=680Q_s = 680 bags
Lowering the price below equilibrium increases buyer demand but disincentivizes supplier production.
3
Determine actual traded quantity using the short-side principle and calculate the volume change
Actual quantity traded =680= 680 bags; Reduction =1,000680=320= 1,000 - 680 = 320 bags
In a market economy, trade requires voluntary exchange; buyers cannot purchase more than suppliers offer at the regulated price ceiling.

Anahtar Kavram

Short-Side Rule and Contraction of Market Traded Volume under Price Ceilings
Soru 1118Soru

The monthly revenue collection (in millions of Naira, ₦’million\text{₦'million}) from six regional revenue offices of a state government was recorded as 1414, 1818, 1212, xx, 2222, and 1616. If the arithmetic mean of the revenue collected across all six offices is 17 million\text{₦}17\text{ million}, what is the value of xx?

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Cevap: 20

Cevap

The value of xx is 20 million Naira20\text{ million Naira} (or simply 2020).
The arithmetic mean is defined as xˉ=xn\bar{x} = \frac{\sum x}{n}. For n=6n = 6 offices with a mean of 17 million17\text{ million}, the total sum must be 6×17=102 million6 \times 17 = 102\text{ million}. Summing the known values gives 14+18+12+22+16=8214 + 18 + 12 + 22 + 16 = 82. Subtracting 8282 from 102102 yields x=20 million Nairax = 20\text{ million Naira}.

Adım Adım Çözüm

1
Calculate the sum of all observations in terms of xx
Sum =14+18+12+x+22+16=82+x= 14 + 18 + 12 + x + 22 + 16 = 82 + x
The mean formula requires the total sum of all values divided by the number of observations.
2
Set up the mean equation using xˉ=xn\bar{x} = \frac{\sum x}{n}
82+x6=17\frac{82 + x}{6} = 17$
The question specifies that the arithmetic mean across the 6 regional offices is 17.
3
Solve for the unknown value xx
82 + x = 102 \implies x = 20$
Subtracting the sum of the five known values (82) from the total required sum (102) yields the missing observation.

Anahtar Kavram

Calculation of a Missing Value from the Arithmetic Mean
Soru 1119Soru

The table below shows the distribution of monthly fuel consumption (in liters) for a sample of 5050 commercial transport vehicles operated by a logistics firm in Lagos:

Fuel Consumption (Liters)Frequency (ff)
10 – 198
20 – 2913
30 – 3916
40 – 499
50 – 594

Calculate the median fuel consumption (in liters) for this sample of vehicles.

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Cevap: 32

Cevap

The median fuel consumption for the sample of vehicles is 3232 liters.
The median of a grouped frequency distribution is computed using continuous class boundaries. With N=50N=50, the median position is 2525. The 303930–39 class has lower boundary 29.529.5, frequency 1616, preceding cumulative frequency 2121, and class interval 1010. Substituting these values gives 29.5+252116×10=3229.5 + \frac{25 - 21}{16} \times 10 = 32 liters.

Adım Adım Çözüm

1
Calculate the total frequency (NN) and construct cumulative frequencies (cfcf).
Total frequency N=8+13+16+9+4=50N = 8 + 13 + 16 + 9 + 4 = 50. Cumulative frequencies are: 10–19 (cf=8cf = 8), 20–29 (cf=21cf = 21), 30–39 (cf=37cf = 37), 40–49 (cf=46cf = 46), 50–59 (cf=50cf = 50).
Cumulative frequencies are required to identify the class containing the median value.
2
Locate the median position and determine the median class parameters.
Position =N2=502=25= \frac{N}{2} = \frac{50}{2} = 25. The 25th25^{\text{th}} item falls in the 303930 - 39 class. Lower boundary (LL) =29.5= 29.5, preceding cumulative frequency (cfpcf_p) =21= 21, median class frequency (fmf_m) =16= 16, class width (cc) =10= 10.
The median class is the first class whose cumulative frequency meets or exceeds N/2N/2.
3
Substitute the parameters into the grouped median formula.
Median=L+(N2cfpfm)×c=29.5+(252116)×10=29.5+(416)×10=29.5+2.5=32\text{Median} = L + \left(\frac{\frac{N}{2} - cf_p}{f_m}\right) \times c = 29.5 + \left(\frac{25 - 21}{16}\right) \times 10 = 29.5 + \left(\frac{4}{16}\right) \times 10 = 29.5 + 2.5 = 32.
Linear interpolation within the median class yields the precise median measurement.

Anahtar Kavram

Median of Grouped Data using Class Boundaries and Linear Interpolation
Tahmini Süre:2m 0s
Soru 1120Soru

A firm operating in an imperfectly competitive market faces a demand function given by P=1604QP = 160 - 4Q, where PP is the unit price in Naira (\text{₦}) and QQ is the output quantity in units. At what output level QQ will the firm maximize its Total Revenue (TRTR)?

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Cevap: 20

Cevap

The firm maximizes its total revenue at an output level of 20 units.
Total revenue (TRTR) is maximized at the point where additional output yields zero additional revenue, meaning marginal revenue (MRMR) equals zero (MR=0MR = 0). Given the demand function P=1604QP = 160 - 4Q, total revenue is TR=P×Q=160Q4Q2TR = P \times Q = 160Q - 4Q^2. The marginal revenue function is MR=dTRdQ=1608QMR = \frac{dTR}{dQ} = 160 - 8Q. Setting MR=0MR = 0 gives 1608Q=0160 - 8Q = 0, which solves to Q=20Q = 20 units.

Adım Adım Çözüm

1
Derive the Total Revenue (TR) function from the demand function.
TR=160Q4Q2TR = 160Q - 4Q^2
Total revenue is calculated by multiplying price (PP) by quantity (QQ).
2
Derive the Marginal Revenue (MR) function.
MR=1608QMR = 160 - 8Q
Marginal revenue is the rate of change of total revenue with respect to output (dTRdQ\frac{dTR}{dQ}).
3
Set Marginal Revenue to zero and solve for output (QQ).
8Q=160    Q=208Q = 160 \implies Q = 20
Total revenue reaches its maximum peak when marginal revenue declines to zero (MR=0MR = 0).

Anahtar Kavram

Total Revenue Maximization Condition (MR=0MR = 0)
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