Introduction to Quantitative Economics Assignment -

Section A: Answer ALL THREE questions.

Q1. Consider a market with inverse demand p = 100 - 2Q. Firms have no fixed cost and constant marginal cost c.

(a) Derive the firms' outputs and profits when this market is served by Cournot duopolists.

(b) How do outputs and profits vary with c?

(c) Suppose the firms also have a fixed cost of F in addition to the marginal cost c. How does F alter the best response functions and Nash equilibrium? Explain in words. (For technical reasons, assume that both firms still produce a positive level of output in equilibrium.)

Q2. Consider two players simultaneously deciding whether to contribute to a public good - the good is said to be public because, if it is made available, an agent who free-rides by paying nothing gets just as much pleasure from its enjoyment as an agent who paid for it. If at least one agent contributes to the construction of the public good, both agents will enjoy a payoff of 4 from the public good. If neither contributes, the good is not constructed and neither player gets enjoyment from the project. If one or both players contribute, then the good is constructed and each player enjoys a payoff of 4 minus the contribution cost 1 if that player has contributed. Assume that the costs are common knowledge to both players.

(a) Fill the payoffs of a, b, c, d, e, f, g, and h in the following table using the information provided above.

(b) Find all pure-strategy Nash Equilibrium(s) to the game.

(c) Find the Mixed Strategy Nash Equilibrium.

Q3. The following figure shows the demand curve for Good X in a perfectly competitive market. Later, the government grants one of the firms the exclusive right to manufacture and sell Good X. MR represents the marginal revenue curve of the firm when it operates as a monopoly. The marginal cost of producing Good X is constant at $5.

(a) What is the quantity supplied when the market is perfectly competitive? What happens to the quantity supplied once the market changes to a monopoly? Explain your answers in words.

(b) What is the market price when the market is perfectly competitive? What is the market price when the market changes to a monopoly? Explain in words.

(c) Compare the consumer surplus when the market is perfectly competitive and the consumer surplus when the market is a monopoly. Is there any producer surplus or deadweight loss in either case? If yes, then how much?

Section B: Answer ALL THREE questions.

Please use a separate booklet.

Q4. Consider a small open economy which is defined by the following system of equations and identities:

Y = C + I + G + NX

G = G^-, T = T^-

C = C₀ + α(Y - T) (α ∈ (0, 1))

I = I₀ + βr (β < 0)

NX = NX₀ + γε (γ < 0)

(a) Explain analytically AND mathematically, why in this economic system IS equation cannot be defined as it was defined in a closed economy?

(b) Find the difference between national saving and investment if:

Y = 8000, G = 2500, T = 2000

C = 500 + 2/3 (Y - T)

I = 900 - 50r

r = r* = 8

(c) Knowing NX = 1500 - 250ε, what should be the real exchange rate ε to equilibrate the current account with the net capital outflow if we assume the income balance (IB) and the net unilateral transfer (NUT) are zero.

Q5. Two countries A and B are described by the Solow growth model. The information we have about these countries are summarised in the following table:

(a) What is the per-worker production function f(k)?

(b) Solve for the ratio of country A's steady state income per-worker to country B's.

(c) If the parameter α in the production function takes the conventional value of about 1/3, how much higher should income per worker be in country A compared to country B?

(d) Income per worker in A is 16 times income per worker in B. Can you explain this fact by changing the value of the parameter α? What must it be?

Q6. Suppose that an economy has the Phillips curve π = π_-1 = 0.5(u - 0.05).

(a) What is the natural rate of unemployment?

(b) Graph (fully labelled) the short-run and long-run relationship between inflation and unemployment.

(c) How much cyclical unemployment is necessary to reduce inflation by 4 percentage points? Using Okun's law, compute the sacrifice ratio.