Practice gce model questions vol1 economics 2018 Past Questions

Question 1 View Details

A firm's total cost function is $TC = 0.02Q^{3} - 0.3Q^{2} + 15Q + 200$, where $Q$ is output (units). The market demand for its product is $P = 120 - 0.5Q$. Determine the integer level of output that maximises the firm's profit.

A. 38

B. 40

Correct C. 39

D. 41

Correct Answer: C

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Question 2 View Details

A savings account offers a nominal interest rate of 8% per year. Inflation is 6% in the first half‑year and 4% in the second half‑year. Using the exact Fisher relation, calculate the real interest rate earned on the account, expressed as a percentage to two decimal places.

A. 3.45%

Correct B. 2.86%

C. 4.10%

D. 1.92%

Correct Answer: B

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Question 3 View Details

A country's population follows the logistic model $P(t)=\frac{K}{1+ae^{-bt}}$ (million people, $t$ in years). At $t=0$ the population is 20 million, at $t=5$ it is 30 million and at $t=10$ it is 38 million. To the nearest year, when will the population reach 45 million?

A. 22

Correct B. 19

C. 25

D. 17

Correct Answer: B

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Question 4 View Details

The market demand for wheat is $Q_d = 500 - 2P$ (tonnes, price £ per tonne). Without any subsidy the supply curve is $Q_s = 3P - 30$. The government introduces a per‑unit subsidy to producers, after which the consumer price falls to £80 per tonne. Determine the increase in producer surplus (in £, rounded to the nearest £) caused by the subsidy.

Correct A. 5443

B. 5120

C. 5800

D. 6300

Correct Answer: A

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Question 5 View Details

The required reserve ratio is 5%, banks hold excess reserves equal to 2% of deposits, and the public keeps cash equal to 10% of their money holdings. If the central bank injects £200 million by purchasing government bonds, calculate the total increase in the money supply (in £ million, to one decimal place).

Correct A. 1176.5

B. 1333.3

C. 2857.1

D. 1176.4

Correct Answer: A

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Question 6 View Details

Given that when the price of a good is $\text{₦}20$ the quantity demanded is 800 units, and when the price is $\text{₦}30$ the quantity demanded falls to 500 units, assume the demand curve is linear. (a) Determine the price elasticity of demand at a price of $\text{₦}25$ using the point‑elasticity formula. (b) If the price is increased by 5 % from $\text{₦}25$, predict whether total revenue will rise or fall.

A. Elasticity ≈ -0.85 (inelastic); total revenue will increase.

Correct B. Elasticity ≈ -1.15 (elastic); total revenue will decrease.

C. Elasticity ≈ -1.50 (elastic); total revenue will increase.

D. Elasticity ≈ -0.60 (inelastic); total revenue will decrease.

Correct Answer: B

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Question 7 View Details

An economy can produce only two goods, cars and wheat. On its production possibilities frontier the following two points are observed: Point A: 10 cars and 2000 units of wheat. Point B: 15 cars and 1500 units of wheat. What is the opportunity cost, in units of wheat, of producing one additional car when moving from point A to point B?

A. 125 units of wheat

B. 75 units of wheat

Correct C. 100 units of wheat

D. 150 units of wheat

Correct Answer: C

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Question 8 View Details

The market for a certain product is described by the linear demand equation $Q_d = 1000 - 5P$ and the linear supply equation $Q_s = -200 + 3P$, where $P$ is the price in dollars and $Q$ is quantity. The government imposes a specific tax of \$20 per unit on producers. Calculate the new equilibrium price paid by consumers, the price received by producers after the tax, the equilibrium quantity, and the total tax revenue collected.

A. Consumer price = $160; producer price = $140; quantity = 215; tax revenue = $4,300

B. Consumer price = $155; producer price = $135; quantity = 205; tax revenue = $4,100

Correct C. Consumer price = $157.5; producer price = $137.5; quantity = 212.5; tax revenue = $4,250

D. Consumer price = $152.5; producer price = $132.5; quantity = 210; tax revenue = $4,200

Correct Answer: C

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Question 9 View Details

Country X's export earnings from coffee are \$200 billion. They increase by 10 % due to a rise in world coffee prices. The marginal propensity to import (MPI) for Country X is 0.25. Assuming that the increase in export earnings translates directly into an equal increase in national income, determine the resulting increase in import expenditure. If the average price of imported wheat is \$50 per tonne, calculate the additional quantity of wheat that will be imported.

Correct A. Import expenditure +$5 billion; wheat imports increase by 100 million tonnes

B. Import expenditure +$4 billion; wheat imports increase by 80 million tonnes

C. Import expenditure +$6 billion; wheat imports increase by 120 million tonnes

D. Import expenditure +$5 billion; wheat imports increase by 90 million tonnes

Correct Answer: A

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Question 10 View Details

The market for wheat is described by the linear demand curve $Q_d = 4800 - 8P$ and the linear supply curve $Q_s = -800 + 6P$, where $P$ is the price in dollars per tonne and $Q$ is quantity in thousands of tonnes. (a) Find the competitive equilibrium price and quantity. (b) The government introduces a price floor of \$500 per tonne. Compute the quantity demanded, quantity supplied, the surplus (excess supply), and the total cost to the government of purchasing the surplus at the floor price. (c) Calculate the dead‑weight loss associated with the price floor. (d) The government also pays a subsidy to producers equal to half the surplus per unit (i.e., $\frac{1}{2}$ of the difference between the floor price and the equilibrium price). Determine the total subsidy payment and the overall government outlay (purchase cost plus subsidy).

Correct A. Equilibrium: $400, 1,600 k t. Floor price: demand 800 k t, supply 2,200 k t, surplus 1,400 k t, purchase cost $700 m. DWL $70 m. Subsidy $50/t, total subsidy $70 m. Total outlay $770 m.

B. Equilibrium: $400, 1,600 k t. Floor price: demand 900 k t, supply 2,100 k t, surplus 1,200 k t, purchase cost $600 m. DWL $60 m. Subsidy $40/t, total subsidy $48 m. Total outlay $648 m.

C. Equilibrium: $420, 1,560 k t. Floor price: demand 750 k t, supply 2,250 k t, surplus 1,500 k t, purchase cost $750 m. DWL $80 m. Subsidy $55/t, total subsidy $82.5 m. Total outlay $832.5 m.

D. Equilibrium: $380, 1,640 k t. Floor price: demand 850 k t, supply 2,150 k t, surplus 1,300 k t, purchase cost $650 m. DWL $65 m. Subsidy $45/t, total subsidy $58.5 m. Total outlay $708.5 m.

Correct Answer: A

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Question 11 View Details

Given the market demand curve $ P = 200 - 4Q $ and the firm's total cost function $ TC = 50 + 20Q + Q^{2} $: a) Determine the monopoly output, price and profit. b) Determine the output, price and profit that would prevail under perfect competition. c) Calculate the percentage by which the monopoly profit exceeds the competitive profit (rounded to one decimal place).

A. 92.1

B. 68.4

Correct C. 84.7

D. 75.3

Correct Answer: C

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Question 12 View Details

Using the income approach, the following data are given (in billions of naira): Consumption $C = 500$, Investment $I = 150$, Government spending $G = 200$, Exports $X = 120$, Imports $M = 80$, Indirect taxes $T = 60$, Subsidies $S = 20$, Depreciation $D = 90$, Net factor income from abroad $NFI = -10$. The population is 25 million. Calculate the national income per capita (NNI per capita).

A. 33200

B. 29800

C. 27400

Correct D. 31600

Correct Answer: D

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Question 13 View Details

A firm faces the demand curve $ P = 120 - Q $ and has total cost $ TC = 100 + 5Q + 0.5Q^{2} $. i) Find the profit‑maximising output, price and profit. ii) If a specific per‑unit tax of $\text{₦}10$ is imposed, determine the new profit‑maximising output, price and profit.

A. Original: Q=36.5, P=₦83.5, Profit=₦2050.25; After tax: Q=34, P=₦84, Profit=₦1750.0

Correct B. Original: Q=38.33, P=₦81.67, Profit=₦2104.17; After tax: Q=35, P=₦85, Profit=₦1737.5

C. Original: Q=38.33, P=₦80.00, Profit=₦2100.00; After tax: Q=35, P=₦88, Profit=₦1800.0

D. Original: Q=40.00, P=₦80.00, Profit=₦2000.00; After tax: Q=33, P=₦86, Profit=₦1700.0

Correct Answer: B

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Question 14 View Details

An automobile industry firm has a long‑run average cost function $ LRAC = 4 + 0.02Q + \frac{10}{Q} $ (costs in thousand naira per unit). The market price is $\text{₦}50$ per unit. a) Find the output level that minimises LRAC (the minimum efficient scale, MES). b) At that output, does the firm make a profit, incur a loss, or break even? State the profit (in thousand naira). c) If a key input price rises, shifting the LRAC upward by 0.5 at every output (new LRAC = 4.5 + 0.02Q + 10/Q), determine the new MES and the profit status.

Correct A. MES ≈ 22.4 units; profit ≈ ₦1,008 (positive); after shift MES ≈ 22.4 units; profit ≈ ₦998 (positive)

B. MES ≈ 20.0 units; profit ≈ ₦900 (positive); after shift MES ≈ 20.0 units; profit ≈ ₦850 (positive)

C. MES ≈ 25.0 units; profit ≈ ₦1,200 (positive); after shift MES ≈ 25.0 units; profit ≈ ₦1,150 (positive)

D. MES ≈ 22.4 units; profit ≈ ₦1,008 (negative); after shift MES ≈ 22.4 units; profit ≈ ₦998 (negative)

Correct Answer: A

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Question 15 View Details

A country's population follows the logistic growth model $ \frac{dP}{dt}= rP\left(1-\frac{P}{K}\right) $ with intrinsic growth rate $ r = 0.04 $ per year, carrying capacity $ K = 50 $ million and initial population $ P_{0}=20 $ million. The current age‑structure is 0‑14: 30 %, 15‑64: 60 %, 65+: 10 %. As the total population approaches $ K $, the proportion of 0‑14 declines linearly to 20 % at $ P=K $ and the proportion of 65+ rises linearly to 15 % at $ P=K $; the 15‑64 proportion adjusts accordingly. a) Estimate the population after 10 years. b) Compute the dependency ratio (dependents 0‑14 and 65+ versus 15‑64) after 10 years (as a percentage, one decimal place). c) To keep the dependency ratio below 55 %, what is the maximum population that can be reached, expressed as a percentage of the carrying capacity $ K $ (rounded to the nearest whole percent)?

Correct A. a) 24.9 million; b) 64.5 %; c) 94 % of K

B. a) 22.9 million; b) 70.3 %; c) 90 % of K

C. a) 25.4 million; b) 60.1 %; c) 96 % of K

D. a) 23.7 million; b) 68.2 %; c) 88 % of K

Correct Answer: A

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Question 16 View Details

A developing economy has two sectors. Agriculture produces output $Q_A = 100 L_A^{0.5}$ and manufacturing produces output $Q_M = 50 L_M^{0.7}$, where $L_A$ and $L_M$ are the numbers of workers employed in each sector. The total labour force is 200 workers and wages are equal to the marginal product of labour in each sector. Determine the equilibrium wage (to two decimal places) and the allocation of labour between the two sectors.

A. Equilibrium wage ≈ £7.00; labour allocation: $L_A \approx 48.0$ workers in agriculture, $L_M \approx 152.0$ workers in manufacturing.

B. Equilibrium wage ≈ £6.50; labour allocation: $L_A \approx 55.0$ workers in agriculture, $L_M \approx 145.0$ workers in manufacturing.

C. Equilibrium wage ≈ £8.20; labour allocation: $L_A \approx 35.0$ workers in agriculture, $L_M \approx 165.0$ workers in manufacturing.

Correct D. Equilibrium wage ≈ £7.68; labour allocation: $L_A \approx 42.5$ workers in agriculture, $L_M \approx 157.5$ workers in manufacturing.

Correct Answer: D

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Question 17 View Details

The market for a good is described by the demand equation $Q_d = 120 - 2P$ and the supply equation $Q_s = -20 + 3P$, where $P$ is the price in dollars per unit. Production of the good generates a negative externality that imposes a cost of $4 per unit on society. The government decides to impose a specific tax $t$ per unit to internalise the externality. (a) What is the optimal specific tax? (b) Calculate the new consumer price, producer price, equilibrium quantity, consumer surplus, producer surplus and tax revenue after the tax is imposed. (c) Compute the dead‑weight loss arising from the tax and state the net welfare loss, taking the externality into account.

Correct A. Optimal tax = $4 per unit. After the tax: consumer price = $30.40, producer price = $26.40, quantity = 59.2 units. Consumer surplus ≈ $876.16, producer surplus ≈ $584.10, tax revenue = $236.80. Dead‑weight loss = $9.60, net welfare loss = $0 (the externality is fully internalised).

B. Optimal tax = $4 per unit. After the tax: consumer price = $29.80, producer price = $25.80, quantity = 60.0 units. Consumer surplus ≈ $860.00, producer surplus ≈ $570.00, tax revenue = $240.00. Dead‑weight loss = $10.00, net welfare loss = $1.00 (partial internalisation).

C. Optimal tax = $3 per unit. After the tax: consumer price = $29.00, producer price = $26.00, quantity = 61.5 units. Consumer surplus ≈ $900.00, producer surplus ≈ $600.00, tax revenue = $184.50. Dead‑weight loss = $7.20, net welfare loss = $-1.20 (over‑compensation).

D. Optimal tax = $5 per unit. After the tax: consumer price = $31.20, producer price = $26.20, quantity = 57.0 units. Consumer surplus ≈ $845.00, producer surplus ≈ $560.00, tax revenue = $285.00. Dead‑weight loss = $12.00, net welfare loss = $2.00 (the externality is not fully internalised).

Correct Answer: A

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Question 18 View Details

The demand for good X is given by $Q_X = 400 - 4P_X + 3P_Y + 0.05I$, where $P_X$ and $P_Y$ are the prices (in £) of X and a related good Y respectively, and $I$ is consumer income in £. Currently $P_X = 20$, $P_Y = 10$ and $I = 2000$. Calculate (i) the own‑price elasticity of demand for X, (ii) the cross‑price elasticity with respect to $P_Y$, and (iii) the income elasticity of demand for X, all evaluated at the given values. Give your answers to two decimal places.

A. Own‑price elasticity ≈ -0.18 (inelastic); cross‑price elasticity ≈ 0.07 (weak substitute); income elasticity ≈ -0.22 (inferior good).

Correct B. Own‑price elasticity ≈ -0.18 (inelastic); cross‑price elasticity ≈ 0.07 (weak substitute); income elasticity ≈ 0.22 (normal good).

C. Own‑price elasticity ≈ -0.25 (inelastic); cross‑price elasticity ≈ 0.12 (substitute); income elasticity ≈ 0.30 (normal good).

D. Own‑price elasticity ≈ -0.10 (inelastic); cross‑price elasticity ≈ -0.05 (complement); income elasticity ≈ 0.15 (normal good).

Correct Answer: B

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Question 19 View Details

A firm produces output according to the Cobb‑Douglas function $Q = L^{0.5}K^{0.5}$. The price of labour is $w = £4$ per unit and the price of capital is $r = £16$ per unit. The firm wishes to produce $Q = 100$ units at minimum cost. Determine the cost‑minimising quantities of labour and capital, the total cost, and the marginal rate of technical substitution (MRTS) at the optimum.

A. Labour L = 200 units, Capital K = 50 units; Minimum total cost = £1,600; MRTS = 0.40.

B. Labour L = 250 units, Capital K = 40 units; Minimum total cost = £1,800; MRTS = 0.20.

C. Labour L = 150 units, Capital K = 75 units; Minimum total cost = £1,500; MRTS = 0.33.

Correct D. Labour L = 200 units, Capital K = 50 units; Minimum total cost = £1,600; MRTS = 0.25.

Correct Answer: D

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Question 20 View Details

The market demand for a product is $P = 120 - 0.5Q$. The firm's total cost function is $TC = 20Q + 0.02Q^{2} + 100$. (a) Find the profit‑maximising output level, the corresponding price and the profit. (b) Compute the price elasticity of demand at the profit‑maximising output and comment on its magnitude in relation to the profit‑maximising rule.

Correct A. Profit‑maximising output ≈ 96.2 units, price ≈ £71.92, profit ≈ £4,707.70. The price elasticity at this output is about -1.5 (elastic), satisfying the rule that profit maximisation requires elastic demand.

B. Profit‑maximising output ≈ 110.5 units, price ≈ £65.30, profit ≈ £5,200.00. The price elasticity at this output is about -2.2 (elastic), satisfying the rule that profit maximisation requires elastic demand.

C. Profit‑maximising output ≈ 85.0 units, price ≈ £78.00, profit ≈ £3,500.00. The price elasticity at this output is about -0.8 (inelastic), which does not satisfy the rule that profit maximisation requires elastic demand.

D. Profit‑maximising output ≈ 92.0 units, price ≈ £70.10, profit ≈ £4,200.00. The price elasticity at this output is about -1.0 (unit elastic), which marginally meets the rule for profit maximisation.

Correct Answer: A

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Question 21 View Details

If consumer income rises and the good is a $\text{normal good}$, what happens to the demand curve? State the direction of the shift and the resulting effect on equilibrium price and quantity, assuming the supply curve does not change.

A. Demand shifts left; equilibrium price falls; equilibrium quantity falls

Correct B. Demand shifts right; equilibrium price rises; equilibrium quantity rises

C. Demand shifts right; equilibrium price falls; equilibrium quantity rises

D. Demand shifts left; equilibrium price rises; equilibrium quantity falls

Correct Answer: B

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Question 22 View Details

In an economy the labour force is divided among three sectors. Agriculture employs 40% of the labour force with an unemployment rate of $8\%$. Manufacturing employs 35% with an unemployment rate of $12\%$. Services employ 25% with an unemployment rate of $5\%$.\n\n(a) Calculate the overall unemployment rate for the economy.\n(b) If the natural rate of unemployment is $6\%$, determine the amount of cyclical unemployment (as a percentage).

A. Overall unemployment 9.10%; cyclical unemployment 3.10%

B. Overall unemployment 7.50%; cyclical unemployment 1.50%

C. Overall unemployment 8.20%; cyclical unemployment 2.20%

Correct D. Overall unemployment 8.65%; cyclical unemployment 2.65%

Correct Answer: D

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Question 23 View Details

The following data (in billions of Naira) are recorded for a country in a given year:\n\nWages = 150, Profits = 80, Rent = 30, Interest = 20, Indirect taxes less subsidies = 40, Depreciation = 25.\nNet factor income from abroad = $-5$ (a net outflow). The population is 5 million.\n\n(a) Compute GDP at market prices.\n(b) Compute GNP.\n(c) Compute GNP per capita, giving the answer in Naira to the nearest whole number.

Correct A. GDP 345 bn; GNP 340 bn; GNP per capita 68 000 Naira

B. GDP 350 bn; GNP 345 bn; GNP per capita 69 000 Naira

C. GDP 340 bn; GNP 335 bn; GNP per capita 67 000 Naira

D. GDP 345 bn; GNP 335 bn; GNP per capita 68 000 Naira

Correct Answer: A

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Question 24 View Details

A firm's short‑run production function is $Q = 5L - 0.5L^{2}$, where $L$ is the number of labour units employed ($0 \le L \le 10$). The wage rate is $\text{₦}20$ per labour unit, fixed costs are $\text{₦}100$, and the output price is $\text{₦}50$ per unit.\n\nDetermine the level of labour that maximises profit and calculate the maximum profit (to the nearest whole Naira).

A. Labour 4.6 units; maximum profit ₦500

B. Labour 4.2 units; maximum profit ₦450

C. Labour 5.0 units; maximum profit ₦400

Correct D. Labour 4.6 units; maximum profit ₦429

Correct Answer: D

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Question 25 View Details

The Human Development Index (HDI) is the geometric mean of three dimension indices: health, education and standard of living.\n\nCurrent data for a country are:\n- Life expectancy at birth = 68 years (minimum 20, maximum 85).\n- Mean years of schooling = 6 years (minimum 0, maximum 15).\n- Expected years of schooling = 10 years (minimum 0, maximum 18).\n- GNI per capita (PPP) = \$8,000 (minimum \$100, maximum \$75,000).\n\nThe HDI is calculated as $\text{HDI}=\sqrt[3]{\text{Health}\times\text{Education}\times\text{Standard\ of\ Living}}$.\n\nA new policy raises life expectancy by 4 years and increases GNI per capita by 20%, while the education indicators remain unchanged.\n\n(a) Compute the current HDI (to three decimal places).\n(b) Compute the new HDI after the policy (to three decimal places).\n(c) State the percentage change in the HDI (to one decimal place).

A. Current HDI 0.610; new HDI 0.639; HDI rises by 4.7%

Correct B. Current HDI 0.615; new HDI 0.641; HDI rises by 4.2%

C. Current HDI 0.618; new HDI 0.642; HDI rises by 3.9%

D. Current HDI 0.615; new HDI 0.650; HDI rises by 5.7%

Correct Answer: B

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