BECC-101 Solved Question Paper

Question 1-1: Technology and the Production Possibility Curve

How does better technology shift the PPC?

The production possibility curve (PPC) shows all the combinations of goods an economy can produce with its existing resources and technology. When technology improves – for example, better machines, improved farming techniques, or more efficient software – the same amount of labour and capital can produce more output.

Because of this increase in productive capacity, every feasible combination of goods rises. Graphically, the entire PPC moves outward (to the right). That outward shift means the economy can now produce more of one good without sacrificing as much of the other, or more of both goods together, indicating economic growth and a higher potential standard of living.

Question 1-2-1: Consumer Surplus vs Producer Surplus

How are the two surplus concepts different?

Consumer surplus measures the extra satisfaction buyers get because the market price is lower than the maximum they were willing to pay. On a demand–supply diagram it is the area between the demand curve and the actual market price, up to the quantity bought.

Producer surplus captures the extra benefit sellers receive because the market price is higher than the minimum price at which they would have been willing to sell (their marginal cost). Graphically it is the area between the market price and the supply curve, up to the quantity sold.

So, consumer surplus is a “gain to buyers” from paying less than their willingness to pay, whereas producer surplus is a “gain to sellers” from receiving more than their minimum acceptable price. Together, they represent the total gains from trade in a market.

Question 1-2-2: Positive and Normative Economics

How do ‘what is’ and ‘what ought to be’ differ?

Positive economics deals with statements that describe and explain economic behaviour without judging it. These are factual or testable claims, such as “an increase in the petrol tax will reduce petrol consumption.” We can check them using data.

Normative economics involves value judgements – it asks what should happen. Statements like “the government should increase the petrol tax to protect the environment” depend on ethical views and social priorities and cannot be proved true or false by data alone.

In short, positive economics is descriptive and objective, while normative economics is prescriptive and based on opinions or social values.

Question 1-3-1: Tax Incidence with Perfectly Elastic Demand

Who bears the tax burden when demand is perfectly elastic?

When demand is perfectly elastic, buyers are extremely price-sensitive: even a tiny increase in price causes quantity demanded to fall to zero. A per-unit tax drives a wedge between what buyers pay and what sellers receive.

Because buyers will not accept any price increase, the market price (inclusive of tax) cannot rise. Firms must absorb the entire tax by accepting a lower net-of-tax price. Consequently, the full tax burden falls on producers when demand is perfectly elastic and supply is upward sloping.

Question 1-3-2: Tax Incidence with Perfectly Elastic Supply

Who bears the tax burden when supply is perfectly elastic?

When supply is perfectly elastic, firms are willing to supply any quantity at a given price but nothing if the price they receive falls even slightly below that level.

With a per-unit tax, producers insist on the same net-of-tax price as before; otherwise they stop supplying. The entire tax therefore appears as an increase in the price paid by buyers. Hence, the whole tax burden is borne by consumers when supply is perfectly elastic and demand is downward sloping.

Question 2-1: Deriving the Demand Curve from Diminishing Marginal Utility

How can we get a demand curve using the law of diminishing marginal utility?

Under the cardinal approach, a rational consumer compares the marginal utility (MU) of each additional unit of a good with its price. They keep buying extra units as long as

$$ MU_x \geq P_x $$

and stop where

$$ MU_x = P_x, $$

because this is the point where the utility gained from the last unit equals the money sacrificed. As consumption rises, MU falls (law of diminishing marginal utility). To keep the equality (MU_x = P_x) true, the price must fall if the consumer is to buy more units.

Plotting the various combinations of price and quantity at which (MU_x = P_x) gives us a downward-sloping demand curve. Each point on the demand curve corresponds to the quantity for which the marginal utility of the last unit equals the market price.

Question 2-2: Hicksian Decomposition of Substitution and Income Effects

How do substitution and income effects work when price changes?

When the price of a good falls, two things happen:

• Substitution effect: The good becomes relatively cheaper than other goods. Holding real satisfaction (utility) constant, the consumer rearranges purchases towards the cheaper good and away from the relatively dearer ones.
• Income effect: At the new lower price, the consumer’s nominal money income can buy more than before. This feels like an increase in real income, which can change quantities demanded depending on whether the good is normal or inferior.

In the Hicksian method, we first keep the consumer on the same indifference curve by reducing their money income just enough to cancel the rise in purchasing power caused by the price cut. The movement along that original indifference curve from the old tangency point to the compensated tangency point shows the substitution effect.

Then we restore the income to its original level while keeping the new lower price. The shift from the compensated tangency point to the final tangency point on a higher indifference curve captures the income effect. The total change in quantity demanded is the sum of these two movements.

Question 2-3: Returns to Scale of the Production Function

What kind of returns to scale does this production function show?

The production function is

$$ Q = A L^{0.8} K^{0.5}. $$

To see the returns to scale, increase both inputs by the same proportion, say by a factor (t):

$$
Q’ = A (tL)^{0.8} (tK)^{0.5}
= A t^{0.8} L^{0.8} t^{0.5} K^{0.5}
= A t^{1.3} L^{0.8} K^{0.5}.
$$

Now compare Q′ with the original Q:
Since the exponent sum (0.8 + 0.5 = 1.3 > 1), we get more than a proportional increase in output when we scale up all inputs by the same proportion. This is a case of increasing returns to scale.

Question 3-1: Three Stages of a Typical Production Function

Why do we say the short-run production function has three stages?

With one variable input (say labour) and other inputs fixed, output passes through three stages as more labour is used:

1. Stage I – Increasing returns: Total product (TP) rises at an increasing rate. Marginal product (MP) rises and average product (AP) also rises. Workers are few relative to fixed capital, so specialisation and better utilisation of fixed inputs make each extra worker more productive.
2. Stage II – Diminishing returns: TP still rises but at a decreasing rate. MP falls but is still positive; AP also starts falling after reaching its maximum. This is the economically relevant stage where the firm normally operates.
3. Stage III – Negative returns: TP starts falling; MP becomes negative. Too many workers crowd the fixed plant, so additional labour actually reduces total output.

Diagrams of TP, AP and MP against labour show these three stages clearly.

Question 3-2: Firm’s Expansion Path (Short Run, Linear Homogeneous Case)

What is the expansion path and how does it look for a linear homogeneous production function?

The expansion path of a firm traces the cost-minimising combinations of inputs (e.g. labour and capital) as the firm moves to higher levels of output, given input prices. It joins all tangency points between isoquants (showing equal output) and isocost lines (showing equal total cost).

For a linear homogeneous production function (constant returns to scale) and given input prices, the slope of the isocost line equals the slope of the isoquant along the ray from the origin. As output expands in the short run with one factor (say capital) fixed, the firm moves along isoquants that intersect the same vertical line for fixed capital, adjusting labour only. The short-run expansion path is therefore a vertical line at that fixed capital level in the L–K space. In the long run, with both inputs variable, the expansion path would be a straight line passing through the origin.

Question 3-3: External Economies and External Diseconomies

How do these two industry-level effects differ?

External economies are cost advantages enjoyed by a firm because the industry as a whole has expanded, not because the firm itself has changed its own scale. Examples include better industry-specific infrastructure, skilled labour pools, or specialised suppliers that appear when the industry grows. These reduce each firm’s cost curves.

External diseconomies arise when the growth of the industry raises each firm’s cost, for example due to congestion, rising input prices, environmental regulations, or overuse of common infrastructure. In that case, a firm’s cost curves shift upward even if its own scale of operation is unchanged.

Question 4-1: Link between Long-Run Marginal Cost and Long-Run Average Cost

How are LRMC and LRAC related?

The long-run average cost (LRAC) curve shows the minimum cost per unit at which each output level can be produced when all inputs are variable. The long-run marginal cost (LRMC) curve shows the extra cost of producing one more unit of output in the long run.

The standard relationships are:

• When LRMC is below LRAC, producing an additional unit costs less than the current average, so LRAC is falling.
• When LRMC is above LRAC, the extra unit is more expensive than the current average, so LRAC is rising.
• LRMC intersects LRAC at the minimum point of the LRAC curve. That output level is the most efficient scale in the long run.

These relationships mirror those between short-run MC and AC, but in the long run they reflect the combined effect of changing plant size and input mix.

Question 4-2: Profit Maximisation for a Perfectly Competitive Firm

Finding optimal output and profit when price and cost functions are given

In perfect competition, the firm is a price taker, so its marginal revenue (MR) equals the market price (P). Profit is maximised where

$$ P = MC $$

provided the MC curve is rising at that point.

Here,

• Market price: (P = 4)
• Marginal cost is given by: $$ MC = 3Q^2 – 14Q + 12 $$
• Slope of MC: $$ (\dfrac{dMC}{dQ} = 6Q – 14) $$

Set (MC = P):

$$ 3Q^2 – 14Q + 12 = 4 \Rightarrow 3Q^2 – 14Q + 8 = 0. $$

Solving, we get two values: (Q = \tfrac{2}{3}) and (Q = 4). At (Q = \tfrac{2}{3}), the MC slope is negative ((6Q – 14 < 0)), so MC is falling and this point does not satisfy the profit-maximising condition. At (Q = 4), the MC slope is positive ((6\cdot4 -14 > 0)), so the firm’s profit-maximising output is

$$ Q^* = 4. $$

Total revenue at this output is

$$ TR = P \times Q^* = 4 \times 4 = 16. $$

Given the total cost function

$$ TC = Q^3 – 7Q^2 + 12Q + 5, $$

the total cost at (Q = 4) is

$$ TC(4) = 4^3 – 7\cdot 4^2 + 12\cdot4 + 5 = 64 – 112 + 48 + 5 = 5. $$

Therefore, total profit is

$$ \pi = TR – TC = 16 – 5 = 11. $$

So, the firm produces 4 units and earns a profit of 11 monetary units.

Question 5-1: Why Taxes Cause Deadweight Loss

Why do taxes reduce total surplus, and what affects the size of the loss?

A per-unit tax raises the price paid by buyers and lowers the price received by sellers. Quantity traded falls below the level where marginal benefit equals marginal cost. The mutually beneficial trades that no longer happen represent a loss of consumer and producer surplus that does not go to the government. This lost surplus is the deadweight loss.

The size of this loss depends mainly on:

• Elasticities of demand and supply: The more responsive buyers and sellers are to price (more elastic curves), the larger the fall in quantity and the bigger the deadweight loss.
• Size of the tax: A higher tax widens the wedge between buyer and seller prices, magnifying the loss in surplus.

Question 5-2: Labour Market Equilibrium and Minimum Wage

Solving for equilibrium wage and employment

Labour supply and demand are:

$$ L_S = 10W, \quad L_D = 140 – 10W, $$

where (W) is the wage per hour.

(a) Free-market equilibrium

Set supply equal to demand:

$$ 10W = 140 – 10W \Rightarrow 20W = 140 \Rightarrow W^* = 7. $$

Substitute into either equation:

$$ L^* = 10 \times 7 = 70. $$

So, the equilibrium wage is 7 per hour and 70 units of labour are employed.

(b) Minimum wage of 9 per hour

At (W = 9):

Supply: $$(L_S = 10 \times 9 = 90)$$

Demand: $$(L_D = 140 – 10 \times 9 = 50)$$

Firms hire only 50 workers, so employment is 50, and 40 workers (90 − 50) are unemployed because of the binding minimum wage.

Question 6-1: Indifference Curves When Coke and Pepsi Are Perfect Substitutes

How do Babu’s indifference curves look if he sees Coke and Pepsi as identical?

If Babu regards Coke and Pepsi as perfect one-for-one substitutes – in other words, he does not care whether he drinks one or the other – then his utility depends only on the total number of soft drinks, not on the brand.

His indifference curves are straight lines with a constant slope of −1, reflecting a constant marginal rate of substitution of one can of Coke for one can of Pepsi. Any combination with the same total number of cans lies on the same indifference curve (for example, 3 Coke + 1 Pepsi is equivalent in satisfaction to 2 Coke + 2 Pepsi).

Question 6-2: Income Consumption Curve and Engel Curve for Good X

How do we trace ICC and Engel curve for a normal good?

Take the price of good X as ₹10 and of good Y as ₹25. Consider three income levels: ₹100, ₹200 and ₹300. For each income, draw a budget line and find the equilibrium point where it is tangent to an indifference curve.

If good X is normal, higher income shifts the budget line outward and the optimal quantity of X rises. Joining the three equilibrium bundles for different incomes in the X–Y space gives the income consumption curve (ICC), which slopes upwards if X is normal.

To obtain the Engel curve for X, plot on a separate graph the quantity of X on the horizontal axis and income on the vertical axis, using the equilibrium quantities of X corresponding to incomes 100, 200 and 300. For a normal good, the Engel curve slopes upward, showing that Babu buys more of X as his income rises.

Question 7: Slutsky vs Hicks Substitution Effects

How do the two decompositions of a price change differ?

Both Slutsky and Hicks break the total effect of a price change into a substitution effect and an income effect, but they hold “real income” constant in slightly different ways.

• Hicksian substitution effect: After a price change, the consumer is moved along the initial indifference curve by adjusting income so that they remain on the same level of utility as before. The substitution effect is the movement along the initial indifference curve due solely to the change in relative prices.
• Slutsky substitution effect: Here income is adjusted so that the consumer can just afford the original bundle at the new prices. This keeps the consumer’s purchasing power with respect to the old bundle constant. The movement from the old bundle to the new “cost-compensated” bundle shows the Slutsky substitution effect.

Because the Hicks method keeps utility constant and the Slutsky method keeps purchasing power (at the old bundle) constant, the two substitution effects differ slightly in size, though they point in the same direction for normal goods.

Question 8-1: Long-Period Economic Efficiency

What does efficiency mean in the long run?

In the long period, firms can adjust all inputs and even enter or leave the industry. Long-period economic efficiency means that resources are allocated in such a way that:

• Each firm is producing at the lowest point of its long-run average cost curve (productive efficiency).
• The price of each good equals its long-run marginal cost, so the value consumers place on the last unit equals the cost of the resources used to produce it (allocative efficiency).

This situation typically emerges under perfect competition in the long run, with free entry and exit driving profits to normal levels and aligning prices with minimum average costs.

Question 8-2: Returns to Scale Using Isoquants

How do isoquants show increasing, constant and decreasing returns to scale?

Isoquants show combinations of labour and capital that yield the same output. To study returns to scale, we see what happens to output when all inputs are increased proportionally.

• Increasing returns to scale: If doubling both inputs moves us to an isoquant representing more than double the output, the distance between successive isoquants shrinks as we move away from the origin. Firms may enjoy specialisation and indivisibilities of capital in this region.
• Constant returns to scale: If doubling both inputs exactly doubles output, isoquants are spaced evenly along a ray from the origin. The expansion path from the origin passes through points where output rises in the same proportion as inputs.
• Decreasing returns to scale: If doubling both inputs results in less than double the output, isoquants become closer to each other near the origin and more widely spaced at higher output levels, reflecting rising difficulties in managing very large operations.

Thus, by observing how quickly isoquants spread out along a ray from the origin, we can infer the type of returns to scale.

Question 9-1: Co-operative vs Non-Co-operative Behaviour

How do firms behave differently in these two strategic settings?

In co-operative behaviour, firms explicitly or implicitly coordinate their actions – for example, agreeing on prices, output quotas or market sharing. Cartels in an oligopolistic industry are classic examples. They act as if they were a single monopolist, sharing the resulting profits.

In non-co-operative behaviour, each firm chooses its strategy independently, taking rivals’ actions as given and trying to maximise its own profit. Models like Cournot, Bertrand and Stackelberg assume non-co-operative behaviour. Outcomes usually involve more output and lower prices than in a cartel arrangement.

Question 9-2: Stackelberg Duopoly with Zero Costs

Finding leader and follower outputs

Let total output be (Q = q_1 + q_2), where firm 1 is the leader and firm 2 the follower. Inverse market demand is

$$ P = 20 – Q. $$

Costs are zero for both firms.

Follower’s best response

Firm 2’s profit is

$$ \pi_2 = P q_2 = (20 – q_1 – q_2) q_2. $$

Differentiating w.r.t. (q_2) and setting to zero:

$$ \frac{\partial \pi_2}{\partial q_2} = 20 – q_1 – 2q_2 = 0 \Rightarrow q_2 = \frac{20 – q_1}{2}. $$

This is firm 2’s reaction function.

Leader’s choice

Firm 1 anticipates this reaction. Its profit is

$$ \pi_1 = (20 – q_1 – q_2) q_1. $$

Substitute $$ (q_2 = \frac{20 – q_1}{2}): $$

$$
\pi_1 = \left(20 – q_1 – \frac{20 – q_1}{2}\right) q_1
= \left(10 – \frac{1}{2} q_1\right) q_1
= 10 q_1 – \frac{1}{2} q_1^2.
$$

FOC:

$$ \frac{d\pi_1}{dq_1} = 10 – q_1 = 0 \Rightarrow q_1^* = 10. $$

Follower’s output:

$$ q_2^* = \frac{20 – 10}{2} = 5. $$

Total output and price:

$$ Q^* = q_1^* + q_2^* = 15, \quad P^* = 20 – 15 = 5. $$

So under Stackelberg competition, the leader produces 10 units, the follower 5 units, and the market price is 5.

Question 10-1: The Kinked Demand Curve

What does the kinked demand model say about oligopoly pricing?

In an oligopoly, each firm believes that:

• If it raises its price, rivals will not follow, so it will lose many customers – demand is relatively elastic above the current price.
• If it cuts its price, rivals will match the cut, so it gains few new customers – demand is relatively inelastic below the current price.

This leads to a kinked demand curve at the prevailing price, with a discontinuous marginal revenue curve. As a result, even if marginal cost changes within a certain range, the optimal price remains unchanged. This helps explain why prices in oligopolistic industries can be rigid for long periods.

Question 10-2: First Fundamental Theorem of Welfare Economics

What does the first welfare theorem tell us?

The first fundamental theorem of welfare economics states that, under certain conditions (perfect competition, complete markets, no externalities, perfect information, etc.), any competitive equilibrium allocation of resources is Pareto efficient. That means no one can be made better off without making someone else worse off.

In other words, if all markets are competitive, the invisible hand of the price system leads self-interested consumers and firms to an allocation of resources that is efficient from society’s point of view – though not necessarily fair or equitable.

Question 11: Meaning and Sources of Market Failure

What is market failure and why does it arise?

Market failure occurs when the free market, left to itself, does not lead to a Pareto-efficient allocation of resources. Prices and quantities chosen by private agents do not fully reflect social costs and benefits, so society either over-produces or under-produces certain goods or services.

Important sources of market failure include:

• Market power: Monopolies or oligopolies restrict output and raise prices, creating deadweight loss.
• Externalities: When production or consumption imposes costs or benefits on third parties (e.g., pollution, vaccination) that are not reflected in market prices, private marginal cost or benefit diverges from the social one.
• Public goods: Non-rival and non-excludable goods (like national defence or street lighting) are under-provided by markets because of free-riding.
• Imperfect information and asymmetric information: When buyers or sellers lack key information (quality of used cars, risk behaviour in insurance, etc.), markets may misallocate resources or even break down.
• Common-pool resources: Open-access resources such as fisheries or grazing land can be overused (the “tragedy of the commons”).

In such cases, government intervention – through taxes, subsidies, regulation, public provision or property-rights reform – is often suggested to move the economy closer to efficiency.

Question 12: Utility Maximisation, Cost Minimisation and General Equilibrium

Why are consumer and firm optimisation important in general equilibrium analysis?

A general equilibrium framework studies how all markets in the economy interact simultaneously. Two optimisation principles lie at its heart:

• Consumer utility maximisation: Each consumer chooses the bundle of goods that maximises their utility, subject to their budget constraint. At an interior optimum, the marginal rate of substitution between any two goods equals their price ratio. This ensures that consumers cannot rearrange their spending to become better off given market prices.
• Firm cost minimisation (and profit maximisation): Each firm chooses the combination of inputs that minimises cost for any given level of output and then chooses output so that price equals marginal cost. This implies that the marginal rate of technical substitution between inputs equals their price ratio, and that resources are used where they are most productive.

When all consumers maximise utility and all firms minimise cost (and thus maximise profit) at the prevailing prices, the resulting allocation of goods and inputs satisfies the efficiency conditions of the first welfare theorem. Hence, utility maximisation and cost minimisation are the behavioural foundations that link individual decisions to an economy-wide, Pareto-efficient general equilibrium.